T^/3  ft 

irinity  College  Library 

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Rec’d  Tun)  2j.  J f 2-  3 } 


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in  2016  with  funding  from 
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PUBLIC  FOUNTAIN,  CINCINNATL 


A 


PRACTICAL  TREATISE 

ON 

HYDRAULIC  AND 


Water-Supply  Engineering: 

RELATING  TO  THE 

HYDROLOGY,  HYDRODYNAMICS,  AND  PRACTICAL 
CONSTRUCTION  OF  WATER-WORKS,  IN 
NORTH  AMERICA. 


WITH  NUMEROUS 

TABLES  AND  ILLUSTRATIONS, 


J.  T.  FANNING,  C.  E., 

MEMBER  OF  THE  AMERICAN  SOCIETY  OF  CIVIL  ENGINEERS;  FELLOW  OF  THE  AMERICAS 
ASSOCIATION  FOR  THE  ADVANCEMENT  OF  SCIENCE  ; MEMBER  OF  THE  AMERICAN 
PUBLIC  HEALTH  ASSOCIATION;  MEMBER  OF  THE  NEW  ENGLAND 
WATER  WORKS  ASSOCIATION  ; PAST  PRESIDENT  OF  THE 
AMERICAN  WATER  WORKS  ASSOCIATION. 


EIGHTEENTH  EDITION,  REVISED,  ENLARGED. 

AND  NEW  TABLES  AND  ILLUSTRATIONS  ADDED. 


NEW  YORK 

D.  VAN  NOSTEAND  COMPANY 

25  Park  Place 
1913 


C Qj  ' 

^7  3 ^ ^ t^v  wt* 

titc 


Copyright,  1877.  188G,  1890,  1901,  1906, 

BY 


J.  T.  FANNING. 


PUMPING  STATION,  CHESTNUT  HILL,  BOSTON,  Page  iii. 


Co  ^ ^ 


PREFACE. 


HEEE  is  at  present  no  sanitary  subject  of  more  general 


interest,  or  attracting  more  general  attention,  than  that 
relating  to  the  abundance  and  wholesomeness  of  domestic  water 


Each  citizen  of  a densely  populated  municipality  must  of 
necessity  be  personally  interested  in  either  its  physiological  or 
its  financial  bearing,  or  in  both.  Each  closely  settled  town  and 
city  must  give  the  subject  earnest  consideration  early  in  its  ex- 
istence. 

At  the  close  of  the  year  1875,  fifty  of  the  chief  cities  of  the 
American  Union  had  provided  themselves  with  public  water  sup- 
plies at  an  aggregate  cost  of  hot  less  than  ninety-five  million 
dollars,  and  two  hundred  and  fifty  lesser  cities  and  towns  were 
also  provided  with  liberal  public  water  supplies  at  an  aggregate 
cost  of  not  less  than  fifty-five  million  dollars. 

The  amount  of  capital  annually  invested  in  newly  inaugurated 
water-works  is  already  a large  sum,  and  is  increasing,  yet  the 
entire  American  literature  relating  to  water-supply  engineering 
exists,  as  yet,  almost  wholly  in  reports  upon  individual  works, 
usually  in  pamphlet  form,  and  accessible  each  to  but  compara- 
tively few  of  those  especially  interested  in  the  subject. 

Scores  of  municipal  water  commissions  receive  appointment 
each  year  in  the  growing  young  cities  of  the  Union,  who  have  to 
inform  themselves,  and  pass  judgment  upon,  sources  and  systems 


supplies. 


vi 


PREFACE. 


of  water  supply,  which  are  to  become  helpful  or  burdensome  to 
the  communities  they  are  intended  to  encourage  accordingly  as 
the  works  prove  successful  or  partially  failures. 

The  individual  members  of  these  “Boards  of  Water  Commis- 
sioners,” resident  in  towns  where  water  supplies  upon  an  extended 
scale  are  not  in  operation,  have  rarely  had  opportunity  to  observe 
and  become  familiar  with  the  varied  practical  details  and  appa- 
ratus of  a water  supply,  or  to  acquaint  themselves  with  even  the 
elementary  principles  governing  the  design  of  the  several  different 
systems  of  supply,  or  reasons  why  one  system  is  most  advanta- 
geous under  one  set  of  local  circumstances  and  another  system 
is  superior  and  preferable  under  other  circumstances. 

A numerous  band  of  engineering  students  are  graduated  each 
year  and  enter  the  field,  many  of  whom  choose  the  specialty  of 
hydraulics,  and  soon  discover  that  their  chosen  science  is  great 
among  the  most  noble  of  the  sciences,  and  that  its  mastery,  ir 
theory  and  practice,  is  a work  of  many  years  of  studious  acquire- 
ment and  labor.  They  discover  also  that  the  accessible  literature 
of  their  profession,  in  the  English  language,  is  intended  for  the 
class-room  rather  than  the  field,  and  that  its  formulae  are  based 
chiefly  upon  very  limited  philosophical  experiments  of  a century 
and  more  ago  hut  partially  applicable  to  the  extended  range  of 
modern  practice. 

Among  the  objects  of  the  author  in  the  compilation  of  the 
following  pioneer  treatise  upon  American  Water- works  are,  to 
supply  water-commissionei’s  with  a general  review  of  the  best 
methods  practised  in  supplying  towns  and  cities  with  water,  and 
with  facts  and  suggestions  that  will  enable  them  to  compare  in- 
telligently the  merits  and  objectionable  features  of  the  different 
potable  water  sources  within  their  reach  ; to  present  to  junior  and 
assistant  hydraulic  engineers  a condensed  summary  of  those  ele- 
mentary theoretical  principles  and  the  involved  formulas  adapted 
to  modern  practice,  which  they  will  have  frequently  to  apply, 
together  with  some  useful  practical  observations ; to  construct 
and  gather,  for  the  convenience  of  the  older  busy  practitioners, 


PREFACE. 


vii 

numerous  tables  and  statistics  that  will  facilitate  their  calcula- 
tions, some  of  which  would  otherwise  cost  them,  in  the  midst  of 
pressing  labors,  as  they  did  the  author,  a great  deal  of  laborious 
research  among  rare  and  not  easily  procurable  scientific  treatises ; 
and  also  to  present  to  civil  engineers  generally  a concise  reference 
manual,  relating  to  the  hydrology,  hydrodynamics,  and  practical 
construction  of  the  water-supply  branch  of  their  profession. 

This  work  is  intended  more  especially  for  those  who  have 
already  had  a task  assigned  them,  and  who,  as  commissioner, 
engineer,  or  assistant,  are  to  proceed  at  once  upon  their  recon- 
noissance  and  surveys,  and  the  preparation  of  plans  for  a public 
water  supply.  To  them  it  is  humbly  submitted,  with  the  hope 
that  it  will  prove  in  some  degree  useful.  Its  aim  is  to  develop 
the  bases  and  principles  of  construction,  rather  than  to  trace  the 
origin  of,  or  to  describe  individual  works.  It  is,  therefore,  prac- 
tical in  text,  illustration,  and  arrangement ; but  it  is  hoped  that 
the  earnest,  active  young  workers  will  find  it  in  sympathy  with 
their  mood,  and  a practical  introduction,  as  well,  to  more  pro- 
found and  elegant  treatises  that  unfold  the  highest  delights  of  the 
science. 

Good  design,  which  is  invariably  founded  upon  sound  mathe- 
matical and  mechanical  theory,  is  a first  requisite  for  good  and 
judicious  practical  engineering  construction.  We  present,  there- 
fore, the  formulae,  many  of  them  new,  which  theory  and  practical 
experiments  suggest  as  aids  to  preliminary  studies  for  designs, 
and  many  tables  based  upon  the  formulas,  which  will  facilitate  the 
labors  of  the  designer,  and  be  useful  as  checks  against  his  own  com- 
putations, and  we  give  in  addition  such  discussions  of  the  elemen- 
tary principles  upon  which  the  theories  are  founded  as  will  enable 
the  student  to  trace  the  origin  of  each  formula ; for  a formula  is 
often  a treacherous  guide  unless  each  of  its  factors  and  experience 
coefficients  are  well  understood.  To  this  end,  the  theoretical  dis- 
cussions are  in  familiar  language,  and  the  formulas  in  simple  ar- 
rangement, so  that  a knowledge  of  elementary  mathematics  only 
is  necessary  to  read  and  use  them. 


PREFACE. 


viii 


We  do  by  no  means  intimate,  however,  that  an  acquaintance 
with  elementary  theories  alone  suffices  for  an  accomplished  en- 
gineer. It  is  sometimes  said  that  genius  spurns  rules,  and  it  is 
true  that  untutored  genius  sometimes  grapples  with  and  accom- 
plishes great  and  worthy  deeds,  but  too  often  in  a bungling 
manner,  not  to  be  imitated. 

In  kindly  spirit  we  urge  the  student  to  bear  in  mind  that  it  is 
the  rigorously  trained  genius  who  oftenest  achieves  mighty  works 
by  methods  at  once  accurate,  economical,  artistic,  and  in  every 
respect  succeessful  and  admirable. 

J.  T.  F. 

Boston,  November,  1876. 


PREFACE  TO  THE  FIFTEENTH  EDITION. 


A T the  time  of  issue  of  the  first  edition  of  this  book  there  were 
1 only  about  300  American  cities  and  towns  having  public  water 
supplies.  On  issue  of  this  fifteenth  edition  there  are  about  5000 
complete  public  water  supplies  in  North  America,  that  have  cost 
in  the  aggregate  many  hundred  millions  of  dollars. 

The  first  preface  stated  that  this  book  was  intended  to  aid 
commissioners  and  engineers  who  were  to  proceed  at  once  with 
plans  and  constructions  of  water  supplies.  That  the  book  found  a 
practical  mission  and  influenced  the  designs  and  constructions  of 
many  public  water  supplies  is  evidenced  by  the  generous  domestic 
and  foreign  purchases  of  the  work.  This  evidence  of  practical  use- 
fulness is  most  gratifying  and  the  kind  reception  of  the  book  in  the 
class-room,  the  office  and  the  field  is  highly  appreciated  by  the 
author. 

To  each  successive  edition  have  been  added  useful  new  tables, 
text  and  illustrations,  so  that  the  book  might,  so  far  as  possible  in 
a general  treatise,  keep  in  progress  with  advances  in  the  art  of 
hydraulic  engineering. 

J.  T.  F. 

Minneapolis,  Minn.,  September,  1901. 


P.  viii/? 


WATER  TOWER,  ST.  LOUIS,  W.  W. 


TANK  STAND-PIPE,  FREMONT,  O. 


IX 


CONTENTS 


SECTION  I. 

COLLECTION  AND  STORAGE  OF  WATER,  AND  ITS 
IMPURITIES. 


CHAPTER  I. 

INTRODUCTORY.— Page  25. 

Art.  1,  Necessity  of  Public  Water  Supplies. — 2,  Physiological  Office  of  Water. 
— 3,  Sanitary  Office  of  Water  Supplies. — 4,  Helpful  Influence  of  Public 
Water  Supplies. — 5,  Municipal  Control  of  Public  Water  Supplies. — 6, 
Value  as  an  Investment. — 7,  Incidental  Advantages. 


CHAPTER  II. 

QUANTITY  OF  WATER  REQUIRED.— Page  31. 

Art.  8,  Statistics  of  Water  Supplied.— 9,  Census  Statistics. — 10,  Approximate 
Consumption  of  Water. — 11,  Water  Supplied  to  Ancient  Cities. — 12,  Water 
Supplied  to  European  Cities. — 13,  Water  Supplied  to  American  Cities. — 
14,  The  Use  of  Water  Steadily  Increasing. — 15,  Increase  in  Various  Cities. 
— 16,  Relation  of  Supply  per  Capita  to  Total  Population. — 17,  Monthly 
and  Hourly  Variations  in  the  Draught. — 18,  Ratio  of  Monthly  Consump 
tion. — 19,  Illustrations  of  Varying  Consumption. — 20,  Reserve  for  Fire 
Extinguishment. 


CHAPTER  III. 

RAINFALL.— Page  45. 

Art.  21,  The  Vapory  Elements  of  Water. — 22,  The  Liquid  and  Gaseous  Succes- 
sions.— 23,  The  Source  of  Showers. — 24,  General  Rainfall. — 25,  Review  of 
Rainfall  Statistics. — 26,  Climatic  Effects. — 27,  Sections  of  Maximum  Rain- 
fall.— 28,  Western  Rain  System. — 29,  Central  Rain  System. — 30,  Eastern 
Coast  System. — 31,  Influence  of  Elevation  upon  Precipitation. — 32,  River 
Basin  Rains. — 33,  Grouped  Rainfall  Statistics. — 34,  Monthly  Fluctuations 


X 


CONTENTS. 


in  Rainfall. — 35,  Secular  Fluctuations  in  Rainfall. — 36,  Local  Physical 
and  Meteorological  Influences. — 37,  Uniform  Effects  of  Natural  Laws. — 
38,  Great  Rain  Storms. — 39,  Maximum  Ratios  of  Floods  to  Rainfalls. — 40, 
Volume  of  Waterfrom  given  Rainfalls. — 41,  Gauging  Rainfalls. 

CHAPTER  IV. 

FLOW  OF  STREAMS.— Page  65. 

Art.  42,  Flood  Volumes  Inversely  as  the  Areas  of  Basins. — 43,  Formulas  for 
Flood  Volumes. — 44,  Table  of  Flood  Volumes.— 45,  Seasons  of  Floods. — 
46,  Influence  of  Absorption  and  Evaporation  upon  Flow. — 47,  Flow  in  Sea- 
sons of  Minimum  Rainfall. — 48,  Periodic  Classification  of  available  Flow. — 
49,  Sub-surface  Equalizers  of  Flow. — 50,  Flashy  and  Steady  Streams. — 
51,  Peculiar  Watersheds. — 52,  Summaries  of  Monthly  Flow  Statistics. — 
53,  Minimum,  Mean,  and  Flood  Flow  of  Streams. — 54,  Ratios  of  Monthly 
Flow  in  Streams. — 55,  Mean  Annual  Flow  of  Streams. — 56,  Estimates  of 
Flow  of  Streams. — 57,  Ordinary  Flow  of  Streams. — 58,  Tables  of  Flow, 
Equivalent  to  given  Depths  of  Rain. 

CHAPTER  V. 

STORAGE  AND  EVAPORATION  OF  WATER.— Page  84. 

Storage. — Art.  59,  Artificial  Storage. — 60,  Losses  Incident  to  Storage. — 6i, 
Sub-strata  of  the  Storage  Basin. — 62,  Percolation  from  Storage  Basins. — 
63,  Rights  of  Riparian  Owners. — 64,  Periodical  Classification  cf  Riparian 
Rights.  — 65,  Compensations. — Evaporation. — 66,  Loss  from  Reservoir 
by  Evaporation. — 67,  Evaporation  Phenomena.— 68,  Evaporation  from 
Water. — 69,  Evaporation  from  Earth. — 70,  Examples  of  Evaporation. — 71, 
Ratios  of  Evaporation. — 72,  Resultant  Effect  of  Rain  and  Evaporation. — 
73,  Practical  Effect  upon  Storage. 

CHAPTER  VI. 

SUPPLYING  CAPACITY  OF  WATER-SHEDS.— Page  94. 

Art.  74,  Estimate  of  Available  Annual  Flow  of  Streams. — 75,  Estimate  of 
Monthly  available  Storage  Required. — 76,  Additional  Storage  Required. — 
/7,  Utilization  of  Flood  Flows. — 78,  Qualification  of  Deduced  Ratios. — 79, 
Influence  of  Storage  upon  a Continuous  Supply. — 80,  Artificial  Gathering 
Areas. — 81,  Recapitulation  of  Rainfall  Ratios. 

CHAPTER  VII. 

SPRINGS  AND  WELLS.— Page  102. 

Art.  82,  Subterranean  Waters. — 83,  Their  Source,  the  Atmosphere. — 84.  Po- 
rosity of  Earths  and  Rocks. — S5,  Percolations  in  the  Upper  Strata. — 86, 
The  Courses  cf  Percolation. — S7  Deep  Percolations.-  88,  Subterranean 


CONTENTS. 


xi 


Reservoirs.— 89,  The  Uncertainties  of  Subterranean  Searches. — 90,  Re- 
nowned Application  of  Geological  Science. — 91,  Conditions  of  Overflow- 
ing Wells.— 92,  Influence  of  Wells  upon  each  other.— 93,  American  Ar- 
tesian Wells. — 94,  Watersheds  of  Wells. — 95,  Evaporation  from  Soils*-. 
96,  Supplying  Capacity  of  Wells  and  Springs. 


CHAPTER  VIII. 

IMPURITIES  OF  WATER. — Page  112. 

Art.  97>  The  Composition  of  Water. — 98,  Solutions  in  Water. — 99,  Properties 
of  Water. — ioo,  Physiological  Effects  of  the  Impurities  of  Water. — ioi, 
Mineral  Impurities.— 102,  Organic  Impurities. — 103,  Tables  of  Analyses 
of  Potable  Waters. — 104,  Ratios  of  Standard  Gallons. — 105,  Atmospheric 
Impurities. — 106,  Sub-surface  Impurities. — 107,  Deep-well  Impurities. — 
108,  Hardening  Impurities. — 109,  Temperature  of  Deep  Sub-surface 
Waters. — no,  Decomposing  Organic  Impurities. — m,  Vegetal  Organic 
Impurities. — 112,  Vegetal  Organisms  in  Water-pipes. — 113,  Animate  Or- 
ganic Impurities. — 114,  Propagation  of  Aquatic  Organisms. — 115,  Purify- 
ing Office  of  Aquatic  Life. — 116,  Intimate  Relation  between  Grade  of 
Organisms  and  Quality  of  Water. — 117,  Animate  Organisms  in  Water- 
pipes. — 118,  Abrasion  Impurities  in  Water. — 119,  Agricultural  Impuri- 
ties.— 120,  Manufacturing  Impurities. — 121,  Sewage  Impurities.  — 122, 
Impure  Ice  in  Drinking-Water. — 123,  A Scientific  Definition  of  Polluted 
Water. 


CHAPTER  IX. 

WELL,  SPRING,  LAKE,  AND  RIVER  SUPPLIES.— Page  139. 

Well  Waters. — Art.  124,  Locations  for  Wells. — 125,  Fouling  of  Old  Wells.— 
Spring  Waters. — 126,  Harmless  Impregnations. — 127,  Mineral  Springs. 
— Lake  Waters. — 128,  Favorite  Supplies. — 129,  Chief  Requisites. — 130, 
Impounding. — 131,  Plant  Growth. — 132,  Strata  Conditions. — 133,  Plant 
and  Insect  Agencies. — 134,  Preservation  of  Purity. — 135,  Natural  Clarifi- 
cation.— 136,  Great  Lakes. — 137,  Dead  Lakes. — River  Waters. — 138, 
Metropolitan  Supplies. — 139,  Harmless  and  Beneficial  Impregnations. — 
140,  Pollutions. — 141,  Sanitary  Discussions. — 142,  Inadmissible  Polluting 
Liquids, — 143,  Precautionary  Views. — 144,  Speculative  Condition  of  the 
Pollution  Question. — 145,  Spontaneous  Purification. — 146,  Artificial  Clari- 
fication.— 147,  A Sugar  Test  of  the  Quality  of  Water. 


xii 


CONTENTS. 


SECTION  II. 

FLOW  OF  WATER  THROUGH  SLUICES,  PIPES,  AND 

CHANNELS. 


CHAPTER  X. 

WEIGHT,  PRESSURE,  AND  MOTION  OF  WATER.— Page  161. 

Art.  148,  Special  Characteristics  ofWater. — 149,  Atomic  Theory. — 150,  Molec- 
ular Theory. — 151,  Influence  of  Caloric. — 152,  Relative  Densities  and 
Volumes. — Weight  of  Water. — 153,  Weight  of  Constituents  of  Water. 
— 154,  Crystalline  Forms  of  Water. — 155,  Formula  for  Volumes  at  Differ 
ent  Temperatures. — 156,  Weight  of  Pond  Water. — 157,  Compressibility 
and  Elasticity  ofWater. — 158,  Weights  of  Individual  Molecules. — 159,  In- 
dividual Molecular  Actions. — Pressure  of  Water. — 160,  Pressure  Propor- 
tional to  Depth. — 161,  Individual  Molecular  Reactions.— -162,  Equilibrium 
destroyed  by  an  Orifice. — 163,  Pressures  from  Vertical,  Inclined,  and  Bent 
Columns  of  Water. — 164,  Artificial  Pressure. — 165,  Pressi  ve  upon  a Unit 
of  Surface. — 166,  Equivalent  Forces.  — 167,  Weight  a Measure  of  Pressure. 
— 168,  A Line  a Measure  of  Weight. — 169,  A Line  a measure  of  Pressure 
upon  a Surface. — 170,  Diagonal  Force  of  Combined  Pressures  Graphically 
Represented. — 171,  Angular  Resultant  of  a Force  Graphically  Repre- 
sented.— 172,  Angular  Effects  of  a Force  Represented  bjr  the  Sine  and 
Cosine  of  the  Angle. — 173,  Total  Pressure. — 174.  Direction  of  Maximum 
Effect. — 175,  Herizontal  and  Vertical  Effects. — 176,  Centres  of  Pressure 
and  of  Gravity — 177,  Pressure  upon  a Curved  Surface,  and  Effect  upon 
its  Projected  Plane. — 178,  Centre  of  Pressure  upon  a Circular  Area.— 
179,  Combined  Pressures. — 180,  Sustaining  Pressure  upon  Floating  and 
Submerged  Bodies. — 181,  Upward  Pressure  upon  a Submerged  Lintel. — 
182,  Atmospheric  Pressure.- — 183,  Rise  of  Water  into  a Vacuum. — 184, 
Siphon. — 185,  Transmission  of  Pressure  to  a Distance. — 186,  Inverted 
Syphon. — 187,  Pressure  Convertible  into  Motion. — Motion  of  Water. — 
188,  Flow  of  Water. — 189,  Action  of  Gravity  upon  Individual  Molecules. 
— igo,  Frictionless  Movement  of  Molecules. — 191,  Acceleration  of  Motion. 
—192,  Equations  of  Motion. — 193,  Parabolic  Path  of  Jet. — 194,  Velocity  of 
Efflux  Proportional  to  the  Head. — 195,  Conversion  of  the  Force  of  Grav- 
ity from  Pressure  into  Motion. — 196,  Resultant  Effects  of  Pressure  and 
Gravity  upon  the  Motion  of  a Jet. — 197,  Equal  Pressures  give  Equal 
Velocities  in  all  Directions. — 198,  Resistance  of  the  Air. — 199,  Theoretical 
Velocities. 

CHAPTER  XI. 

FLOW  OF  WATER  THROUGH  ORIFICES.— Page  194. 

Art.  200,  Motion  of  the  Individual  Particles. — 201,  Theoretical  Volume  of 
Efflux. — 202,  Converging  Path  of  Particles. — 203,  Classes  of  Orifices.— 


CONTENTS. 


yin 

204,  Form  of  Submerged  Orifice  Jet. — 205,  Ratio  of  Minimum  Section  of 
Jet. — 206,  Volume  of  Efflux. — 207,  Coefficient  of  Efflux. — 208,  Maximum 
Velocity  of  the  fet. — 209,  Factors  of  the  Coefficient  of  Efflux. — 210,  Prac- 
tical Use  of  a Coefficient. — 211,  Experimental  Coefficients.  (From  Michel- 
ott1',  Abbe  Bosset,  Rennie,  Castel,  Lespinasse,  General  Ellis.) — 212,  Co- 
efficients Diagramed. — 213,  Effect  of  Varying  the  Head,  or  the  Proportions 
of  the  Orifice. — 214,  Peculiarities  of  Efflux  from  an  Orifice.- — 215,  Mean 
Velocity  of  the  Issuing  Particles. — 216,  Coefficients  of  Velocity  and 
Contraction. —217.  Velocity  of  Particles  Dependent  upon  their  Angular 
Positions. — 218,  Equation  of  Volume  of  Efflux  from  a Submerged  Orifice. 
— 219,  Effect  of  Outline  of  Geometrical  Orifices  upon  Efflux. — 220,  Vari- 
able Value  of  Coefficients. — 221,  Assumed  Mean  Value  of  Efflux. — 222, 
Circular  Jets,  Potygonal  do..  Complex  do. — 223,  Cylindrical  and  Divergent 
Orifices. — 224,  Converging  Orifices. 

CHAPTER  XII. 

FLOW  OF  WATER  THROUGH  SHORT  TUBES.— Page  213. 

Art.  225,  An  Ajutage. — 226,  Increase  of  Coefficient. — 227,  Adjutage  Vacuum, 
and  its  Effect. — 228,  Increased  Volume  of  Efflux. — 229,  Imperfect  Va- 
cuum.— 230,  Divergent  Tube. — 231,  Convergent  Tube. — 232,  Additional 
Contraction. — 233,  Coefficients  of  Convergent  Tubes. — 234,  Increase  and 
Decrease  of  Coefficient  of  Smaller  Diameter. — 235,  Coefficient  of  Final 
Velocity. — 236,  Inward  Projecting  Ajutage. — 237,  Compound  Tube. — 
238,  Coefficients  of  Compound  Tubes. — 239,  Experiments  with  Cylindri- 
cal and  Compound  Tubes. — 240,  Tendenc)'  to  Vacuum. — 241,  Percussive 
Force  of  Particles. — 242,  Range  of  Eytelwein’s  Table. — 243,  Cylindrical 
Tubes  to  be  Preferred. 


CHAPTER  XIII. 

FLOW  OP  WATER  THROUGH  PIPES,  UNDER  PRESSURE.— 

Page  223. 

Art.  244,  Pipe  and  Conduit.--245,  Short  Pipes  give  Greatest  Discharge. — 246, 
Theoretical  Volume  from  Pipes. — 247,  Mean  Efflux  from  Pipes. — 248,  Sub- 
division of  the  Head. — 249,  Mechanical  Effect  of  the  Efflux. — 250,  Ratio 
of  Resistance  at  Entrance  to  the  Pipe. — Resistance  to  Flow  within 
A Pipe. — 251,  Resistance  of  Pipe-Wall. — 252,  Conversion  of  Velocity  into 
Pressure. — 253,  Coefficients  of  Efflux  from  Pipes. — 254,  Reactions  from  the 
Pipe-Wall. — 255,  Origin  of  Formulas  of  Flow. — 256,  Formula- of  Resist- 
ance to  Flow. — 257,  Coefficient  of  Flow. — 258,  Opposition  of  Gravity  and 
Reaction. — 259,  Conversion  of  Pressure  into  Mechanical  Effect. — 260, 
Measure  of  Resistance  to  Flow — 261,  Resistance  Inversely  as  the  Square 
of  the  Velocity. — 262,  Increase  of  Bursting  Pressure. — 263,  Acceleration 
and  Resistance. — 264,  Equation  of  Head  Required  to  Overcome  the  Re- 
sistance.— 265,  Designation  of  h"  and  l. — 266,  Variable  Value  of  in. — 267, 
Investigation  of  Values  of  m. — 268,  Definition  of  Symbols. — 269,  Experi- 


CONTENTS. 


xiv 


mental  Values  of  the  Coefficient  of  Floxv. — 270,  Peculiarities  of  the  Coeffi- 
cient (m)  of  Flow. — 271,  Effects  of  Tubercles. — 272,  Classification  of  Pipes 
and  their  Mean  Coefficients. — 273,  Equation  of  the  Velocity  Neutralized 
by  Resistance  to  Flow. — 274,  Equation  of  Resistance  Head.— 275,  Equation 
of  Total  Head. — 276,  Equation  of  Volume. — 277,  Equation  of  Diameter. — 
278,  Relative  Value  of  Subdivisions  of  Total  Head. — 279,  Many  Popular 
Formulas  Incomplete. — 280 — Formula  of  M.  Chezy. — 281,  Various  Pop- 
ular Formulas  Compared. — 282,  Sub-heads  Compared. — 283,  Investiga- 
tions by  Dubuat,  and  Coloumb,  and  Prony. — 284,  Prony’s  Anal)-sis. — 285, 
Eytelwein’s  Equation  of  Resistance  to  Flow. — 286,  D’Abuisson’s  Equation 
of  Resistance  to  Flow. — 287,  Weisbach’s  Equation  of  Resistance  to  Flow. 
— 288,  Transpositions  of  an  Original  Formula. — 289,  Unintelligent  Use  of 
Partial  Formulas. — 290,  A Formula  of  more  General  Application. — 291, 
Values  of  v for  Given  Slopes. — 292,  Values  of  h and  Ji!  for  Given  Velocities. 
— 293,  Classified  Equations  for  Velocity,  Head,  Volume,  and  Diameter. — 
294,  Coefficients  of  Entrance  of  Jet. — 295,  Mean  Coefficients  for  Smoothi 
Rough,  and  Foul  Pipes. — 296,  Mean  Equations  for  Smooth,  Rough,  and 
Foul  Pipes. — 297,  Modification  of  a Fundamental  Equation  of  Velocity. 
■ — 298,  Values  of  P. — 299,  Bends. — 300,  Branches. — 301,  How  to  Economize 
Head. 

CHAPTER  XIV. 

MEASURING  WEIRS,  AND  WEIR  GAUGING.— Page  277. 

Art.  302,  Gauged  Volumes  of  Flow. — 303,  Form  of  Weir. — 304,  Dimensions. 
— 305,  Stability. — 306,  Varying  Length. — 307,  End  Contractions. — 308, 
Crest  Contractions. — 309,  Theory  of  Flow  over  a Weir. — 310,  Formulas 
for  Flow,  without  and  with  Contractions. — 3 11,  Increase  of  Volume  due 
to  Initial  Velocity  of  Water. — 312,  Coefficients  for  Weir  Formulas. — 313, 
Discharges  for  Given  Depths. — 314,  Vacuum  under  the  Crest. — 315,  Ex- 
amples of  Initial  Velocity. — 316,  Wide-crested  Weirs. — 317,  Triangular- 
Notch  Weirs. — 318,  Obstacles  to  Accurate  Measures. — 319,  Hook  Gauge. 
—320,  Rule  Gauge. — 321,  Tube  and  Scale  Gauge. 

CHAPTER  XV. 

FLOW  OF  WATER  IN  OPEN  CHANNELS.— Page  299. 

Art.  322,  Gravity  the  Origin  of  Flow. — 323,  Resistance  to  Flow. — 324,  Equa- 
tions of  Resistance  and  Velocity. — 325,  Equation  of  Inclination. — 326,  Co- 
efficients of  Flow  for  Channels. — 327,  Observed  Data  of  Flow  in  Channels. 
— 328,  Table  of  Coefficients  for  Channels. — 329,  Various  Formulas  of  Flow 
Compared. — 330,  Velocities  of  Given  Films. — 331,  Surface  Velocities. — 
332,  Ratios  of  Surface  to  Mean  Velocities. — 333,  Hydrometer  Gaugings. — 
334,  Tube  Gauges — 335,  Gauge  Formulas. — 336,  Pitot  Tube  Gauge — 337, 
Woltmann’s  Tachometer. — 338,  Hydrometer  Coefficients. — 339.  Henry's 
Telegraphic  Mouiinet. — 340,  Earlier  Hydrometers. — 341,  Double  Floats. — 
342,  Mid-depth  Floats. — 343,  Maximum  Velocity  Floats. — 344,  Relative 
Velocities  and  Volumes  due  to  Different  Depths. 


CONTENTS. 


XY 


SECTION  III. 

PRACTICAL  CONSTRUCTION  OF  WATER-WORKS. 


CHAPTER  XVI. 

RESERVOIR  EMBANKMENTS  AND  CHAMBERS.— Page  333. 

Art.  345,  Ultimate  Economy  of  Skillful  Construction. — 346,  Embankment  Foun- 
dations. — 347,  Springs  under  Foundations. — 348,  Surface  Soils. — 349,  Con- 
crete Cut-off  Walls. — 350,  Treacherous  Strata. — 351,  Embankment  Core 
Materials. — 352,  Peculiar  Pressures. — 353,  Earthwork  Slopes. — 354,  Re- 
connaissance for  Site.— 355,  Detailed  Surveys. — 356,  Illustrative  Case. — 
357,  Cut-off  Wall. — 358,  Embankment  Core. — 359,  Frost  Covering. — 360, 
Slope  Paving. — 361,  Puddle  Wall. — 362,  Rubble  Priming  Wall. — 363,  A 
Light  Embankment.— 364,  Distribution  Reservoirs. — 365,  Application  of 
Fine  Sand. — 366,  Masonry — Faced  Embankment. — 367,  Concrete  Paving. 
368,  Embankment  Sluices  and  Pipes. — 369,  Gate  Chambers. — 370,  Sluice 
Valve  Areas. — 371,  Stop-valve  Indicator. — 372,  Power  required  to  Open 
a Valve, — 373,  Adjustable  Effluent  Pipe. — 374,  Fish  Screens. — 375,  Gate 
Chamber  Foundations. — 376,  Foundation  Concrete. — 377,  Chamber 
Walls. 

CHAPTER  XVII. 

OPEN  CANALS. — Page  370. 

Art.  378,  Canal  Banks. — 379,  Inclinations  and  Velocities  in  Practice. — 380, 
Ice  Covering. — 381,  Table  of  Dimensions  of  Supply  Canals. — 382,  Canal 
Gates. — 383,  Miners’  Canals. 

CHAPTER  XVII  I. 

WASTE  WEIRS.— Page  377. 

Art.  384,  The  Office  and  Influence  of  a Waste-Weir. — 385,  Discharges  over 
Waste-Weirs. — 386,  Required  Lengths  of  Waste- Weirs. — 387.  Forms  of 
Waste-Weirs. — 388.  Isolated  Weirs. — 389,  Timber  Weirs. — 390,  Ice-Thrust 
upon  Storage  Reservoir  Weirs. — 391,  Breadths  of  Weir-Caps. — 392,  Thick- 
nesses of  Waste-Weirs  and  Dams. — 393,  Force  of  Overflowing  Water.^ 
394,  Heights  of  Waves. 

CHAPTER  XIX. 

PARTITIONS  AND  RETAINING  WALLS.— Page  390. 

Art.  395,  Design. — 396,  Theory  of  Water-Pressure  upon  a Vertical  Surface. — 
397,  Water  Pressure  upon  an  Inclined  Surface.— 398,  Frictional  Stability 


CONTENTS. 


xvi 


of  Masonry. — 399,  Coefficients  of  Masonry  Friction. — 400,  Pressure  Lever- 
age of  Water.— 401,  Leverage  Stability  of  Masonry. — 402,  Moment  of 
Weight  Leverage  of  Masonry. — 403,  Thickness  of  a Vertical  Rectangular 
Wall  for  Water  Pressure. — 404,  Moments  of  Rectangular  and  Trapedoidal 
Sections. — 405,  Graphical  Method  of  Finding  the  Leverage  Resistance. — 
406,  Granular  Stability. — 407,  Limiting  Pressures. — 408,  Table  of  Walls  for 
Quiet  Water. — 409,  Economic  Profiles. — 410,  Theory  of  Earth  Pressures. 
— 41 1,  Equation  of  Weight  of  Earth  Wedge. — 412,  Equation  of  Pressure  of 
Earth  Wedge. — 413,  Equation  of  Moment  of  Pressure  Leverage. — 414, 
Thickness  of  a Vertical  Rectangular  Wall  for  Earth  Pressure. — 415,  Sur- 
charged Earth  Wedge. — 416,  Pressure  of  a Surcharged  Earth  "Wedge. — 
417,  Moment  of  a Surcharged  Pressure  Leverage. — 418,  Pressure  of  an 
Infinite  Surcharge. — 419,  Resistance  of  Masonry  Revetments. — 420,  Final 
Resultants  in  Revetments. — 421.  Table  of  Trapezoidal  Revetments. — 422, 
Curved-face  Batter  Equation. — 423,  Back  Batters  and  their  Equations. — 
424,  Inclination  of  Foundation. — 425,  Front  Batters  and  Steps. — 426, 
Top  Breadth. — 427,  Wharf  Walls. — 428,  Counterforted  Walls. — 429,  Ele- 
ments of  Failure. — 430,  End  Supports. — 431,  Faced  and  Concrete  Revet- 
ments. 

CHAPTER  XX. 

MASONRY  CONDUITS.— Page  431. 

Art.  432,  Protection  of  Channels  for  Domestic  Water  Supplies. — 433,  Examples 
of  Conduits. — 434,  Foundations  of  Conduits. — 435,  Conduit  Shells. — 436, 
Ventilation  of  Conduits. — 437,  Conduits  under  Pressure. — 438,  Protection 
from  Frost. — 439,  Masonry  to  be  Self-sustaining. — 440,  A Concrete  Con- 
duit.— 441,  Example  of  a Conduit  under  Heavy  Pressure. — 442,  Mean 
Radii  of  Conduits. — 443,  Formulas  of  Flow  for  Conduits. — 444,  Table  of 
Conduit  Data. 


CHAPTER  XXI. 

MAINS  AND  DISTRIBUTION  PIPES— Page  446. 

Art.  445,  Static  Pressures  in  Pipes. — 446,  Thickness  of  Shell  resisting  Static 
Pressure. — 447,  Water-Ram. — 448,  Formulas  of  Thickness  for  Ductile 
Pipes. — 449,  Strengths  of  Wrought  Pipe  Metals. — 450,  Moulding  of  Pipes. 
— 451,  Casting  of  Pipes. — 452,  Formulas  of  Thickness  for  Cast-iron  Pipes. 
453,  Thicknesses  found  Graphically. — 454,  Table  of  Thicknesses  of  Cast- 
iron  Pipes. — 455,  Table  of  Equivalent  Fractional  Expressions. — 456,  Cast- 
iron  Pipe-Joints. — 457,  Dimensions  of  Pipe-Joints. — 45S,  Templets  for 
Bolt  Holes. — 459,  Flexible  Pipe-Joint. — 460,  Thickness  Formulas  Com- 
pared.— 461,  Formulas  for  Weights  of  Cast-iron  Pipes. — 462,  Table  of 
Weights  of  Cast-iron  Pipes. — 463,  Interchangeable  Joints. — 464,  Charac- 
teristics of  Pipe  Metals. — 465,  Tests  of  Pipe-Metals. — 466,  The  Preserva- 
tion of  Pipe  Surfaces. — 467,  Varnishes  for  Pipes  and  Iron  "Work. — 468, 
Hydraulic  Proof  of  Pipes. — 469,  Special  Pipes.— 470,  Cement-lined  and 


CONTENTS. 


svii 


Coated  Pipes. — 471,  Methods  of  Lining. — 472,  Covering. — 473,  Cement 
Joints. — 474,  Cast  Hub  Joint. — 475,  CQmposite  Branches. — 476,  Thickness 
of  Shells  for  Cement  Linings. — 477,  Gauge  Thickness  and  Weights  of 
Rolled  Iron. — 478,  Lining,  Covering,  and  Joint  Mortar. — 479,  Asphaltum- 
Coated  Wrought-iron  Pipes. — 480,  Asphaltum  Bath,  for  Pipes. — 481, 
Wrought  Pipe  Plates. — 482,  Bored  Pipes.  — 483,  Wyckoff’s  Patent 
Pipe. 

CHAPTER  XXII. 

DISTRIBUTION  SYSTEMS,  AND  APPENDAGES.— Page  493. 

Art.  484,  Loss  of  Head  by  Friction — 485,  Table  of  Frictional  Heads  in  Pipes. 
— 486,  Relative  Discharging  Capacities  of  Pipes. — 487,  Table  of  Relative 
Capacities  of  Pipes. — 488,  Depths  of  Pipes. — 489,  Elementary  Dimensions 
of  Pipes.— 490,  Distribution  Systems. — 491,  Rates  of  Consumption  of 
Water. — 492,  Rates  of  Fire  Supplies. — 493,  Diameter  of  Supply  Main. — 
494,  Diameters  of  Sub-mains. — 495,  Maximum  Velocities  of  Flow. — 496, 
Comparative  Frictions. — 497,  Relative  Rates  of  Flow  for  Domestic  and 
Fire  Supplies. — 498,  Required  Diameters  for  Fire  Supplies. — 499,  Duplica- 
tion Arrangement  of  Sub  Mains. — 500,  Stop-Valve  Systems. — 501,  Stop- 
Valve  Locations. — 502,  Blow-off  and  Waste  Valves. — 503,  Stop-Valve  De- 
tails.— 504,  Valve  Curbs. — 505,  Fire  Hydrants. — 506,  Post  Hydrants. — 507, 
Hydrant  Details. — 508,  Flush  Hydrants. — 509,  Gate  Hydrants. — 510,  High 
Pressures. — 511,  Air  Valves. — 512,  Union  of  High  and  Low  Services. — 513, 
Combined  Reservoir  and  Direct  Systems. — 514,  Stand  Pipes. — 515,  Fric- 
tional Heads  in  Service-Pipes. 


CHAPTER  XXIII. 

CLARIFICATION  OF  WATER.— Page  530. 

Art.  516,  Rarity  of  Clear  Waters. — 517,  Floating  Debris. — 518,  Mineral  Sedi- 
ments.— 519,  Organic  Sediments. — 520,  Organic  Solutions. — 521,  Natural 
Processes  of  Clarification  — 522,  Chemical  Processes  of  Clarification. — 523, 
Charcoal  Process. — 524,  Infiltration. — 525,  Infiltration  Basins. — 526,  Ex- 
amples of  Infiltration. — 527,  Practical  Considerations. — 528,  Examples 
of  European  Infiltration. — 529,  Example  of  Intercepting  Well. — 530, 
Filter  Beds. — 531,  Settling  and  Clear-Water  Basins. — 532,  Introduction 
of  Filter-Bed  System. — 533.  Capacity  of  Filter  Beds. — 534,  Cleaning  of 
Filter  Beds. — 535,  Renewal  of  Sand  Surface.— 536,  Basin  Coverings. 


CHAPTER  XXIV. 


PUMPING  OF  WATER— Page  557. 

“Art.  537,  Types  of  Pumps. — 538,  Prime  Movers. — 539,  Expense  of  VariibJ* 
Delivery  of  Water — 540,  Variable  Motions  of  a Piston. — 541,  Ratios  of 
Variable  Delivery  of  Water. — 542,  Office  of  Stand-Pipe  and  Air-Vessel.— 


xviii 


CONTENTS. 


543,  Capacities  of  Air-Vessels. — 544,  Valves. — 545,  Motions  of  Water 
through  Pumps. — 546,  Double-Acting  Pumping  Engines. — 547,  Geared 
Pumping  Engines. — 548,  Costs  of  Pumping  Water. — 549,  Duty  of 
Pumping  Engines. — 550,  Special  Trial  Duties. — 551,  Economy  of  a High 
Duty. 


CHAPTER  XXV. 

TANK  STAND-PIPES. 

Art.  552,  Their  Function. — 553,  Foundations. — 554,  Wind  Strains. — 555,  Ten- 
dency to  Slide. — 556,  Tendency  to  Overturn. — 557,  Tank  Materials. — 
558,  Riveting. — 559,  Pressures  in  Inclosed  Stand-Pipes. — 560,  Factors  of 
Safety. — 561,  Grades  of  Metals. — 562,  Limiting  Depths  and  Thicknesses 
of  Metals. — 563,  Thicknesses  of  Metals  Graphically  Shown. — 564,  Exposed 
Stand-Pipes. — 565,  Stand-Pipe  Data. 


CHAPTER  XXVI. 

SYSTEMS  OF  WATER  SUPPLY.— Page  603. 

Art.  566,  Permanence  of  Supply  Essential. — 567 , Methods  of  Gathering  and 
Delivering  Water.  — 568,  Choice  of  Water.  — 569,  Gravitation.  — 570, 
Pumping  with  Reservoir  Reserve. — 571,  Pumping  with  Direct  Pressure. 


LIST  OF  TABLES. 


Table  No.  Page 

1.  Population,  Families,  and  Dwellings  in  Fifty  American  Cities 32 

1 a.  Population,  Families,  and  Dwellings  in  One  Hundred  American 

Cities  in  1880 33a 

lb.  Water  Supplied  to  European  Cities 36 

2.  Water  Supplied,  and  Piping  in  several  Cities  38 

3.  Water  Supplied  in  years  1870  and  1874 39 

4.  Average  Gallons  of  Water  Supplied  to  each  Inhabitant 40 

5.  Ratios  of  Monthly  Consumption  of  Water  in  1874 43 

6.  Mean  Rainfall  in  different  River  Basins 51 

7.  Rainfall  in  the  United  States 53 

8.  Volumes  of  Rainfall  per  minute  for  given  inches  of  Rain  per  twenty- 

four  hours 62 

9.  Flood  Volumes  from  given  Watershed  Areas 67 

10.  Summary  of  Rainfall  upon  the  Cochituate  Basin 72 

11.  Summary  of  Rainfall  upon  the  Croton  Basin 72 

12.  Summary  of  Rainfall  upon  the  Croton  West-Branch  Basin 73 

13.  Summary  of  Percentage  of  Rain  Flowing  from  the  Cochituate  Basin,  73 

14.  Summary  of  Percentage  of  Rain  Flowing  from  the  Croton  Basin. ...  73 

15.  Summary  of  Percentage  of  Rain  Flowing  from  the  Croton  West- 

Branch  Basin 74 

16.  Summary  of  Volume  of  Flow  from  the  Cochituate  Basin 74 

17.  Summary  of  Volume  of  Flow  from  the  Croton  Basin 74 

18.  Summary  of  Volume  of  Flow  from  the  Croton  West-Branch  Basin..  75 

19.  Estimates  of  Minimum,  Mean,  and  Maximum  Flow  of  Streams....  75 

20.  Monthly  Ratios  of  Flow  of  Streams 76 

21.  Ratios  of  Mean  Monthly  Rain  and  Inches  of  Rain  Flowing  each 

Month 77 

22.  Equivalent  Volumes  of  Flow  for  given  Depths  of  Rain  in  One 

Month 82 

23.  Equivalent  Volumes  of  Flow  for  given  Depths  of  Rain  in  One  Year.  83 

23a.  Statistics  of  Flow  of  Sudbury  River,  Mass 83d 

23 b.  Summary  of  Rainfall  on  the  Sudbury  Basin 83a 

23^.  Percentage  of  Rainfall  Flowing  from  the  Sudbury  Basin 83^ 

23 d.  Volume  of  Flow  from  the  Sudbury  Basin  83^ 


LIST  OF  TABLES. 


Tabic  No.  Page 

24.  Evaporation  from  Water 89 

25.  Mean  Evaporation  from  Earth 89 

26.  Monthly  Ratios  of  Evaporation  from  Reservoirs 92 

27.  Multipliers  for  Equivalent  Inches  of  Rain  Evaporated 92 

17a.  Ratios  and  Equivalent  Inches  of  Rain 93 

27 b.  Monthly  Gains  and  Losses  in  Storage  Reservoirs 93 

28.  Monthly  Supply  to  and  Draft  from  a Reservoir  (with  Compensation).  96 

29.  Monthly  Supply  to  and  Draft  from  a Reservoir  (without  Compensa- 

tion  97 

30.  Ratios  of  Monthly  Rain,  Flow,  Evaporation,  and  Consumption 101 

30a.  Estimate  of  Collectible  Rainfall  ...  101 

31.  Percolation  of  Rain  into  One  Square  Mile  of  Porous  Soil in 

32.  Analyses  of  Various  Lake,  Spring,  and  Well  Waters 117 

33.  Analyses  of  Various  River  and  Brook  Waters 118 

34.  Analyses  of  Various  Streams  in  Massachusetts 120 

35.  Analyses  of  Various  Water  Supplies  from  Domestic  Wells 121 

36.  Artesian  Well  Temperatures 127 

36a.  Analyses  of  Ice  from  a Stagnant  Pond 136 

37.  Analyses  of  Various  Mineral  Spring  Waters 143 

38.  Weights  and  Volumes  of  Water  at  Different  Temperatures 166 

39.  Pressures  of  Water  at  Stated  Depths 172 

40.  Correspondent  Heights,  Velocities,  and  Times  of  Falling  Bodies. . . 190 

41.  Coefficients  from  Michelotti’s  Experiments  with  Orifices 198 

42.  Coefficients  from  Bossut’s  Experiments  with  Orifices 199 

43.  Coefficients  from  Rennie’s  Experiments  with  Orifices 199 

44.  Coefficients  from  Lespinasse’s  Experiments  with  Orifices 201 

45.  Coefficients  from  General  Ellis’s  Experiments  with  Orifices 203 

46.  Coefficients  for  Rectangular  Orifices  (vertical) 205 

47.  Coefficients  for  Rectangular  Orifices  (horizontal) 206 

48.  Castel’s  Experiments  with  Convergent  Tubes 217 

49.  Venturi’s  Experiments  with  Divergent  Tubes 219 

50.  Eytelwein’s  Experiments  with  Compound  Tubes 220 

51.  Coefficients  of  Efflux  ( c ) for  Short  Pipes 227 

520.  Experimental  Coefficients  of  Flow,  by  H.  Smith  Jr 236 

52.  Experimental  Coefficients  of  Flow  ( in ) by  Darcy 237 

53.  Experimental  Coefficients  of  Flow  (in)  bj^  Fanning 238 

54.  Experimental  Coefficients  of  Flow  ( m ) by  Du  Buat 238 

55.  Experimental  Coefficients  of  Flow  (ot)  by  Bossut  238 

56.  Experimental  Coefficients  of  Flow  ( in ) by  Couplet 239 

57.  Experimental  Coefficients  of  Flow  (in)  by  Provis 239 

58.  Experimental  Coefficients  of  Flow  ( m ) by  Rennie 239 

59.  Experimental  Coefficients  of  Flow  {in)  by  Darcy 240 

60.  Experimental  Coefficients  of  Flow  (in)  b}^  General  Greene  and  others  240 

61.  Tabulated  Series  of  Coefficients  of  Flow  (in) 242 

62.  Coefficients  for  Clean,  Slightl)r  Tuberculated,  and  Foul  Pipes 24S 

63.  Various  Formulas  for  Flow  of  Water  in  Pipes 254 

64.  Velocities  (v)  for  given  Slopes  and  Diameters 259 


LIST  OF  TABLES.  xxi 

Table  No.  Page 

65.  Tables  of  h and  Ji  due  to  given  Velocities 264 

66.  Values  of  cv,  and  c for  Tubes 267 

66 a.  Coefficients  (r)  for  Smooth  Cast-iron  Pipes 268 

66 b.  Coefficients  for  Classified  Rough  Pipes 269a 

66r.  Tables  of  Values  of  b,  n , and  m for  given  Diameters i~\c 

67.  Coefficients  of  Resistance  in  Bends 274 

68.  Experimental  Weir  Coefficients 288 

69.  Coefficients  for  given  Depths  upon  Weirs 2S9 

70.  Discharge  for  given  Depths  upon  Weirs 290 

71.  Weir  Coefficients  by  Castel 291 

72.  Series  of  Weir  Coefficients  by  Smeaton  and  others 291 

73.  Coefficients  for  Wide  Weir-crests 294 

73 a.  Computed  Weir  Volumes 298a 

74.  Observed  and  Computed  Flows  in  Canals  and  Rivers 307 

75.  Coefficients  (pi)  for  Open  Channels 308 

75 a.  Coefficients,  Classified  for  Channels 308c 

76.  Various  Formulas  for  Flow  in  Open  Channels 310 

76 a.  Current  Meter  Rating  Experiments 325a 

77.  Weights  of  Embankment  Materials 341 

78.  Angles  of  Repose,  and  Frictions  of  Embankment  Materials 345 

79.  Dimensions  of  Water  Supply  and  Irrigation  Canals 373 

79 a.  Dimensions  of  Irrigation  Canals 376# 

80.  Waste-Weir  Volumes  for  given  Depths 380 

81.  Lengths  and  Discharges  of  Waste-Weirs  and  Dams 381 

81a.  Data  of  Flood  Flow  of  Streams 381^ 

82.  Thicknesses  of  Masonry  Weirs  and  Dams 387 

83.  Heights  of  Reservoir  and  Lake  Waves 388 

84.  Coefficients  of  Masonry  Frictions 396 

85.  Computed  Pressures  in  Masonry 403 

86.  Limiting  Pressures  upon  Masonry 404 

87.  Dimension  of  Walls  to  Retain  Water 406 

88.  Dimension  of  Walls  to  Sustain  Earth 420 

89.  Thicknesses  of  a Curved-face  Wall 422 

90.  Hydraulic  Mean  Radii  for  Circular  Conduits 442 

90 a.  Velocities  in  the  Sudbury  Conduit 443 

90 b.  Coefficients  for  the  Croton  New  Aqueduct 44/ 

91.  Conduit  Data 445 

9i<z.  Coefficients  of  Flow  in  Conduits 445 

92.  Tenacities  of  Wrought  Pipe  Metals  451 

93.  Thicknesses  of  Cast-iron  Pipes 455 

93a.  Thicknesses  of  Cast-iron  Pipes  as  used  in  several  Cities 456 

94.  Parts  of  an  Inch  and  Foot  expressed  Decimally 457 

95.  Dimensions  of  Cast-iron  Water-pipes 461 

96.  Flange  Data  of  Flanged  Cast-iron  Pipes 462 

97.  Various  Formulas  for  Thicknesses  of  Cast-iron  Pipes 466 

98.  Weights  of  Cast-iron  Pipes 468 

98a.  Weights  of  Cast-iron  Pipes  as  used  in  several  Cities 469 

99.  Thicknesses  of  Wrought-iron  Pipe  Shells 486 


xxii  LIST  OP  TABLES. 

Table  No.  Page 

100.  Thicknesses  and  Weights  of  Iron  Plates 488 

101.  Frictional  Head  in  Pipes 495 

102.  Relative  Discharging  Capacities  of  Pipes 500 

103.  Depths  to  lay  Water-pipes  in  different  Latitudes 502 

104.  Elementary  Dimensions  of  Pipes 504 

105.  Maximum  Advisable  Velocity  of  Flow  in  Pipes 508 

106.  Diameters  of  Pipes  to  Supply  given  Numbers  of  Hose  Streams.  . 510 

107.  Experimental  Volumes  of  Fire  Hydrant  Streams 520 

107 a.  Pressure  Lost  by  Friction  in  Hose 520a 

107^.  Hydrant  and  Hose  Stream  Data 520a 

107c.  Combined  Domestic  and  Fire  Flow  in  Pipes 520^ 

108.  Frictional  Head  in  Service  Pipes.  52S 

109.  Dimensions  of  Filter-beds  for  given  Volumes ....  554 

109a.  Rates  of  Filtration  through  Sand  Beds 556 d 

no.  Piston  Spaces  for  given  Arcs  of  Crank  Motion 562 

in.  Ratios  of  Piston  Motions  for  given  Crank  Arcs 564 

112.  Costs  of  Pumping  in  Various  Cities 575 

113.  Special  Trial  Duties  of  Various  Pumping  Engines 580 

114.  Comparative  Consumptions  of  Coal  at  Different  Duties 581 

115.  Fuel  Expenses  for  Pumping  compared  on  Duty  Bases 582 

116.  Comparison  of  Values  of  Pumping  Engines  on  Fuel  Bases 584 

11 6a.  Duties  of  Pumping-engines 584a 

117.  Tank  Stabilities  of  Position 589 

118.  Pitch  and  Sizes  of  Rivets 592 

119.  Factors  for  Metal  Tank  Stand  Pipes 594 

120.  Thickness  of  Sheets  for  Metal  Stand  Pipes 596 

121.  Experiments  with  Hollow  Cylindrical  Beams 599 

122.  Stand  Pipe  Data 602a 

APPENDIX. 

French  Measures  and  U.  S.  Equivalents 612 

Comparative  Heads,  Pressures  and  Volumes 614 

Weights  and  Elasticities  of  Materials 615 

Dimensions  of  Bolts  and  Nuts 624 

Water  Works  Statistics 625 


LIST  OF  FULL  PAGE  ILLUSTRATIONS. 

Public  Fountain,  Cincinnati ii 

Pumping  Station,  Chestnut  Hill,  Boston iii 

Water  Tower,  St.  Louis,  W.  W viiia 

Tank  Stand-Pipe,  Fremont,  O ix 

Gateway,  Chestnut  Hill  Reservoir,  Boston 24 

Pumping  Station,  Toledo 31 

Laboratory,  Mt.  Prospect,  Brooklyn 33 d 

Pumping  Station,  Milwaukee 45 

Section  of  Plan  of  Pump-House 65 

Section  of  Croton  New  Aqueduct 74 

Reservoir  Embankment,  Norwich 84 

Sudbury  Dam,  Boston,  W.  W 84^ 

Croton  Dam 93 d 

Intercepting  Well,  Prospect  Park,  Brooklyn 102 

Artesian  Well  Strata,  Wisconsin 108 

Horizontal  Turbines  and  Pumps 112 

Pumping  Station,  New  Bedford 139 

Stand-Pipe,  Boston 160 

Pumping  Station,  Manchester 213 

Compound  Duplex  Pumping-Engine 223 

Diagram  of  Coefficients  of  Flow  in  Pipes 246 

Diagram  of  Frictional  Head  in  Branch  Pipes 250 

Diagram  of  Velocities  and  Friction  Heads,  in  Pipes 259 

Diagram  of  Coefficient  Values  for  Rough  Pipes 269 

Logarithmic  Diagram  of  Velocities 270 b 

Measuring  Weir,  for  Turbine  Test 277 

Modern  Current  Meters 299 

Diagram  of  Coefficients  for  Channels 309 

Improved  Current  Meters 326a 

Dam  at  Head  of  St.  Anthony  Falls 326^ 

Fairmount  Turbines  and  Pumps,  Philadelphia 331 

Distributing  Reservoir 333 

Sluice  Valve  364 

Compound  Inverted  Pumping-Engine 376 

Gate  House,  Baltimore  Water  Works 377 

Trial  Sections  for  Weirs  and  Dams 387 

Dam  on  a Soft  Rock  Foundation 389a 

Dam  on  Natchaug  River 3S93 

Conduit  Sections 431 

Cylindrical  Penstocks 440 

Sections  of  Croton  New  Aqueduct 445 

Branch,  Reducer,  and  Bend 478 

Double-Faced  Stop-Valves 493 

Diagram  of  Frictional  Head  in  Main  Pipes 495 

Plan  of  a Pipe  System 505 

Flush  Fire  Hydrants 521 

Mechanical  Filter  Plant 528 

The  Warren  Filter 529 

Pumping  Engine,  Reynolds  (2  cuts) 55^)  556^ 

Pumping-Engine,  No.  3,  Brooklyn 557 

Cornish  Plunger  Pump 563 

Compound  Beam  Pumping-Engine,  Lynn 567 

Geared  Pumping-Engine,  Providence 573 

Plan  of  Geared  Pumping-Engine 574 

Elevation  of  Geared  Pumping-Engine 575 

Pumping-Engine,  Gaskell’s  (2  cuts) 57^,  577 

Triplex  Tubular  Boiler 580 

Tank  Stand-Pipe,  South  Abington 585 

Jonval  Turbine 593 

Hydraulic  Power  Pumping  Machinery,  Manchester 603 

Whole  Number  of  Illustrations  . . 245 


APPENDIX 


Page 

Metric  Weights  and  Measures 6n 

Table  of  French  Measures  and  United  States  Equivalents  612 

Cubic  Inch,  and  Equivalents 613 

Gallon,  and  Equivalents 613 

Cubic  Foot,  and  Equivalents 613 

Imperial  Gallon,  and  Equivalents 614 

Cubic  Yard,  and  Equivalents 614 

Table  of  Units  of  Heads  and  Pressures  of  Water,  and  Equivalents 614 

Table  of  Average  Weights,  Strengths,  and  Elasticities  of  Materials 616 

Formulas  for  Diameters  and  Strengths  of  Shafts . 617 

Trigonometrical  Expressions 617 

Trigonometrical  Equivalents 618 

Table  of  Sines,  Tangents,  &c 619 

What  Constitutes  a Car  Load .......  620 

Lubricating  Compounds  for  Gears 620 

Compound  for  Cleaning  Brass 620 

Iron  Cement,  for  Repairing  Cracks  in  Castings 620 

Alloys,  Table  of 621 

Velocities  of  Flow  in  Channels,  that  Move  Sediments 622 

Tensile  Strengths  of  Cements  and  Mortars 623 

Dimensions  of  Bolts  and  Nuts 624 

General  Water  Works  Statistics,  1880 625 

Comparative  Water  Works  Statistics 626 

General  Water  Works  Statistics,  1882 627 

Stand-Pipe  Data 628 

Weights  of  Lead  and  Tin-lined  Service-Pipes 629 

Safe  Weights  of  Lead  Service-Pipes 630 

Weights  of  Lead  Pipes  for  given  Pressures 631 

Resuscitation  from  Apparent  Death  by  Drowning 632 


GATEWAY.  CHESTNUT  HILR  RESERVOIR.  BOSTON. 


SECTION  I. 


Collection  and  Storage  of  Water,  and  its  Impurities, 


CHAPTER  I. 

INTRODUCTORY. 

1.  Necessity  of  Public  Water  Supplies. — A new  or 

an  additional  water  supply  is  an  inevitable  necessity  when- 
ever and  wherever  a new  settlement  establishes  itself  in  an 
isolated  position ; again  whenever  the  settlement  receives 
any  considerable  increase ; and  again  when  it  becomes  a 
great  metropolis  or  manufacturing  centre. 

In  all  the  wonderful  and  complex  transformations  in 
Nature,  in  the  sustenance  of  all  organized  beings,  and  in 
the  convenience  and  delight  of  man,  water  is  appointed  to 
perform  an  important  and  essential  part. 

Life  cannot  long  exist  in  either  plant  or  animal,  unless 
water,  in  some  of  its  forms,  is  provided  in  due  quantity. 

Wholesome  water  is  indispensable  in  the  preparation  of 
all  our  foods  ; clear  and  soft  water  is  essential  for  promot- 
ing the  cleanliness  and  health  of  our  bodies ; and  pure 
water  is  demanded  for  a great  variety  of  the  operations  of 
the  useful  and  mechanic  arts. 

2.  Physiological  Office  of  Water.  — Of  the  three 
essentials  to  human  life,  air , water , and  food , the  one  now 


26 


INTRODUCTORY. 


to  be  specially  considered,  water , has  for  its  physiological 
office  to  maintain  all  the  tissues  of  the  body  in  healthy 
action. 

If  the  water  received  into  the  system  is  unfit  for  such 
special  duty,  all  the  animal  functions  suffer  and  are  weak- 
ened, air  then  but  partially  clarifies  the  blood,  food  then  is 
imperfectly  assimilated,  and  the  body  degenerates. 

Vigor  is  essential  to  the  uniform  success  and  happiness 
of  every  individual,  and  strength  and  happiness  of  the 
people  are  essential  to  good  public  morals,  good  public 
government,  and  sound  public  prosperity. 

Sanitary  improvements  are,  therefore,  among  the  first 
and  chief  duties  of  public  officers  and  guardians,  and  have 
ever  been  the  objects  of  the  most  earnest  thought  and  labor 
of  great  public  philanthropists. 

3.  Sanitary  Office  of  Public  Water  Supplies. — 
Water  has  thus  far  proved  the  most  effectual  and  econom 
ical  agent,  as  sanitary  scavenger,  in  the  removal  from  our 
habitations  of  waste  slops  and  sewage,  and  also  the  most 
effectual  * and  economical  agency  in  the  protection  of  life 
and  property  from  destruction  by  fire. 

The  necessity  of  a judiciously  executed  system  of  public 
water-supply  increases  as  the  population  of  a town  increases; 
as  the  mass  of  buildings  thickens ; as  the  lands  upon  which 
the  town  is  built  become  saturated  with  sewage,  and  the 
individual  sources  within  the  town  are  polluted;  as  the 
atmosphere  over  and  within  the  town  is  fouled  by  gases 

* We  need  refer  to  but  one  of  many  experiences,  viz. : At  Columbus, 
Ohio,  the  average  loss  by  fire  for  the  four  years  preceding  the  completion  of 
the  public  water-works  was  of  one  per  cent,  of  the  valuation.  The  average 

loss  during  the  first  four  years  after  the  completion  of  the  works  was  and 
during  the  fifth  year,  from  April  1,  1875,  to  April  1,  1876,  was  of  the  valu- 
ation. These  statistics  show  a probable  saving  in  the  first  four  vears  of  upward 
of  one-half  million  dollars,  and  in  five  years  of  more  than  the  entire  cost  of  the 
water-works. 


HELPFUL  INFLUENCE  OF  PUBLIC  WATER  SUPPLIES.  27 


arising  therefrom  ; and  as  the  dangers  of  epidemics,  fevers, 
and  contagious  diseases  increase. 

4.  Helpful  Influence  of  Public  Water  Supplies. — 
No  town  or  city  can  submit  to  a continued  want  of  an 
adequate  supply  of  pure  and  wholesome  water  without  a 
serious  check  in  its  prosperity. 

Capital  is  always  wary  of  investment  where  the  elements 
of  safety  and  health  are  lacking,  and  industry  dreads  fre- 
quent failures  and  objectionable  quality  in  its  water  supply. 

It  is  true  that  considerations  of  profit  sometimes  induce 
the  assembling  of  a town  where  potable  waters  are  procur- 
able with  difficulty,  but  in  such  cases  the  lack  is  sure  to 
prove  a growing  hindrance  to  its  prosperity,  and  before  the 
town  arrives  at  considerable  magnitude,  its  remedy  will 
present  one  of  the  most  difficult  problems  with  which  its 
municipal  authorities  are  obliged  to  cope. 

In  the  experience  of  all  large  and  thriving  cities,  there 
has  come  a time  when  an  additional  or  new  and  abundant 
water  supply  was  a necessity,  terribly  real,  that  would  not 
be  talked  down,  or  resolved  out  of  existence  by  public 
meetings,  or  wait  for  a more  convenient  season ; a time 
when  it  was  not  possible  for  every  citizen  to  supply  his 
household  or  his  place  of  business  independently,  or  even 
for  a majority  of  the  citizens  to  do  so,  and  when  prompt, 
united,  and  systematic  action  must  be  taken  to  ensure  the 
health,  prosperity,  and  safety  of  the  people.  Such  stern 
necessity  often  appears  to  present  difficulties  almost  insur- 
mountable by  the  available  mechanical  and  financial  re- 
sources of  the  citizens. 

Out  of  such  simple  but  positive  necessities  have  grown 
the  grandest  illustrations,  in  our  great  public  water  sup- 
plies, of  the  benefits  of  co-operative  action,  recorded  in  the 
annals  of  political  economy.  Out  of  such  simple  necessi- 


28 


INTRODUCTORY. 


ties  grew  some  of  the  most  magnificent  and  enduring  con- 
structions of  the  powerful  empires  of  the  Middle  Ages,  the 
architectural  grandeur  of  which  the  moderns  have  not 
attempted  to  surpass. 

5.  Municipal  Control  of  Public  Water  Supplies. 

— The  magnitude  of  the  labors  to  be  performed  and  the 
amount  of  capital  required  to  be  invested  in  the  construc- 
tion of  a system  of  water  supplies  invariably  brings  into 
prominence  the  question,  Shall  the  construction,  operation, 
and  control  of  these  works  be  entrusted  to  private  capital, 
or  shall  they  be  executed  under  the  patronage  of  the  muni- 
cipal authorities  and  under  the  direction  of  a commission 
delegated  by  the  people?  The  conclusion  reached  in  a 
majority  of  the  American  cities  lias  been  that  the  works 
ought  to  be  conducted  as  public  enterprises.  They  have 
been  believed  to  be  so  intimately  connected  with  the  public 
interests  and  welfare  as  to  be  peculiarly  subjects  for  pub- 
lic promotion ; and  that,  under  the  direction  of  a commis- 
sion appointed  by  the  people  to  study  and  comprehend  all 
their  needs,  to  consider,  with  the  aid  of  expert  advice,  and 
to  suggest  plans,  the  works  would  be  projected  on  such  a 
liberal  and  comprehensive  scale  as  would  best  fulfil  the 
objects  desired  to  be  attained,  and  that  the  true  interests  of 
the  people  would  not  be  subordinated  to  mere  considera- 
tions of  profit. 

Further,  that  if  the  works  when  complete  were  operated 
under  municipal  care,  their  standard  and  effectiveness  would 
more  certainly  be  maintained ; their  extension  into  new 
territory  might  keep  pace  with  and  encourage  the  growth 
of  the  city  ; they  might  not,  by  excessive  rates,  be  made  to 
oppress  important  industries  ; their  advantages  might  more 
surely  be  kept  within  the  reach  of  the  poorer  classes  : they 
might  more  economically  be  applied  to  the  adornment  of 


INCIDENTAL  ADVANTAGES. 


29 


the  public  buildings  and  grounds  ; and  that  they  might, 
when  judiciously  planned,  constructed,  and  managed,  be- 
come a source  of  public  revenue. 

Nearly  all  the  objects  desirable  to  be  attained  in  a pub- 
lic water  supply  have,  however,  been  accomplished,  in 
numerous  instances  that  might  be  cited,  under  the  auspices 
of  private  enterprise. 

6.  Value  as  an  Investment. — The  necessary  capital 
honestly  applied  to  the  construction  of  an  intelligently  and 
judiciously  planned  effective  public  water  supply  has 
almost  invariably  proved,  both  directly  and  indirectly,  a 
remunerative  investment. 

Many,  though  not  all,  of  our  American  Water- supply 
Reports,  show  annual  incomes  from  water-rates  in  excess 
of  the  combined  annual  operating  expenses  and  interest  on 
the  capital  expended.  In  addition  to  this  cash  return,  there 
are  in  all  cases  benefits  accruing  to  the  public,  usually 
exceeding  in  real  value  that  of  the  more  generally  recog- 
nized money  income. 

7.  Incidental  Advantages. — The  construction  of  water- 
works  is  almost  sure  to  enhance  the  value  of  property  along 
its  lines,  under  its  protection,  and  availing  of  its  conve- 
niences. There  is,  also,  a perpetual  reduction*  in  the 


* In  a recently  adopted  schedule  of  the  National  Board  of  Underwriters, 
there  are  additions  to  a minimum  standard  rate  in  a standard  city,  which  is 
provided  with  good  water  supply,  fire  alarm,  police,  etc.,  as  follows,  termed 
deficiency  charges  : 

Minimum  standard  rate  of  insurance  of  a standard  building. . 25  cents. 


If  no  water  supply add  15  ‘ 

If  only  cisterns,  or  equivalent “ 10  ‘ 

If  system  is  other  than  gravity “ 05  ‘ 

If  no  fire  department “ 25  ‘ 

If  no  police  organization “ 05  ‘ 

If  no  building  law  in  force “ 05  ‘ 


The  financial  value  of  the  enhanced  fire  risk,  as  deduced  hv  the  Board  from 
an  immense  mass  of  statistics,  and  the  additional  premium  charged  on  the 


30 


INTRODUCTORY. 


yearly  rates  of  insurance.  The  substitution  of  soft  water 
for  hard  water,  as  almost  all  waters  are,  results  in  a mate- 
rial reduction  in  the  daily  waste  accompanying  the  prepa- 
ration of  foods,  in  laundry  and  cleansing  operations,  in  the 
production  of  steam  power,  and  in  many  of  the  processes 
employed  in  the  useful  arts. 

There  are  many  industries,  the  introduction  of  which  are 
of  value  to  a community,  that  cannot  be  prosecuted  with- 
out the  use  of  tolerably  pure  and  soft  water.  To  save  the 
annual  aggregate  of  labor  required  to  convey  water  from 
wells  into  and  to  the  upper  floors  of  city  tenements  or  resi- 
dences, is  a matter  of  no  inconsiderable  importance ; but 
paramount  to  all  these  is  the  value  of  the  sanitary  results 
growing  out  of  the  maintenance  of  health,  and  the  induce- 
ment to  cleanliness  of  person  and  habitation,  by  the  con- 
venience of  an  abundance  of  water  delivered  constantly  in 
the  household,  and  the  enhanced  safety  to  human  life  and 
to  property  from  destroying  flames,  accompanying  a liberal 
distribution  of  public  fire  hydrants  under  adequate  pressure 
throughout  the  populous  districts. 


most  favorable  buildings,  is  60  per  cent,  without  good  water-works,  and  40  pei 
cent,  if  only  fire  cisterns  are  provided. 


DUMPING  STATION.  TOLEDO. 


CHAPTEB  II. 


QUANTITY  OF  WATER  REQUIRED. 

8.  Statistics  of  Water  Supplied.— One  of  the  first 
duties  of  a Commission  to  whom  lias  been  assigned  the 
task  of  examining  into  and  reporting  upon  a proposed 
supply  of  water  for  a community,  is  to  determine  not  only 
what  is  a wholesome  water,  hut  what  quantity  of  such 
wholesome  water  will  he  required,  and  adequate  for  its 
present  and  prospective  uses. 

In  many  cases,  this  problem  is  parallel  with  the  deter- 
mination of  a product  from  two  factors,  one  of  which  only 
is  a known  quantity.  Often  all  factors  must  he  assumed. 

The  total  number  of  inhabitants,  the  total  number  of 
dwellings,  and  the  total  number  of  manufacturing  and 
commercial  tirms  can  be  obtained  without  great  difficulty, 
and  it  can  safely  be  assumed  that  eighty  per  cent,  of  all 
these  within  reach  of  a new  and  improved  water  supply 
will  be  among  its  patrons  within  a few  years  after  the  intro- 
duction of  the  new  supply ; but  how  much  water  will  be 
required  for  actual  use,  or  will  be  wasted,  per  person,  per 
dwelling,  or  per  firm,  is  always  quite  uncertain. 

Rarely  can  any  data  worthy  of  confidence  respecting 
these  quantities  be  obtained.  The  practice,  therefore,  gen- 
erally is,  to  obtain  statistics  from  towns  and  cities  already 
supplied,  and  to  attempt  to  reduce  these  to  some  general 
average  that  will  apply  to  the  case  in  hand. 

9.  Census  Statistics. — In  a small  portion  of  the  water- 
supply  reports  there  is  given,  in  addition  to  the  total  quan- 


32 


QUANTITY  OF  WATER  REQUIRED. 


tity  of  wafer  supplied,  the  number  of  families  supplied  ; in 
other  reports,  the  number  of  dwellings,  or  the  number  of 
fixtures  of  the  several  classes  supplied,  and  occasionally 
the  population  supplied,  or  the  total  population  of  the 
municipality. 

In  the  investigations  for  facts  applicable  to  a new  sup- 
ply, when  information  must  necessarily  be  culled  from 
various  water  reports,  it  is  often  desirable  to  know  the 
populations  of  the  places  from  which  the  reports  are  re- 
ceived, their  number  of  families,  persons  to  a family,  num- 
ber of  dwellings  and  persons  to  a dwelling,  so  as  to  be  able 
to  reduce  their  water-supply  data  to  a uniform  classifica- 
tion. We  therefore  present  an  abstract  from  the  United 
States  Census  for  the  year  1870,  giving  such  information 
respecting  fifty  prominent  American  cities,  and  similar  data 
in  table  No.  la,  for  the  year  1880. 

TABLE  No.  1. 


Population,  Families,  and  Dwellings  in  Fifty  American  Cities. 

IN  THE  YEAR  1870. 


CITIES. 

Size.* 

Population. 

Families. 

Dwellings. 

Number. 

Persons 
.to  a 
family. 

Persons 

Number.  to  a 

dwelling 

Albany,  N.  Y 

20 

69,422 

14,105 

4.92 

8.748 

7-94 

Allegheny,  Penn 

23 

53A8o 

10,147 

5-24 

8,347 

6-37 

Baltimore,  Md 

6 

267,354 

49,929 

5-35 

40,35° 

6.63 

Boston,  Mass.  

7 

250,526 

48,  l88 

5.20 

29,623 

8.46 

Brooklyn,  N.  Y 

3 

396,099 

80,066 

4-95 

45,834 

8.64 

Buffalo,  N.  Y 

1 1 

117,74 

22,325 

5-27 

18,285 

6.44 

Cambridge,  Mass 

33 

39,634 

7,897 

S'02 

6,348 

6.24 

Charleston,  S.  C 

26 

48,956 

9,098 

5-38 

6,861 

7-x4 

Charlestown,  Mass.  . . . 

47 

28,323 

6,155 

4.60 

4,396 

6.44 

Chicago,  111 

3 

298,977 

59,497 

5-°3 

44.620 

6.70 

Cincinnati,  Ohio 

8 

216,239 

42,937 

5-°4 

24,550 

8.81 

* This  column  expresses  the  order  of  size  as  numbered  from  largest  to 
smallest ; New  York,  the  largest,  being  numbered  1. 


STATISTICS  OF  FIFTY  AMERICAN  CITIES 


33 


Population,  Etc.,  in  Fifty  American  Cities — {Continued ). 


CITIES. 

Size. 

Population. 

Families. 

Dwell 

INGS. 

Number. 

Persons 
to  a 
family. 

Number. 

Persons 
to  a 

dwelling 

Cleveland,  Ohio 

*5 

92,829 

18,41 1 

5-°4 

16,692 

5-56 

Columbus,  Ohio 

42 

31.274 

5,79° 

5-4° 

5,0*1 

6.24 

Dayton,  Ohio 

44 

30,473 

6,109 

4.99 

5,6n 

5-43 

Detroit,  Michigan 

18 

79’577 

15,636 

5-09 

14,688 

5-42 

Fall  River,  Mass 

5° 

26,766 

5,2*6 

5-*3 

2,687 

9.96 

Hartford,  Conn 

34 

37>i8o 

7,427 

5-0* 

6,688 

5 56 

Indianapolis,  Ind 

27 

48,244 

9,200 

5-24 

7,820 

6.17 

Jersey  City,  N.  J 

*7 

82,546 

16,687 

4-95 

9,867 

8-37 

Kansas  City,  Mo 

38 

32,260 

5,585 

5.78 

5,424 

5 95 

Lawrence,  Mass 

45 

28,921 

5,287 

5-47 

3,443 

8.40 

Louisville,  Ky 

14 

*00,753 

*9,i77 

5.25 

14,670 

6 87 

Lowell,  Mass 

3i 

40,928 

7,649 

5-35 

6,362 

6.43 

Lynn,  Mass 

49 

28,233 

6,100 

4.63 

4,625 

6.10 

Memphis,  Tenn 

32 

40,226 

7,824 

5.14 

6,408 

6.28 

Milwaukee,  Wis 

*9 

71,440 

14,226 

5.02 

*3,048 

5-48 

Mobile,  Ala 

39 

32,034 

6,301 

5.o8 

5,738 

5-58 

Newark,  N.  J 

13 

105,059 

21,631 

4.86 

*4,35° 

7-32 

New  Haven,  Conn. . . . 

25 

50,840 

10,482 

4.85 

8,100 

6.28 

New  Orleans,  La 

9 

191,418 

39,i39 

4.89 

33,656 

5-69 

New  York,  N.  Y 

1 

942,292 

185,789 

5.07 

64,044 

14.72 

Paterson,  N.  T 

37 

33,579 

7,048 

4.76 

4,653 

7.22 

Philadelphia,  Pa 

2 

674,022 

127,746 

5.28 

112,366 

6.01 

Pittsburg,  Pa.  

16 

86,076 

16,182 

5-32 

14,224 

6.05 

Portland,  Me 

41 

3i,4i3 

6,632 

4.74 

4,836 

6.50 

Providence,  R.  I 

21 

68,904 

*4,775 

4.66 

9,227 

7.46 

Reading,  Pa 

36 

33,930 

6,932 

4.89 

6,294 

5-39 

Richmond,  Ya 

24 

51,038 

9,792 

5-21 

8,033 

6-35 

Rochester,  N.  Y 

22 

62,386 

12,213 

5-1* 

11,649 

5-36 

San  Francisco,  Cal. . . . 

10 

*49,473 

30,553 

4.89 

25,905 

5-77 

Savannah,  Ga 

48 

28,235 

5,0*3 

5-63 

4,56i 

6.19 

Scranton,  Pa 

35 

35,°92 

6,642 

5.28 

5,646 

6.21 

St.  Louis,  Mo 

4 

3*0,864 

59,43* 

5-23 

39,675 

7.84 

Syracuse,  N.  Y 

29 

43>°5* 

8,677 

4.96 

7,088 

6.07 

Toledo,  Ohio 

40 

31,584 

6,457 

4.89 

6,069 

5.20 

Troy,  N.  Y 

28 

46,465 

9,302 

5.00 

5,893 

7.88 

Utica,  N.  Y 

46 

28,804 

5,793 

4-97 

4,799 

6.00 

Washington,  D.  C 

12 

109,199 

2i,343 

5-12 

*9,545 

5-59 

Wilmington,  Del 

43 

30,841 

5,808 

5-3* 

5,398 

5-7* 

Worcester,  Mass 

3° 

41,105 

8,658 

4-74 

4,922 

8-35 

3 


33  a 


STATISTICS  OF  HUNDRED  AMERICAN  CITIES. 


TABLE  No.  la. 

Population,  Families,  and  Dwellings  in  ioo  American  Cities 

in  THE  \EAR  1880.  ( Front  the  U.  S.  Census  of  1880.) 


CITIES. 

Size. 

Population. 

Families. 

Dwellings. 

Number. 

Persons  to 
a family. 

Number. 

Persons 
to  a 

dwelling 

Albany,  N.  Y 

21 

90,758 

18,297 

4.96 

13,259 

6.85 

Allegheny,  Pa 

23 

78,682 

14,747 

5-34 

IU943 

6,59 

Atlanta,  Ga 

49 

37,409 

7,799 

4.80 

6,494 

5.76 

Auburn,  N.  Y 

84 

21,924 

4,417 

4.96 

3,879 

5-65 

Augusta,  Ga 

86 

21,891 

4,998 

4.38 

3,938 

5.56 

Baltimore,  Md 

7 

332,313 

65,356 

5.08 

50,833 

6.54 

Bay  ( 'it)',  Mich 

95 

20,693 

3,728 

5-55 

3,244 

6.38 

Boston,  Mass 

5 

362,839 

72,763 

4.99 

43,944 

8.26 

Bridgeport,  Conn. . . 

7i 

27.643 

5,958 

4.64 

3,735 

7.40 

Brooklyn,  N.  Y 

3 

566,663 

115,076 

4.92 

62,233 

9. II 

Buffalo,  N Y 

13 

155,134 

30,946 

5-oi 

23,680 

6.55 

Cambridge,  Mass. . . 

3i 

52,669 

10,833 

4.86 

8,260 

6.38 

Camden,  N.  J 

44 

41659 

8,772 

4-75 

8,246 

5.05 

Charleston,  S’.  C 

36 

49,984 

11,406 

4.38 

6,552 

7.63 

Chelsea,  Mass 

88 

21,782 

4,834 

4-51 

3,725 

5-85 

Chicago,  111 

4 

503,185 

96,992 

5-19 

61,069 

8.24 

Cincinnati,  Ohio. . . . 

8 

255439 

52,025 

4.90 

28,017 

9. II 

Cleveland,  Ohio 

II 

160,146 

32,H3 

4.99 

27.1S1 

5-89 

Columbus,  Ohio  .... 

33 

51.647 

9,396 

5-50 

8,527 

6.06 

Covington,  Ky 

65 

29,720 

6,076 

4.89 

4,792 

6.20 

Davenport,  Iowa.  . . . 

87 

21,831 

4,544 

4.80 

4,342 

5.03 

Dayton,  ( iliio 

47 

38,678 

8,106 

4-77 

6,990 

5-53 

Denver,  Col 

50 

35,629 

5,945 

5-99 

5,279 

6.75 

Des  Moines,  Iowa.. . 

80 

22,408 

4,359 

5-14 

4U7o 

5-37 

Detroit,  Mich 

18 

116,340 

23,290 

5.00 

20,493 

5-68 

Dubuque,  Iowa 

81 

22,254 

4,281 

5.20 

3-S74 

5-74 

Elizabeth,  N.  I 

69 

28,229 

5.332 

5-29 

4,308 

6-55 

Elmira,  N.  Y 

97 

20,541 

4.431 

4.64 

3,810 

5-39 

Erie,  Pa 

70 

27.737 

5,294 

5-24 

4,903 

5.66 

Evansville,  Ind 

66 

29,280 

5,803 

5-05 

5,296 

5-53 

Fall  River,  Mass. . . . 

37 

48,961 

9,706 

5.04 

5,594 

8.75 

Fort  Wayne,  Ind. . . . 

74 

26,880 

5,455 

4-93 

4,866 

5-52 

Galveston,  Texas. . . . 

82 

22,248 

4,670 

4.76 

4.221 

5-27 

Grand  Rapids,  Mich. 

58 

32,016 

6,817 

4.70 

5,752 

5-57 

Harrisburg,  Pa 

60 

30,762 

6,429 

4.78 

5.967 

5- 16 

Hartford,  Conn 

43 

42,015 

9U37 

4.60 

5,736 

7 • 32 

Hoboken.  N.  J 

59 

30,999 

6,717 

4.62 

2.695 

11.50 

Holvoke,  Mass 

85 

21,915 

3,881 

5.65 

2,084 

10.52 

Indianapolis,  Ind.. . . 

24 

75,056 

15,650 

4.80 

13,727 

5-47 

Jersey  City,  N.  J . . . . 

17 

120,722 

23,957 

5-04 

14,049 

8.59 

Kansas  City,  Mo.  . . . 

30 

55,785 

9.347 

5-97 

8,609 

6.48 

Lancaster,  Pa 

77 

25,769 

5,379 

4-79 

5A33 

5-02 

Lawrence,  Mass 

46 

sgusi 

7,488 

5-23 

4, 60S 

8.50 

Louisville,  Ky 

l6 

123,758 

24,343 

5.08 

iS.SgS 

6-55 

Lowell,  Mass 

27 

59,475 

n,439 

5-20 

8.245 

7.21 

Lynn,  Mass 

48 

38,274 

8,209 

4.66 

6.315 

6.06 

Manchester,  N.  H . . . 

56 

32,630 

6,338 

5-15 

3.589 

9.09 

Memphis,  Tenn 

54 

33,592 

7,943 

4.23 

7U74 

4.68 

STATISTICS  OF  HUNDRED  AMERICAN  CITIES, 


335 


Population,  Etc.,  in  Hundred  American  Cities. — (Continued.) 


Families. 

Dwellings. 

CITIES. 

Size. 

Population. 

Number. 

Persons  to 
a lamily. 

Number. 

Persons 
to  a 

dwelling. 

Milwaukee,  Wis 

19 

115.587 

23,024 

5.02 

18,748 

6.17 

Minneapolis,  Minn.  . 

38 

46,887 

8,584 

5.46 

6,932 

6.76 

Mobile,  Ala 

68 

29.132 

6,133 

4-75 

5,276 

5-52 

Nashville,  lenn 

40 

43  350 

8,525 

5.09 

7,072 

6.13 

Newark,  N.  I 

15 

136,508 

28,386 

4.-81 

18,796 

7.26 

New  Bedford,  Mass.. 

75 

26,845 

6,147 

4-37 

5,038 

5-33 

New  Haven,  Conn.. . 

26 

62,882 

13,638 

4.61 

9,961 

6.31 

New  Orleans,  La. . . . 

IO 

216,090 

45,316 

4-77 

36,347 

5-95 

Newport,  Ky 

98 

20,433 

4,111 

4-97 

3.225 

6-34 

New  York,  N.  Y.... 

I 

1,206,299 

243,157 

4.96 

73,684 

16.37 

Norfolk,  Va 

83 

24,966 

5,098 

4.31 

3.277 

6.70 

Oakland,  Cal 

5i 

34.555 

7,018 

4.92 

6,416 

5-39 

Omaha,  Neb 

63 

30.518 

5,612 

5-44 

5,110 

5-97 

Oswego,  N.  Y 

92 

21,116 

4,398 

4.80 

4,153 

5.08 

Paterson,  N.  J 

34 

5L03I 

10,679 

4.78 

6,712 

7.60 

Peoria,  111 

67 

29.259 

5,879 

4.98 

5,482 

5-34 

Petersburg,  Va 

89 

21,656 

4,779 

4-53 

3,426 

6.32 

Philadelphia,  Pa 

2 

847,170 

165,044 

5-13 

146,412 

5-79 

Pittsburg,  Pa 

12 

156.389 

29,868 

5-24 

24,289 

6-44 

Portland,  Me 

53 

33.8io 

7,295 

4-63 

5.157 

6.56 

Poughkeepsie,  N.  Y. 

99 

20,207 

4,302 

4.70 

3,403 

5-94 

Providence,  R.  I 

20 

104,857 

23,178 

4-52 

14,153 

7.41 

Ouincy,  111 

73 

27,268 

5,532 

4-93 

4,715 

5-78 

Reading,  Pa 

41 

43.278 

8,876 

4.88 

8,267 

5-24 

Richmond,  Va 

25 

63,600 

12,180 

5.22 

9.532 

6.67 

Rochester,  N.  Y 

22 

89,366 

18,039 

4-95 

15,825 

5-65 

Sacramento.  Cal 

90 

21,420 

4,752 

4-51 

4,222 

5-07 

St.  Joseph,  Mo 

57 

32,431 

5,630 

5.76 

5.260 

6.17 

St.  Louis,  Mo 

6 

350,518 

65,142 

5-38 

43,026 

8.15 

St  Paul,  Minn 

45 

4L473 

7,224 

5-74 

6,343 

6-54 

Salem,  Mass 

72 

27,563 

6,167 

4-47 

4,241 

6.50 

Salt  Lake  City,  Utah. 

93 

20,768 

4,207 

4-94 

3,755 

5-53 

San  Antonio.  Texas. . 

96 

20,550 

3,864 

5-32 

3,632 

5.66 

San  Francisco,  Cal..  . 

9 

233,959 

43.463 

5.38 

34,110 

6.86 

Savannah,  Ga 

62 

30,709 

6,684 

4-59 

5,572 

5-5i 

Scranton,  Pa 

39 

45,850 

8,926 

5-14 

7,334 

6.25 

Somerville,  Mass.  .. 

78 

24.933 

5,417 

4.60 

4,106 

6.07 

Springfield,  111 

100 

19,743 

3,9l6 

5-04 

3,525 

5.60 

Springfield,  Mass.. . . 

55 

33.340 

7,368 

4-52 

5,033 

6.62 

Springfield,  Ohio. . . . 

94 

20,730 

4.339 

4.78 

3,786 

5-48 

Syracuse,  N.  Y 

32 

5L792 

11,046 

4.69 

8,825 

587 

Taunton,  Mass 

9i 

21,213 

4.450 

4-77 

3,261 

6.  si 

Terre  Haute,  Ind. . . . 

76 

26,042 

5,078 

5-13 

4,581 

5-68 

Toledo,  Ohio 

35 

50437 

10,191 

4.92 

9,717 

5.16 

Trenton,  N.  J 

Troy,  N.  Y 

64 

29,910 

5,472 

5-47 

5,115 

5.85 

29 

56,747 

11,491 

4.94 

6,955 

8.16 

Utica,  N.  Y 

52 

33.9H 

6,996 

4-85 

5,815 

5-83 

Washington,  D.  C. . . 

14 

147.293 

29,603 

4.98 

24,107 

6.  ii 

Wheeling,  W.  Va. . . . 

6l 

30,737 

6,233 

4-93 

5,128 

5-99 

Wilkesbarre,  Pa 

79 

23,339 

- 4.424 

5-28 

4,157 

5.61 

Wilmington,  Del.  . . . 

42 

42,478 

8,243 

5-15 

7,641 

5-56 

Worcester,  Mass .... 

28 

58,291 

11,931 

4.89 

6,634 

8.79 

33c 


STATISTICS  OF  LARGER  AMERICAN  CITIES 


TABLE  No.  lb. 


Populations  in  1900,  of  142  American  Cities. 


Cities 


New  York,  N.  Y 

Chicago,  111 

Philadelphia,  Pa 

St.  Louis,  Mo 

Boston,  Mass 

Baltimore,  Md 

Cleveland,  Ohio 

Buffalo,  N.  Y 

San  Francisco,  Cal. . 

Cincinnati,  Ohio 

Pittsburg,  Pa 

New  Orleans,  La 

Detroit,  Mich 

Milwaukee,  Wis 

Washington,  D C... 

Newark,  N.  J 

Jersey  City,  N.  J 

Louisville,  Ky 

Minneapolis,  Minn... 

Providence.  R.  I. 

Indianapolis,  Ind. 

Kansas  City,  Mo 

St.  Paul,  Minn 

Rochester,  N.  Y 

Denver,  Col 

Toledo,  Ohio 

Allegheny,  Pa 

Columbus,  Ohio 

Worcester,  Mass 

Syracuse,  N.  Y 

New  Haven,  Conn . . . 

Paterson,  N.  J 

Fall  River,  Mass 

St.  Joseph,  Mo 

Omaha,  Neb 

Los  Angeles,  Cal. . . . 

Memphis,  Tenn 

Scranton,  Pa 

Lowell,  Mass 

Albany,  N.  Y 

Cambridge,  Mass 

Portland,  Oregon 

Atlanta,  Ga 

Grand  Rapids,  Mich. 

Dayton,  Ohio 

Richmond,  Va 

Nashville,  Tenn 

Seattle,  Wash 

Hartford,  Conn 

Reading,  Pa 

Wilmington,  Del 

Camden,  N.  J 

Trenton,  N.  J 

Bridgeport,  Conn 

Lynn,  Mass 

Oakland,  Cal 

Lawrence,  Mass 

New  Bedford,  Mass.. 
Des  Moines,  Iowa. . . , 

Springfield,  Mass 

Somerville,  Mass 

Troy,  N.  Y 

Hoboken,  N.  J 

Evansville,  Ind 

Manchester,  N.  H. . . 

Utica,  N.  Y 

Peoria,  111 

Charleston,  S.  C 

Savannah,  Ga 

Salt  Lake  City,  Utah 
San  Antonio,  Texas. 


pulation 

Per  cent* 
Increase 

3,347,202 

37-8 

1,698,57s 

54-4 

1,293,697 

23-5 

575,238 

27-3 

560,892 

25.0 

508,957 

17.1 

381,768 

46.0 

352,387 

37-8 

342,782 

I4.6 

325,902 

9-7 

321,616 

34-7 

287,104 

18.6 

283,704 

38.7 

285,315 

39-5 

278,718 

20.9 

246,070 

35-3 

206,433 

26.6 

204,731 

27.0 

202,718 

23.0 

175,597 

32.8 

169,164 

60.4 

, 163,752 

23-3 

163,065 

22.4 

162,608 

21.4 

133,859 

25-4 

131,822 

61.8 

129,896 

23-3 

125,560 

42.4 

118,421 

39-8 

108,374 

22.9 

108,027 

32.0 

105,171 

34-2 

104,863 

409 

102,979 

96.8 

102,555 

— 26.9 

102,479 

103.3 

102,320 

58.6 

102,026 

35-6 

94,969 

22.2 

94,T5i 

-0.8 

91,886 

31.2 

90,426 

94.9 

89,872 

37-i 

87,56s 

45-2 

85,333 

39-3 

85,050 

4-4 

80,865 

6.1 

80,671 

88.3 

79,850 

50.0 

78,961 

34-6 

76,508 

24-5 

75»935 

30.2 

73,307 

27-5 

70,996 

45-2 

68,513 

22.9 

66,960 

37-5 

62,559 

40.0 

62,442 

53-2 

62,139 

24.0 

62,059 

40.4 

61,643 

53-5 

60,651 

-0.5 

59,364 

36.0 

59,007 

16.2 

56,987 

29.1 

56,383 

28.1 

56,100 

36-7 

55,807 

i-5 

54,244 

25-5 

53,53i 

J9-3 

53,32i 

4i-5 

Cities 


Duluth,  Minn 

Erie,  Pa 

Elizabeth,  N.  J 

Wilkesbarre,  Pa 

•Kansas  City,  Kan. 

Harrisburg,  Pa 

Portland,  Me 

Yonkers,  N.  Y 

Norfolk,  Va 

Waterbury,  Conn. 

Holyoke,  Mass 

Fort  Wayne,  Ind . . . 
Youngstown,  Ohio 

Houston,  Texas 

Covington,  Ky 

Akron,  Ohio 

Dallas,  Texas 

Saginaw,  Mich 

Lancaster,  Pa 

Lincoln,  Neb 

Brockton,  Mass.... 
Binghamton,  N.  Y.. 

Augusta,  Ga 

Honolulu,  Hawaii., 

Pawtucket,  R.  I 

Altoona,  Pa 

Wheelings  W.  Va. . 

Mobile,  Ala 

Birmingham,  Ala.. 
Little  Rock,  Ark. . 
Springfield,  Ohio. . , 
Galveston,  Texas.. 

Tacoma,  Wash 

Haverhill,  Mass.... 

Spokane,  Wash 

Terre  Haute,  Ind. 

Dubuque,  Iowa 

Quincy,  111 

South  Bend,  Ind. . . 

Salem,  Mass 

Johnstown,  Pa 

Elmira,  N.  Y 

Allentown,  Pa 

Davenport,  Iowa. . 
McKeesport,  Pa. . . 

Springfield.  Ill 

Chelsea,  Mass 

Chester,  Pa 

York,  Pa 

Malden,  Mass 

Topeka,  Kan 

Newton,  Mass 

Sioux  City,  Iowa.. 

Bayonne,  N.  J 

Knoxville,  Tenn... 
Chattanooga,  Tenn. 
Schenectady,  N.  Y. 
Fitchburg,  Mass... 

Superior,  Wis 

Rockford,  111 

Taunton.  Mass 

Canton,  Ohio 

Butte,  Mont 

Montgomery,  Ala.. 

Auburn,  N.  Y 

East  St.  Louis,  111. . 

Joliet,  111 

Sacramento.  Cal 

Racine,  Wis 

La  Crosse,  Wis 

Williamsport,  Pa... 


Population 

Per  cent 
Increase 

• ■ • 52,969 

59-9 

• ■ • 52,733 

29.7 

38.0 

51,721 

37-i 

...  51.418 

34-1 

50, 167 

27.3 

50,145 

37-0 

47,931 

49-o 

33-7 

45.859 

60.0 

45,712 

28.2 

45,H5 

27.4 

44,885 

35-i 

44,633 

61.0 

42,938 

14.8 

42,728 

54-8 

12.0 

• • • 42,345 

-8-5 

41,459 

29.5 

—27.1 

40,063 

46.7 

39,647 

13.2 

39,441 

18.4 

39,306 

71.6 

39,231 

41.9 

• ■ • 38,973 

28.4 

. . . 38,878 

12.6 

. . . 38,469 

23-7 

38,415 

46.7 

38,307 

48.0 

38,253 

19.9 

37,789 

29.9 

37,7H 

4-7 

37-175 

35-6 

84.9 

36,673 

21.3 

36,927 

19.7 

36,252 

i5-i 

35,999 

• • • 35.956 

64.9 

16.7 

. . . 35,936 

64.8 

■ ■-  35,672 

IS- 4 

35,416 

40.3 

. • • 35,254 

311 

34,227 

65.0 

36.8 

34,072 

22.0 

33,998 

6S.0 

...  33,708 

62.1 

46.  1 

8-3 

37-7 

...  33, nr 

— 12.4 

32,722 

7i-9 

• • • 32,637 

44.8 

32,490 

11. 6 

59- 1 

43-o 

159-4 

31,051 

31.6 

...  31.036 

21.9 

17.0 

30,470 

184.1 

. . . 30.346 

3s.6 

• - . 30,345 

J7-3 

. . . 29,655 

95-4 

26.1 

10.9 

38-4 

15- 1 

5-9 

LABORATORY,  MOUNT  PROSPECT,  BROOKLYN, 

Page  33 d. 


34 


QUANTITY  OF  WATER  REQUIRED. 


10.  Approximate  Consumption  of  Water. — In 

American  cities,  having  well  arranged  and  maintained  sys- 
tems of  water  supply,  and  furnishing  good  wholesome 
water  for  domestic  us.e,  and  clear  soft  water  adapted  to  the 
uses  of  the  arts  and  for  mechanical  purposes,  the  average 
consumption  is  found  to  he  approximately  as  follows,  in 
United  States  gallons : 

(a.)  For  ordinary  domestic  use,  not  including  hose  use, 
20  gallons  per  capita  per  day. 

(. b .)  For  private  stables,  including  carnage  washing, 
when  reckoned  on  the  basis  of  inhabitants,  3 gallons  per 
capita  per  day. 

(c.)  For  commercial  and  manufacturing  purposes,  5 to 
15  gallons  per  capita  per  day. 

(i d .)  For  fountains,  drinking  and  ornamental,  3 to  10 
gallons  per  capita  per  day. 

(e.)  For  tire  purposes,  ^ gallon  per  capita  per  day. 

{/.)  For  private  hose,  sprinkling  streets  and  yards, 
10  gallons  per  capita  per  day,  during  the  four  dryest 
months  of  the  year. 

(g. ) Waste  to  prevent  freezing  of  water  in  service-pipes 
and  house-fixtures,  in  Northern  cities,  10  gallons  per  capita 
per  day,  during  the  three  coldest  months  of  the  year. 

(h.)  Waste  by  leakage  of  fixtures  and  pipes,  and  use 
;or  flushing  purposes,  from  5 gallons  per  capita  per  day 
upward. 

The  above  estimates  are  on  the  basis  of  the  total  popu- 
lations of  the  municipalities. 

There  will  be  variations  from  the  above  approximate 
general  average,  with  increased  or  decreased  consumption 
for  each  individual  town  or  city,  according  to  its  social  and 
business  peculiarities. 


WATER  SUPPLIED  TO  ANCIENT  CITIES. 


35 


The  domestic  use  is  greatest  in  the  towns  and  cities,  and 
in  the  portions  of  the  towns  and  cities  having  the  greatest 
wealth  and  refinement,  where  water  is  appreciated  as  a 
luxury  as  well  as  a necessity,  and  this  is  true  of  the  yard 
sprinkling  and  ornamental  fountain  use,  and  the  private 
stable  use. 

The  greatest  drinking-fountain  use,  and  fire  use,  and 
general  waste,  will  ordinarily  be  in  the  most  densely- 
populated  portions,  while  the  commercial  and  manufactur- 
ing use  will  be  in  excess  where  the  steam-engines  are  most 
numerous,  where  the  hydraulic  elevators  and  motors  are,  on 
the  steamer  docks,  and  where  the  brewing  and  chemical 
arts  are  practiced. 

The  ratio  of  length  of  piping  to  the  population  is  greater 
in  wealthy  suburban  towns  than  in  commercial  and  manu- 
facturing towns.  * 

Some  of  these  peculiarities  are  brought  out  in  a follow* 
ing  table  of  the  quantity  of  water  supplied  and  of  piping  in 
several  cities,  which  is  based  upon  the  census  table  hereto- 
fore given  and  upon  various  water-works  reports  for  the 
year  1870. 

The  general  introduction  of  public  water- works,  on  the 
constant- supply  system,  with  liberal  pressures  in  the  mains 
and  house-services,  throughout  the  American  towns  and 
cities,  has  encouraged  its  liberal  use  in  the  households,  so 
that  it  is  believed  that  the  legitimate  and  economical  domes- 
tic use  of  water  is  of  greater  average  in  the  American  cities 
than  in  the  cities  of  any  other  country,  at  the  present  time, 
and  its  general  use  is  steadily  increasing. 

11.  Water  Supplied  to  Ancient  Cities. — The  sup- 
plies to  ancient  Jerusalem,  imperial  Rome,  Byzantium,  and 
Alexandria,  were  formerly  equal  to  three  hundred  gallons 
per  individual  daily  ; and,  later,  the  supplies  to  Nismes, 


36  QUANTITY  OF  WATER  REQUIRED. 

Metz,  ancl  Lyons,  in  France,  and  Lisbon,  Segovia,  and 
Seville,  in  Spain,  were  most  liberal,  but  a small  proportion 
only  of  the  water  supplied  from  these  magnificent  public 
works  was  applied  to  domestic  use,  except  in  tlie  palaces 
of  those  attached  to  the  royal  courts. 

12.  Water  Supplied  to  European  Cities. — In  the 
year  1870,  the  average  daily  supply  to  some  of  the  leading 
European  cities  was  approximately  as  follows : 


CITIES. 


Imp.  Gallons. 


London,  England 
Manchester,  “ 
Sheffield, 

Liverpool,  “ 

Leeds,  “ 

Edinburgh,  Scotland 
Glasgow, 

Paris,  France  . . . 
Marseilles,  “ .... 

Genoa,  Italy 

Geneva,  Switzerland 

Madrid,  Spain 

Berlin,  Prussia 


29 

24 

29 
27 
23 

30 

40 

3° 

40 

3° 

16 

16 

18 


In  the  year  1866,  public  water  supplies  0 were,  in  vol- 
ume, as  follows,  in  the  cities  named  : 


CITIES. 

Population. 

Supply  per  Capita. 

Hamburg,  Prussia 

200,000 

34  gals. 

Altona,  “ 

52,000 

20  “ 

Tours,  France 

42,000 

22  “ 

Angers,  “ 

53;°°° 

1 1 -5  ‘‘ 

Toulouse,  “ ...  

100,000 

I3.-5  “ 

Nantes,  “ 

I 12,000 

13.6  “ 

Lyons,  “ 

300,000 

22  “ 

* Vide  Kirkwood’s  “ Filtration  of  River  Waters.”  Van  Nostrand.  N.  Y..  1869 


WATER  SUPPLIED  TO  AMERICAN  CITIES. 


37 


Prof.  Rankine  gives,*  as  a fair  estimate  of  the  real  daily 
demand  for  water,  per  inhabitant,  amongst  inhabitants  of 
different  habits  as  to  the  quantity  of  water  they  consume, 
the  following,  based  upon  British  water  supply  and  con- 
sumption : 


Rankine’s  Estimate  for  England. 


Imp.  Gallons  per 

Day. 

Least. 

Average. 

Greatest. 

Used  for  domestic  purposes 

Washing  streets,  extinguishing  fires,  sup- 

7 

10 

*5 

plying  fountains,  etc 

3 

3 

3 

Trade  and  manufactures 

7 

7 

7 

Waste  under  careful  regulations,  say.  . . . 

2 

2 

2 i 
z 2 

Total  demand 

l9 

22 

27i 

13.  Water  Supplied  to  American  Cities.— The  lim- 
ited use  of  water  for  domestic  purposes  in  many  of  the 
European  cities  during  the  last  half  century,  led  the  engi- 
neers who  constructed  the  pioneer  water-works  of  some  of 
the  American  States  to  believe  that  30  gallons  of  water  per 
capita  daily  would  be  an  ample  allowance  here ; and  in 
them  day  there  was  scarce  a precedent  to  lead  them  to 
anticipate  the  present  large  consumption  of  water  for  lawn 
and  street  sprinkling  by  hand-liose,  or  for  waste  to  prevent 
freezing  in  our  Northern  cities. 

The  following  tables  will  show  that  this  early  estimated 
demand  for  water  has  been  doubled,  trebled,  and  in  some 
instances  even  quadrupled  ; and  this  considerable  excess, 
to  which  there  are  few  exceptions,  has  been  the  cause  of 
much  annoyance  and  anxiety. 


* “ Civil  Engineering,”  London,  1872,  p.  731. 


38 


QUANTITY  OF  WATER  REQUIRED. 


In  the  year  1870,  the  average  daily  supply  to  some  of 
the  American  cities  was  as  follows,  in  United  States  gallons : 

TABLE  No.  2. 


Water  Supplied  and  Piping  in  Several  Cities,  in  the  year  1870? 


CITIES. 

Popula- 
tion 
in  1870. 

Supply 

per 

Person, 

Daily 

Average 

Supply 

per 

Family, 

Daily 

Average. 

Supply 

per 

Dwelling, 

Daily 

Average. 

Total 

Daily  Supply, 
Average. 

to  « 1 H „• 

<-  \n * 5 

it  h * 

Gallons. 

Gallons. 

Gallons. 

Gallons. 

Miles.  Allies. 

Baltimore .... 

267,354 

52.81 

282.53 

35°-!3 

14,122,032 

214  0.80 

Boston  

250,526 

60.15 

312- 78 

508.87 

15,070,400 

194  0.78 

Brooklyn  .... 

396,099 

47. r6 

233-44 

407.46 

18,682,2 19 

258  0.65 

Buffalo  

58.08 

306.08 

374-°4 

6,838,303 

56  0.48 

Cambridge . . . 

39,634 

43-9° 

220.38 

273-94 

1,739,869 

60  1.64 

Charlestown. . 

28,323 

43-9° 

201.94 

282.72 

1,243,38° 

25  °-9c 

Chicago 

298,977 

62.32 

3I3-47 

417-54 

18,633,000 

240  0.81 

Cincinnati  . . . 

216,239 

40.00 

201.60 

352-40 

10,812,609 

132  0.61 

Cleveland.  . . . 

92,829 

33-24 

i67-53 

184.81 

3,085,559 

5°  °-54 

Detroit 

79,577 

64.24 

236.98 

348.18 

5,!  12,493 

129  1.61 

Hartford 

37, 180 

65.81 

329-71 

365-90 

2,447,000 

48  1.3c 

Jersey  City.  . . 

82,546 

83.66 

414.12 

700.23 

6,906,056 

70  0.85 

Louisville .... 

1 °°,7  53 

28.95 

!5!-99 

iq8.8q 

2,817.300 

58  0.58 

Montreal,  Can. 

117,500 

49.00 

5,720.306 

96  0.81 

Newark.  .... 

105,059 

20.20 

98.17 

147.86 

2,121,842 

52  o-5° 

New  Haven . . 

50,840 

59.00 

286.15 

370-52 

3,000,000 

53  i-°4 

New  Orleans  . 

191,418 

3°-I9 

i47-63 

171.78 

5,779,317 

58  0.30 

New  York  . . . 

942,292 

90.20 

457-31 

i,327-74 

85,000,000 

346  0.37 

Philadelphia  . 

674,022 

S5-11 

290.98 

33I-2I 

37,!45,385 

488  071 

Salem 

24,117 

41.46 

1 ,000,000 

35  !°4 

St.  Louis  .... 

310,864 

35-38 

185.04 

277-38 

1 1,000,000 

105  0.34 

Washington  . . 

1 09, 1 99 

127.00 

650.24 

7°9-93 

13,868,273 

102  O.93 

Worcester.  . . . 

41,105 

48.65 

230.60 

406.23 

2,000,000 

45  1 °9 

The  average  quantity  of  water  supplied  to  some  of  the 
same  cities  in  1874  is  indicated  in  the  following  table,  show- 
ing also  the  extensions  of  the  pipe  systems,  and  the  increase 
in  the  average  daily  consumption  of  water  per  capita,  from 
year  to  year : 

~N 


* See  also  statistics  on  pages  625-627. 


INCREASE  IN  VARIOUS  CITIES. 


39 


TABLE  No.  3. 


Water  Supplied  in  Years  1870- and  1874. 


CITIES 

Average 
Daily  Supply 
per  Capita. 

Total  Average  Daily  Supply. 

Total 

Miles  of  Pipes 

1870. 

1874. 

1870. 

1874. 

187O. 

1S74. 

Boston 

60 

60 

I5)°7°>400 

18,000,000 

194 

262 

Brooklyn 

47 

58 

18,682,219 

24,772,467 

258 

323 

Buffalo  

58 

60 

6,838,303 

8,509,481 

56 

87 

Cambridge 

44 

54 

L739>869 

2,300,000 

60 

76 

Charlestown  . . . 

44 

62 

1,243.380 

7,643,OI7 

25 

132 

Chicago 

64 

84 

18,633,000 

38,090,952 

240 

386 

Cincinnati 

40 

45 

10,812,609 

!3, 600, 596 

132 

x56 

Cleveland 

32 

45 

3,085,559 

5,625,150 

5° 

81 

Detroit 

64 

87 

5,1 12,493 

9,OI3,35° 

129 

*77 

Jersey  City 

84 

86 

6,906,056 

10,42 1,001 

70 

III 

Louisville 

29 

24 

2,817,300 

3,598,730 

58 

91 

Newark.  . 

20 

38 

2,12 1,842 

4,732,7x8 

52 

I 12 

Philadelphia  . . . 

55 

58 

37,i45,385 

42,111,730 

488 

625 

Salem 

41 

55 

1,000,000 

1,380,000 

35 

40 

Washington  .... 

I27 

138 

13,868,273 

18,000,000 

102 

141 

Worcester 

49 

80 

2,000,000 

3,000,000 

45 

63 

Montreal 

49 

66 

5,720,306 

8,395,8io 

96 

114 

14.  The  Use  of  Water  Steadily  Increasing-. — The 
legitimate  use  of  water  is  steadily  being  popularized,  calling 
for  an  increased  average  in  the  amount  of  household  appa- 
ratus, increased  facilities  for  garden  irrigation  and  jets 
d'eau,  increased  street  areas  moistened  in  dusty  seasons, 
and  increased  appliances  for  its  mechanical  use ; from  all 
which  follows  increased  waste  of  water. 

15.  Increase  in  Various  Cities. — The  following  table 
is  introduced  to  show  the  average  daily  supply  in  various 
cities  through  a succession  of  years : 


40 


QUANTITY  OF  WATER  REQUIRED. 


TABLE  No.  4. 

Average  Gallons  Water  Supplied  to  Each  Inhabitant  Daily  in 


YEAR. 

Boston. 

Buffalo. 

Brooklyn. 

Cleveland. 

Cincinnati. 

Chicago. 

Detroit. 

Jersey  City. 

Louisville. 

Montreal. 

New  York. 

Philadelphia. 

Washington. 

i8 

8 

55 

/ 

1858 

— 

— 

— 

8 

33 

4U 

46 

75 

— 

— 

— 

— 

— 

i859 

— 

— 

— 

11 



40 

48 

— 

— 

— 

— 

— 

— 

i860  .... 

— 

— 

— 

14 

— 

43 

52 

77 

— 

— 

— 

— 

— 

1861 

— 

— 

— 

16 

— 

43 

53 

— 

9 

— 

— 

— 

— 

1862 

— 

— 

*7 

J9 

39 

44 

58 

— 

14 

— 

— 

— 

— 

1863 

— 

— 

22 

2 I 

— 

43 

58 

— 

12 

— 

— 

— 

— 

1864 

— 

26 

22 

— 

4i 

57 

— 

14 

— 

62 

— 

— 

1865 

— 

— 

29 

22 

— 

42 

55 

77 

17 

— 

— 

— 

— 

1866 

55 

— 

33 

22 

— 

43 

60 



17 

— 

— 

— 

— 

1867 

59 

— 

36 

24 

— 

5° 

64 

— 

15 

— 

62 

46 

— 

1868 

62 

— 

43 

25 

— 

58 

67 

— 

l6 

— 

68 

51 

— 

1869 

62 

— 

46 

27 

— 

62 

61 

— 

18 

— 

84 

51 

— 

1870 

60 

58 

47 

33 

40 

63 

64 

84 

29 

49 

90 

55 

127 

187 1 ....  . 

54 

51 

46 

36 

— 

73 

73 

— 

W 

55 

85 

55 

!30 

1872 

55 

6l 

50 

40 

60 

75 

83 

99 

22 

55 

88 

54 

134 

i873 

58 

60 

55 

43 

— 

75 

90 

— 

22 

60 

104 

56 

138 

1874. .... 

60 

60 

58 

45 

45 

84 

87 

86 

24 

66 

— 

58 

U3S 

1882 

99 

106 

55 

65 

76 

114 

149 

124 

52 

66 

79 

66 

176 

1890 

io5 

186 

— 

106 

114 

138 

161 

1 18 

69 

66 

— 

131 

!58 

16.  Relation  of  Supply  per  Capita  to  Total  Pop- 
ulation.— In  the  larger  cities  there  are  generally  the  great- 
est variety  of  purposes  for  which  water  is  required,  and 
consequently  a greater  average  daily  consumption  per  cap- 
ita. Exceptions  to  this  general  rule  may  be  found  in  a few 
suburban  towns  largely  engaged  in  the  growth  of  garden 
truck,  and  plants,  and  shrubs  for  the  urban  markets,  in 
which  there  is  a large  demand  for  water  for  purposes  of 
irrigation. 

In  the  New  England  towns  and  cities  the  average  daily 
consumption  and  waste  of  water  according  to  population  is 
approximately  as  follows : 


MONTHLY  AND  HOURLY  VARIATIONS. 


41 


Places  of  10,000  population,  35  to  45  gallons  per  capita. 

“ “ 20,000  “ 40  to  50  “ “ “ 

“ “ 30,000  “ 45  to  65  “ “ “ 

“ “ 50,000  “ 55  to  75  “ “ “ 

Places  of  75,000  population  and  upward,  60  to  100  gal- 
lons per  capita. 

17.  Monthly  and  Hourly  Variations  in  the  Draught. 

--The  data  heretofore  given  relating  to  the  daily  average 
consumption  of  water  have  referred  to  annual  quantities 
reduced  to  their  daily  average.  The  daily  draught  is  not, 
however,  uniform  throughout  the  year,  but  at  times  is 
greatly  in  excess  of  the  average  for  the  year,  and  at  other 
times  falls  below. 

It  may  be  twenty  to  thirty  per  cent,  in  excess  during 
several  consecutive  weeks,  fifty  jjer  cent,  during  several 
consecutive  days,  and  not  infrequently  one  hundred  per 
cent,  in  excess  during  several  consecutive  hours,  independ- 
ently of  the  occasional  heavy  drafts  for  fires.  Diagrams  of 
this  daily  consumption  of  water  in  the  cities  usually  show 
two  principal  maxima  and  two  principal  minima.  The 
earliest  maximum  in  the  year  occurs,  in  the  Eastern  and 
Middle  States,  about  the  time  the  frost  is  deepest  in  the 
ground  and  the  weather  is  coldest,  that  is,  between  the 
middle  of  January  and  the  first  of  March,  and  in  New 
ngland  cities  this  period  sometimes  gives  the  maximum  of 
the  year.  The  second  maximum  occurs  usually  during  the 
hottest  and  dryest  portion  of  the  year,  or  between  the  mid- 
dle of  July  and  the  first  of  September.  The  two  principal 
minima  occur  in  the  spring  and  autumn,  about  midway 
between  the  maxima.  Between  these  four  periods  the  pro- 
file shows  irregular  wavy  lines,  and  a profile  diagram 
continued  for  a series  of  years  shows  a very  jagged  line. 

To  illustrate  the  irregular  consumption  of  water,  we 


Fig.  1. 


Chicago.  Brooklyn.  Cincinnati.  Montrea. 


•S33UI3AB  A[l|}UOJ^  'Uiaip  J3(i  SUO[[Lo  UOI[|lOi  JO  'OfJ 


MONTHLY  DIAGRAM  Ol''  WATER  SUPPLIED  TO  CHICAGO,  BROOKLYN,  CINCINNATI,  AND  MONTREAL. 

IN  YEARS  1871,  187a,  1873,  AND  187a. 


RATIO  OF  MONTHLY  CONSUMPTION. 


48 


have  prepared  the  diagrams,  Fig.  1,  of  the  operations  of  the 
pumps  at  Chicago,  Brooklyn,  Cincinnati,  and  Montreal, 
during  the  years  1871,  1872,  1873,  and  1874. 

18.  Ratio  of  Monthly  Consumption. — The  varia- 
tions in  draught,  as  by  monthly  classification,  in  several 
prominent  cities,  in  the  year  1874,  have  been  reduced  tr 
ratios  of  mean  monthly  draughts  for  convenience  of  compar- 
ison, and  are  here  presented  ; unity  representing  the  mean 
monthly  draught  for  the  year : 


TABLE  No.  5. 


Ratios  of  Monthly  Consumption  of  Water  in  1874. 


CITIES. 

C 

■—» 

Feb. 

March. 

April. 

May. 

June. 

July. 

Aug. 

Sept. 

0 

O 

Nov. 

Dec. 

Rrooklyn 

1.029 

1. 132 

.971 

.892 

.941 

I 008 

1.069 

1-034 

I.044 

.987 

■9I9 

■974 

3uffalo. 

1.008 

1.007 

.960 

.941 

•983 

■963 

.996 

1.020 

I.044 

i. on 

1.040 

I.OOG 

Cleveland. . . 

.883 

.901 

.850 

.871 

.992 

I 180 

1.181 

1.206 

I 058 

1. 001 

.942 

■915 

Detroit 

.856 

.807 

■905 

.844 

1.029 

1.065^ 

I. 051 

1.167 

I-I7I 

1.115 

.987 

1.003 

Philadelphia. 

.850 

.844 

•834 

.898 

I.056 

I-I99 

1.289 

1-145 

I. O9I 

-990 

.952 

.853 

Chicago  .... 

.862 

.844 

.904 

.904 

.942 

.942 

I.I7I 

1-193 

1.162 

I.03Q 

.966 

I.O29 

Cincinnati.. . 

.792 

.762 

.778 

.856 

I. on 

1. 217 

I.207 

L257 

I.302 

1.058 

.q6o 

•799 

Louisville.  . . 

.842 

.819 

.848 

.841 

.960 

1. 192 

I.207 

1.223 

1.202 

1.138 

•V40 

.876 

Montreal 

.864 

•959 

943 

I.025 

.9x6 

•9°7 

I.IOI 

1.151 

1.096 

1-043 

.971 

1.023 

Mean. . . 

.887 

.897 

.888 

.897 

.960 

1075 

1.144 

I-I55 

1. 130 

1.042 

.964 

.941 

There  is  also  a very  perceptible  daily  variation  in  each 
week,  and  hourly  variation  in  each  day,  in  the  domestic 
consumption  of  water. 

The  Brooklyn  diagram  shows  that  the  average  draught 
in  the  month  of  maximum  consumption  was  in  1872,  fifteen 
per  cent,  in  excess  of  the  average  annual  draught ; in  1873, 
seventeen  per  cent,  in  excess  ; in  1874,  thirteen  per  cent,  in 
excess. 

A Boston  Highlands  direct  pumping  diagram  lying  be- 
fore the  writer  shows  that  the  average  draught  at  nine 
o’clock  in  the  forenoon  was  thirty-seven  per  cent,  in  excess 


44 


QUANTITY  OF  WATER  REQUIRED. 


of  the  average  draught  for  the  three  months,  and  that  at 
eight  o’clock  a.m.  on  the  Mondays  the  draught  was  sixty 
per  cent,  in  excess  of  the  average  hourly  draught  for  the 
three  months. 

The  maximum  hourly  draught  indicated  hy  the  two 
diagrams  taken  together  is  nearly  seventy-five  per  cent,  in 
excess  of  the  average  throughout  the  year. 

19.  Illustrations  of  Varying-  Consumption.  — In 
illustration,  we  will  assume  a case  of  a suburban  town  re- 
quiring, say,  an  average  daily  consumption  for  the  year  of 
1,000,000  United  States  gallons  of  water,  and  compute  the 
maximum  rate  of  draught  on  the  bases  shown  by  the  above- 
named  diagrams,  thus : 


Gallons 
per  Day. 

Gallons 
per  Min. 

Cubic  Feet 
per  Min. 

Average  draught  per  year 

Add  17  per  cent,  for  max.  monthly  average 

1,000,000 

694.4 

92.8 

draught,  making 

Add  to  the  last  quantity  io  per  cent,  for  the 

1,170,000 

812.5 

108.6 

max.  weekly  average  draught,  making. .... 
Add  to  the  last  quantity  37  per  cent,  for  the 

1,270,000 

881.9 

II7.9 

max.  hourly  average  draught,  making  

Add  to  the  last  Quantity  23  per  cent,  for  the 

1,640,000 

1,138.9 

152.3 

max.  hourly  av.  draught  on  Mondays,  making 

1,870,000 

1,300.0 

250.0 

The  experience  of  nearly  every  water-supply  shows  that 
the  maximum  draught,  aside  from  fire-service,  is  at  time* 
more  than  double  the  average  draught. 

20.  Reserve  for  Fire  Extinguishment. — In  addi- 
tion to  the  above,  there  should  be  an  ample  reserve  of  water 
for  fire  service,  and  extra  conduit  and  distribution  capacity 
for  its  delivery.  There  is  a possibility  of  two  or  three  fires 
being  in  progress  at  the  same  time,  in  even  the  smaller 
cities,  requiring  nine  to  twelve  hydrant  streams,  or  say  3 DC' 
cubic  feet  of  water  per  minute,  for  each  fire. 


QUANTITY  OF  WATER  REQUIRED 


44a 


TABLE  No.  5a. 

Financial  and  Water  Pipe  Statistics. 

Compiled  from  Tables  in  the  “Journal  of  the  New  England  Water 
Works  Association,”  September , Charles  IV.  Sherman , Editor. 


Name  of  Town 


e -3 


Essex  Junction,  Vt. . 

Leicester,  Mass. 

Billerica,  Mass 

Nantucket,  Mass 

Ipswich,  Mass 

Oberlin,  Ohio. ....... 

Reading,  Mass 

Winchendon,  Mass  . . 
Wellesley,  Mass...... 

Whitman,  Mass...... 

Andover,  Mass 

Middleboro,  Mass 

Ware,  Mass.. 

Arlington,  Mass 

Keene,  N.  H... 

Plymouth,  Mass 

Watertown.  Mass 

Geneva,  N.  Y .... 

Attleboro,  Mass 

Leominster,  Mass 

Marlboro,  Mass 

Woburn,  Mass 

New  London,  Ct 

Burlington,  Vt.. . . . . . 

Madison,  Wis. ....... 

Concord,  N.  H 

Waltham,  Mass 

Lewiston,  Me ... 

Quincy,  Mass 

Atlantic  City,  N.J — 

Bay  City,  Mich 

Taunton,  Mass 

Fitchburg,  Mass 

Schenectady,  N.  Y.. 
Woonsocket.  R.  I — 

Newton,  Mass 

Chelsea,  Mass 

Salem,  Mass 

Haverhill,  Mass ■ 

Brockton,  Mass 1 

Holyoke,  Mass 

Yonkers,  N.  Y 

Erie,  Penn 

Manchester,  N.  H 

Springfield,  Mass 

New  Bedford,  Mass — 

Somerville,  Mass 

Lynn,  Mass 

Wilmington,  Del  

Cambridge,  Mass 

Albany,  N.  Y. 

Lowell,  Mass 

Fall  River,  Mass 

Worcester,  Mass. 

Providence,  R.  I. 

Minneapolis,  Minn. 

Boston,  Mass 

Metrop’n  W.  W.,  Mass. 


I, 125 

1*398 

2,780 

3,002 

4*658 

4,800 

4*969 

5,001 

5,o72 

6,172 

6,813 

6,qoo 

8,263 

8,603 

9*3°° 

9*592 

9,706 

II, 000 
ii*335 
12,392 
13*609 

14*254 
17*500 
. 18,800 
19,164 
i9,632 
23*700 

23*76 

23,896 

28,000 

28.000 
31,006 
3I*53I 

32.000 

32.500 
33.587 

34.000 

35,956 

37,17s 

40,063 

46,204 

47*93! 

52*733 

56,987 

62,059 

62.500 

62.500 
73*6oo 

76.500 
91,886 
94*i5i 

95.000 
107,623 
118,421 
187,297 
202,718 
560,892 
815,400 


$38,500.00 

81.002.87 

91.705.87 


86,381.42 

265,462.18 

111,553.03 

322,718.24 

129,632.93 

208,624.48 

116,420.15 

131,090.08 


313,189.09 

309,169.56 

181.628.73 
374,488.18 
5I9,2I5-43 

586.261.13 
597,049.1:4 
706,978.44 

468.039.73 

337.360.13 
857,440.98 
614,000.00 


a ^ 

"<U 


916,723.59 

598,082.21 

1,243,185.49 

452,091,09 


390,841.78 

2,034,808.07 

483*335-52 

1,917,590.39 

i,3°o,I42.54 

913,211.06 

1,244,742.23 

I*577*I°5*I5 


$1,655.00 

7,430.04 

5,984.90 


1,513,012.79 

2,128,559.56 

1,820,107.73 

766,484,63 

2,472,821.85 


5,670,229.52 


9*244.19 

15,620.19 

7,772.81 

19*835-50 

9*930.30 


16,323.62 

10,859.39 

43*835-45 

30,599.72 

22,568.53 

29,156.06 

18,980.89 

27,424.41 


40,076.60 

44,201.44 

63.933-89 

51,008.15 


70,2(37.09 


1,937,862.93 

6,470,093.35 

23,054,387.81 


123,246.45 

46,746.25 

69,ji5-97 

73,014.91 


* >• 


$5,460.51 

5,606.56 


4,368.88 

15*153-99 

5,861.37 

17,288.52 

8,017.75 


7,758.5t 

7,875-99 


5,144.61 

14.727.72 


22,421.83 

14,857-55 


23,970.04 

36,200.82 


37,129.19 

54,258.18 

36,740.69 


9 

7 

14 
9 

26 

15 

30 
*7 

25 

17 

11 

33 
35 
37 

34 

27 

31 
46 
37 


50 
38 
34 
60 

51 


85,932.11  -30,130.59 

114,624.42 

88,340.61  26,799.41 


77,381.92 

182,767.79 

147*944.93 


138,241.94 

274*954-75 

237*484-59 


208,823.03 


180,333.44 

263,208.41 


48,370.06 

45,999.29 

124,529.67 


116,014.24 

127,000.92 


i36*5I4-°I 


132,937-39 

149,820.47 

194,087.06 


84 

47 

45 

78 

66 

4° 

45 

136 

37 


64 

8 

74 

10 

3 

14 

9 


12 

10 


129.5 
127.  £ 

87.3 

173-3 
330- 5 
269.2 
7I3-‘= 
1430.] 


Number  of 
Service  Taps 

Number  of 
Fire  Hydrants 

96 

27 

3°5 

205 

101 

929 

50 

647 

137 

625 

87 

1*057 

140 

388 

121 

878 

270 

988 

*5r 

876 

196 

820 

120 

727 

114 

i*57o 

326 

1*725 

215 

1,894 

132 

1,583 

337 

1,679 

207 

263 

326 

2,181 

343 

2,896 

352 

3,088 

258 

3*350 

213 

2,758 

169 

3*340 

267 

3,285 

33i 

173 

4*330 

539 

4*249 

5I9 

2,201 

413 

4*502 

783 

4*432 

499 

469 

2,193 

548 

7,087 

935 

6,146 

253 

5*319 

322 

5,275 

608 

3-6i° 

860 

4,968 

771 

1,154 

595 

5*513 

343 

9,764 

955 

9,280 

738 

10,291 

897 

13*504 

952 

765 

14,207 

968 

808 

10,634 

1,098 

6.943 

954 

13,292 

1,763 

21,566 

1,978 

20,064 

3*!72 

87,525 

7,606 

134,496 

11*913 

446 


QUANTITY  OF  WATER  REQUIRED 


TABLE  No.  S b . 


Water  Supply  Consumption  Statistics. 

Compiled  from  Tables  in  the  “Journal  of  the  New  England  Water 
Works  Association,”  September,  igoi,  Charles  W.  Sherman,  Editor. 


Name  of  Town 


Leicester,  Mass 

Billerica,  Mass 

Nantucket,  Mass 

Ipswich,  Mass 

Oberlin,  Ohio 

Reading,  Mass 

Winchendon,  Mass 

Wellesley,  Mass 

Whitman,  Mass 

Andover,  Mass 

Middleboro,  Mass 

Ware,  Mass 

Arlington,  Mass 

Keene,  N.  H 

Plymouth,  Mass 

Attleboro,  Mass 

Marlboro,  Mass 

Woburn,  Mass 

New  London,  Conn 

Burlington,  Vt 

Madison,  Wis 

Waltham,  Mass 

Lewiston,  Me 

Nashua,  N.  H 

Atlantic  City,  N.  J 

Bay  City,  Mich 

Taunton,  Mass 

Fitchburg,  Mass 

Schenectady,  N.  Y 

Woonsocket,  R.  I 

Newton,  Mass 

Chelsea,  Mass 

Salem,  Mass 

Haverhill,  Mass 

Brockton,  Mass 

Holyoke,  Mass 

Yonkers,  N.  Y 

Erie,  Penn 

Springfield,  Mass 

New  Bedford,  Mass 

Lynn,  Mass 

Wilmington,  Del 

Cambridge,  Mass 

Albany,  N.  Y 

Lowell,  Mass 

Fall  River,  Mass 

Worcester,  Mass 

Providence,  R.  I 

Minneapolis,  Minn 

Metropolitan  W.  W.,  Mass. 


1.398 

2,780 

3,002 

4.658 

4,800 
4,969 
5, 001 
5.072 
6,172 
6,813 
6,900 
8,263 
8,603 
9,300 
9.592 
H.335 
13,609 

14,254 

17.500 
18,800 
19,164 
23,700 

23.761 

25.000 

28.000 

28.000 
31,006 
3i,53i 

32.000 

32.500 

33-587 

34.000 

35,956 

37,175 

40,063 
46,204 
47, 931 
52,733 
62,059 

62.500 
73,600 

76.500 
91,886 
94,i5i 

95.000 
107,623 
118,421 
187,297 
202,718 
815,4^ 


a 

a 

u 

<u 

> 

< 


c 

jO 

O 

*aj 

o 


•a 

<D 

6 

3 

c 

o 

U 


82,230 

56,139 

125,233 
109,164 
100,000 
148,631 
57,835 
238,884 
I33,3l8 
407,172 
232.964 
294,471 
297,400 
1,395,000 
407,172 
452,532 
942,936 
1, 1 16,811 
1,585,770 
857,250 

837,332 

2,117,863 

3,990,041 

3,832,704 


3,129,697 

1,619,985 

2,800,000 


933,244 

2,086,374 

3,000,000 

2.577.000 
2,268,868 
1,165,376 

4.750.000 
3,626,564 
8,560,111 

5,47i,5oo 

6,320,542 

4,679,871 


7,263,773 

18.099.000 
7,892,356 
3,804,867 
7,9I9,45S 

10,131,489 

l8,803,IIO 

94.205.000 


Gallons  per 
Inhabitant 
Daily 

Gallons  per 
Consumer 
Daily 

Gallons 
per  Tap 
Daily 

Percentage 
of  Water 
Metered 

59 

46 

52 

20 

42 

23 

21 

30 

12 

47 

22 

60 

34 

36 

i34 

36 

35 

28 

48 

160 

141 

154 

270 

43 

47 

53 

62 

284 

48 

56 

634 

808 

150 

43 
39 
36 

80 

9i 

46 

44 
90 

174 

45 

42 

IC 

100 

47 

51 

92 

514 

256 

304 

644 

53 

5 

153 

737 

1,425 

359 

112 

53 

196 

62 

103 

166 

29 

64 

87 

21 

37 

28 
62 

87 

72 

61 

29 

103 

76 

162 

88 
101 

397 

294 

488 

55 

12 

33 

105 

221 

1,321 

5i 

14 

48 

114 

115 
65 

560 

681 

21 

23 

20 

40 

90 

79 

191 

83 

35 

36 

70 

54 

198 

52 

60 

19 

54 

93 

116 

470 

PUMPING  STATION,  MILWAUKEE 


CHAPTER  III. 


RAINFALL. 

21.  The  Yapory  Elements. — The  elements  ot  water 
fill  the  ethereal  blue  above  and  the  eartli  crust  beneath. 
They,  with  unceasing  activity,  permeate  the  ah',  the  rocks, 
the  sand,  the  fruits  we  eat,  and  the  muscles  that  aid  our 
motion. 

Since  first  “there  went  up  a mist  from  the  earth,”  the 
struggle  between  the  ethereal  elements  and  earth’s  internal 
fire,  between  the  intense  cold  of  space  and  direct  and 
radiated  heat  enveloping  the  face  of  the  earth,  has  gone 
on  unceasingly. 

22.  The  Liquid  and  Gaseous  Successions. — If  we 
hold  a drop  of  water  in  the  clear  sunshine  and  watch  it 
intently,  soon  it  is  gone  and  we  could  not  see  it  depart ; if 
we  expose  a dish  of  water  to  the  heat  of  fire,  silently  it 
disappears,  and  we  know  not  how  it  gathered  in  its  activity ; 
if  we  leave  a tank  of  water  uncovered  to  the  sun  and  wind, 
it  gradually  disappears,  and  is  replenished  by  many  showers 
of  summer,  still  it  departs  and  is  replenished  by  snows  of 
winter.  Under  certain  extreme  conditions  it  may  never  be 
full,  it  may  never  be  exhausted,  the  rising  vapor  may  equal 
the  falling  liquid,  as  where  “ the  rivers  flow  into  the  sea,  yet 
the  sea  is  not  full.” 

23.  The  Source  of  Showers.— Physical'  laws  whose 
origin  we  cannot  comprehend  but  whose  steady  effects  we 
observe,  lift  from  the  saline  ocean,  the  fouled  river,  the  moist 
earth,  a stream  of  vapor  broad  as  the  circuit  of  the  globe, 


46 


RAINFALL. 


but  their  solid  impurities  remain,  arrd  the  flow  goes  up  t*dth 
ethereal  clearness. 

From  hence  are  the  sources  of  water  supply  replenished. 
From  hence  comes  the  showers  upon  the  face  of  the  earth. 

24.  General  Rainfall. — But  there  is  irregularity  in 
the  physical  features  of  the  earth,  and  unevenness  in  the 
temperature  about  it,  and  the  showers  are  not  called  down 
alike  upon  all  its  surface.  Upon  the  temperate  zone  in 
America  enough  water  falls  in  the  form  of  rain  and  snow 
to  cover  the  surface  of  the  ground  to  an  average  depth  of 
about  40  inches,  in  the  frigid  zone  a lesser  quantity,  and  in 
the  torrid  zone  full  90  inches,  and  in  certain  localities  to 
depths  of  100  and  150,  and  at  times  to  even  200  inches. 

We  recognize  in  the  rain  an  ultimate  source  of  water 
supply,  but  the  immediate  sources  of  local  domestic  water 
supply  are,  shallow  or  deep  wells , springs,  lakes , and  r iters. 
The  amplitude  of  their  supply  is  dependent  upon  the  avail- 
able amount  of  the  rainfall  that  replenishes  them.  In 
cases  of  large  rivers,  and  lakes  like  the  American  inland 
seas,  there  can  be  no  question  as  to  their  answering  all 
demands,  as  respects  quantity,  that  can  be  made  upon  them, 
but  often  upon  watersheds  of  limited  extent,  margins  of 
doubt  demand  special  investigations  of  their  volumes  of 
rainfall,  and  the  portions  of  them  that  can  be  utilized. 

25.  Review  of  Rainfall  Statistics. — Looking  broadly 
over  some  of  the  principal  river  valleys  of  the  United  States 
we  find  their  average  annual  rainfalls  to  be  approxi- 
mately as  follows : Penobscot,  45  inches  ; Merrimack.  43 ; 
Connecticut,  44 ; Hudson,  39  ; Susquehanna,  37 ; Eoanoke, 
40 ; Savannah,  48 ; Appalachicola,  48 ; Mobile,  60 ; Mis- 
sissippi, 46  ; Rio  Grande,  19  ; Arizonian  Colorado,  12  ; Sac- 
ramento, 28  ; and  Columbia,  33  inches  ; but  the  amount 
of  rainfall  at  the  various  points  from  source  to  mouth  of 


WESTERN  RAIN  SYSTEM. 


47 


each  river  is  by  no  means  uniform  ; as,  for  instance,  upon 
the  Susquehanna  it  ranges  from  26  to  44  inches ; on  the 
Rio  Grande,  from  8 to  87  inches  ; and  on  the  Columbia, 
from  12  to  86  inches. 

26.  Climatic  Effects. — The  North  American  Continent 
presents,  in  consequence  of  its  varied  features  and  reach 
from  near  extreme  torrid  to  extreme  polar  regions,  almost 
all  the  special  rainfall  characteristics  to  be  found  upon  the 
face  of  the  globe ; and  even  the  United  States  of  America 
includes  within  its  limits  the  most  varied  classes  of  climato- 
logical and  meteorological  effects,  in  consequence  of  its  range 
of  elevation,  from  the  Florida  Keys  to  the  Rocky  Mountain 
summits,  and  its  range  of  humidity  from  the  sage-bush 
plains  between  the  Sierras  and  Wahsatch  Mountains,  and 
the  moist  atmosphere  of  the  lower  Mississippi  valley,  and 
from  the  rainless  Yuma  and  Gila  deserts  of  southern  Cali- 
fornia to  the  rainy  slopes  of  north-western  California  and  of 
Oregon,  where  almost  daily  showers  maintain  eternal  verdure. 

27.  Sections  of  Maximum  Rainfall — The  maxi- 
mum recorded  rainfall,  an  annual  mean  of  86  inches,  occurs 
in  the  region  bordering  upon  the  mouth  of  the  Columbia 
River  and  Puget  Sound.  A narrow  belt  of  excessive  hu- 
midity extends  along  the  Pacific  coast  from  Vancouver's 
Island  southerly  past  the  borders  of  W ashington  Territory, 
Oregon  and  California,  to  latitude  40°. 

Next  in  order  of  humidity  is  the  region  bordering  upon 
the  Delta  of  the  Mississippi  River  and  the  embouchure  of 
the  Mobile,  whose  annual  mean  of  rain  reaches  64  inches. 

Next  in  order  is  a section  in  the  heart  of  Florida  of 
about  one-lialf  the  breadth  of  the  State,  whose  mean  annual 
rain  reaches  60  inches. 

28.  Western  Rain  System. — The  great  northerly 
ocean  current  of  the  Pacific  moves  up  past  the  coast  of 


48 


RAINFALL. 


China  and  the  Aleutian  Islands  and  impinges  upon  the 
North  American  shore,  then  sweeps  down  along  the  coast 
of  Washington  Territory,  Oregon  and  California  ; and  from 
its  saturated  atmosphere,  flowing  up  their  bold  western 
slopes,  is  drawn  the  excessive  aqueous  precipitations  that 
water  these  regions. 

Their  moist  winds  temper  the  climate  and  their  condensed 
vapors  irrigate  the  land,  so  that  the  southerly  portion  of  the 
favored  region  referred  to  is  often  termed  the  garden  of 
America. 

Fig.  2 is  a profile,  showing  a general  contour  across  the 
North  American  Continent,  along  the  thirty-ninth  parallel 
of  latitude. 


A.  Pacific  Ocean.  a.  Sacramento  City 82 

B.  Coast  Range.  b.  Carson  City 4,629 

C.  Sierra  Nevada.  c.  Salt  Lake  Region 4,382 

D.  Wahsatch  Mountains.  d.  Colorado  River — 

' E.  Rocky  Mountains.  e.  Colorado  City 6,000 

F.  Mississippi  River.  f.  St.  Louis 481 

G.  Alleghanjr  Mountains.  g.  Cincinnati 582 

H.  Blue  Ridge.  h.  Washington 70 

I.  Atlantic  Ocean. 


The  California  coast  range  and  the  western  slope  of  the 
Sierra  Nevadas  are  the  condensers  that  gather  from  the 
prevailing  westerly  ocean  breezes  their  moisture.  From 
thence  the  winds  pass  easterly  over  the  Sierra  summit 
almost  entirely  deprived  of  moisture,  and  yield  but  rarely 
any  rain  upon  the  broad  interior  basin  stretching  between 
the  bases  of  the  Sierra  and  Wahsatch  Mountains.  Upon  the 


CENTRAL  RAIN  SYSTEM 


49 


arid  plains  of  this  region,  above  the  Gulf  of  California, 
whose  average  annual  rainfall  reaches  scarce  4 inches,  the 
winds  roll  down  like  a thirsty  sponge. 

Further  to  the  east,  the  western  slopes  of  the  Walisatch 
and  Rocky  Mountains  lift  up  and  condense  again  the  west- 
ern winds,  and  gather  in  their  storms  of  rain  and  snow. 
In  the  lesser  valley  between  these  mountains,  12  to  20 
inches  of  rain  falls  annually,  and  the  tributaries  of  the 
Colorado  River  gathers  its  scanty  surplus  of  waters  and 
leads  them  from  thence  around  the  southerly  end  of  the 
Wahsatch  Mountains  past  the  Yuma  Desert  to  the  Gulf. 

Over  the  summit  of  the  Rocky  Mountains  onward  moves 
the  westerly  wind,  again  deprived  of  its  vapor,  and  down 
it  rolls  with  thirsty  swoop  upon  those  broad  arid  regions, 
skirting  the  eastern  base  of  the  mountains.  Farther  on,  it 
is  again  charged  with  moisture  by  the  saturated  wind-eddy 
from  the  Caribbean  Sea  and  Gulf  of  Mexico. 

The  great  Pacific  currents  of  water  and  wind,  and  the 
extended  ridges  and  furrows  of  the  westerly  half  of  our 
Continent  lend  their  combined  influence,  in  a marked  man- 
ner, to  develop  its  special  local  and  its  peculiar  general 
climatic  and  meteorological  systems. 

29.  Central  Rain  System. — A second  system  of  anti- 
trade winds  bears  the  saturated  atmosphere  of  the  Gulf  of 
Mexico  up  along  the  great  plain 'of  the  Mississippi.  Its 
moisture  is  precipitated  in  greatest  abundance  about  the 
delta,  and  more  sparingly  in  the  more  elevated  vaileys  of 
the  Red  and  Arkansas  rivers  upon  the  left,  and  the  Tennes- 
see and  Ohio  rivers  upon  the  right.  Its  influence  is  per- 
ceptible along  the  plain  from  the  Gulf  to  the  southern  bor- 
der of  Lake  Michigan,  and  easterly  along  the  lower  lakes 
and  across  Yew  England,  where  the  chills  of  the  Arctic 
polar  current  sweeping  through  the  Gulf  of  St.  Lawrence 
4 


50 


RAINFALL. 


and  down  tlie  Nova  Scotia  coast  into  Massachusetts  Bay, 
throws  down  abundantly  its  remaining  moisture. 

30.  Eastern  Coast  System.  — A third  system  en- 
velops Florida,  Georgia,  and  the  eastern  Carolinas,  espe- 
cially in  summer,  with  an  abundance  of  rain. 

A fourth  subordinate  system  shows  the  contending 
thermic  and  electric  influences  of  the  warm  and  moist 
atmosphere  from  the  Gulf  Stream,  flowing  northerly  past, 
and  of  the  cooler  atmosphere  from  the  polar  current  flowing 
Southerly  upon  the  New  England  coast,  where  an  abundant 
rain  is  distributed  more  evenly  throughout  the  seasons  than 
elsewhere  upon  the  Continent. 

31.  Influence  of  Elevation  upon  Precipitation. — 

The  influence  of  elevation  above  the  sea-level  is  far  less 
active  in  producing  excessive  rain  upon  our  mountain 
ranges  and  high  river  sources  than  upon  other  continents 
and  some  of  the  mountainous  islands,  being  quite  subordi- 
nate to  general  wind  currents. 

Upon  the  mountainous  island  of  Guadaloupe,  in  latitude 
16°,  for  instance,  a rainfall  of  292  inches  per  annum  at  an 
elevation  of  4500  feet  is  recorded. 

Upon  the  Western  Ghauts  of  Bombay,  at  an  elevation 
of  4,500  feet,  an  average  rainfall  for  fifteen  years  is  given  as 
254  inches. 

On  the  southerly  slope  of  the  Himalayas,  northerly  of 
the  Bay  of  Bengal,  at  au  elevation  of  4,500  feet,  the  rainfall 
of  1851  was  610  inches.  These  localities  all  face  prevailing 
saturated  wind  currents. 

33.  River-basin  Rains. — A study  of  some  of  our 
principal  river  valleys  independently,  reveals  the  fact  that 
their  rainfall  gradually  decreases  from  their  outlets  to  their 
more  elevated  sources. 


RIVER-BASIN  RAINS. 


51 


In  illustration  of  this  fact,  we  present  the  following  river- 
calley  statistics  relating  to  the  principal  basins  along  the 
Atlantic,  Gulf,  and  Pacific  coasts. 


TABLE  No.  6. 

Mean  Rainfall  Along  River  Courses,  showing  the  Decrease 
in  Precipitation  of  Rain  and  Melted  Snow  from  the 
River  Mouths,  upward. 


ST.  JOHN’S  RIVER. 


Name  of  Station. 

Summer. 

Winter. 

Year. 

Distance  from  Mouth. 

St.  Johns 

Inches. 

IO 

12 

Inches. 

14 

IO 

Inches. 

5i 

36 

Miles  {approximate'). 

5 ) Distances  from 
onr\i  the  Atlantic 
23° ) Ocean. 

Average  rain, 
43  inches. 

Fort  Kent 

MERRIMACK  RIVER. 


Newburyport 

12 

12 

41 

5] 

Lawrence 

19 

II 

45 

25  ' 

Manchester 

II 

II 

45 

60  1 

Concord  

II 

9 

41 

78  J 

Distances  from 
the  Atlantic 
Ocean. 


Average  rain, 
43  inches. 


CONNECTICUT  RIVER. 


Saj'brook 

13 

13 

49 

4l 

Middletown 

13 

12 

46 

25 

Distances  from 

Hartford 

IO 

II 

44 

40 

^ Long  Island 

Hanover 

II 

9 

40 

180 

Sound. 

St.  Johnsbury 

II 

8 

36 

235  J 

Average  rain, 
44  inches. 


HUDSON  RIVER. 


New  York  City 

12 

IO 

44 

8 

Poughkeepsie 

12 

9 

40 

75 

Hudson 

IO 

7 

35 

115 

Albany 

9 

8 

36 

145 

Distances  from 
the  Atlantic 
Ocean. 


Average  rain.. 
39  inches. 


Havre  de  Grace 

Harrisburg 

Lewisburg 

Williamsport 

Owe  go 

Elmira 


SUSQUEHANNA  RIVER. 


13 

IO 

44 

5' 

12 

8 

49 

70 

II 

8 

39 

120 

IO 

7 

39 

I40 

8 

6 

34 

200 

7 

4 

26 

200^ 

Distances  from  Average  rain, 
Che|apeake  3?  ;nches> 


52 


RAINFALL. 


Mean  Rainfall  Along  River  Courses — ( Continued ). 

MISSISSIPPI  RIVER. 


Name  of  Station. 


Delta 

New  Orleans 

Baton  Rouge 

June,  of  Red  River  . . 

Vicksburg 

Memphis 

Cairo 

St.  Louis 

Dubuque  

Lacrosse 

St.  Paul’s 

Brownsville 

June.  Pecos  River  . . 

El  Paso 

Albuquerque 


Summer. 

Winter. 

Y EAR. 

Distance  from  Mouth. 

Inches. 

Inches. 

Inches . 

Miles  ( approximate ). 

20 

18 

60 

10  j 

20 

16 

60 

95 

18 

15 

60 

190 

14 

16 

56 

24O 

II 

15 

55 

350 

Distances  from 

8 

15 

42 

560 

>-  the  Gulf  of 

II 

12 

42 

700 

Mexico. 

13 

8 

42 

850 

14 

5 

38 

I IOO 

II 

3 

30 

1200 

II 

3 

25 

1500J 

RIO 

GRANDE. 

8 

6 

37 

30 1 

5 

4 

3 

18 

400 

Distances  from 

2 

12 

800 

- the  Gulf  of 
Mexico. 

3 

2 

8 

1050  J 

46  inches. 


Average  rain, 
19  inches. 


COLUMBIA  RIVER. 


Astoria 

4 

44 

86 

5") 

Walla-Walla 

2 

5 

20 

275 1 

Boise  City 

2 

7 

13 

600  ( 

Fort  Hall 

I 

6 

12 

850J 

Distances  from  Average  rain, 

the  | inrhps 
Pacific  Ocean.  inches. 


Reference  to  the  above,  from  among  the  principal  river 
valleys,  is  sufficient  to  show  that  the  oft-made  statement, 
that  “rain  falls  most  abundantly  on  the  high  land,”  is 
applicable,  in  the  United  States,  to  subordinate  watersheds 
only,  and  in  rare  instances. 

33.  Grouped  Rainfall  Statistics. — The  following 
table  gives  the  minimum,  maximum,  and  mean  rainfalls, 
according  to  the  most  extended  series  of  observations,  at 
various  stations  in  the  United  States.  They  are  grouped  by 
territorial  divisions,  having  uniformity  of  meteorological 
characteristics. 


RAINFALL  IN  THE  UNITED  STATES. 


53 


TABLE  No.  7. 


Rainfall  in  the  United  States. 

{From  Records  to  1866  inclusive .) 

GROUP  1.— Atlantic  Sea-coast  from  Portland  to  Washington. 


Station. 

Lat. 

Long. 

Height 

above 

Sea. 

Years 

of 

Record 

Min. 

Annual 

Rain. 

Max. 

Annual 

Rain. 

Mean 

Annual 

Rain. 

Inches. 

Inches. 

Inches . 

Gardiner,  Me 

44°  10' 

69°  46' 

76 

27 

30.19 

5x-47 

42.09 

Brunswick  “ 

43  54 

69  57 

74 

32 

26.38 

75.64 

44.68 

Worcester,  Mass 

42  16 

71  49 

5^ 

26 

34.60 

61.83 

46  92 

Cambridge,  “ ...  

42  23 

71  07 

71 

31 

30.04 

59-34 

46.39 

Boston,  “ 

42  22 

71  04 

28 

27.20 

67.78 

44.99 

New  Bedford  “ 

41 39 

70  56 

90 

54 

30.68 

58.14 

41.42 

Providence,  R.  I 

4i  50 

7i  23 

uo 

35 

3°-5i 

54.17 

4!-54 

Flatbush,  N.  Y 

40  37 

74  °2 

54 

36 

:.z-i4 

58.92 

43-52 

Fort  Hamilton,  “ 

40  36 

74  02 

25 

*9 

29-75 

62.69 

42.55 

Fort  Columbus,  “ 

40  41 

74  oi 

23 

24 

27-57 

65-51 

43-24 

New  York  City,  “ 

40  43 

74  00 

50 

3i 

34-79 

62.87 

43.00 

West  Point,  “ 

41  24 

73  57 

167 

20 

35-°5 

63.56 

47-65 

Newark,  N.  J 

40  45 

74 10 

35 

23 

34-54 

57-05 

44-85 

Lambertville,  “ 

40  23 

74  56 

96 

17 

32-33 

57-37 

43-99 

Philadelphia,  PeDn 

39  57 

75  « 

60 

43 

29-57 

62.94 

44-05 

Baltimore,  Md 

Fort  McHenry,  “ 

39  is 

76  37 

28 

28.75 

62.04 

42.33 

39 16 

76  34 

36 

23 

22.87 

51-50 

41.10 

A ashington,  t).  C 

38  54 

77  03 

no 

28 

23.24 

53-45 

37-52 

43-44 

GROUP  2. — Atlantic  Sea-coast,  Virginia  to  Florida. 


Fortress  Monroe,  Va 

Charleston,  S.  C 

Fort  Moultrie,  “ 

Savannah,  Ga 

Fort  Brooke,  Fla 


37°oo/ 

76°i8' 

8 

19 

19.32 

74.10 

47.04 

32  47 

79  56 

25 

12 

23.69 

56.16 

43-63 

32  46 

79  5i 

25 

1 7 

33-98 

65-31 

45-51 

32  05 

81  05 

42 

23 

25.98 

69.93 

48.32 

28  00 

82  28 

20 

V 

35-93 

89.86 

53-63 

47-63 

GROUP  3.— Hudson  River  Valley,  Vermont, 


Newburgh,  N.  Y 

Poughkeepsie,  “ 

Kingston,  “ 

Hudson,  “ 

Kinderhook,  “ 

Albany,  “ 

Watervliet  Arsenal,  “ 

Lansingburg,  “ 

Granville,  “ 

Hanover,  N.  H 

Burlington,  Vt 

Fairfield,  N.  Y 

Clinton,  “ 

Utica,  “ 

Lowville,  “ 

Gouverneur,  “ 

Potsdam,  “ 

Cazenovia,  “ 

Oxford,  “ 

Pompey,  “ 

Auburn  “ 

Ithaca,  “ 

Geneva,  “ 

Penn  Yan,  “ 

Rochester,  “ 

Middlebury,  “ 

Fredonia,  “ 


New  York. 


4i 

31' 

74 

05' 

150 

4i 

41 

73 

55 

4i 

55 

74 

02 

*i88 

42 

13 

73 

46 

150 

42 

22 

73 

43 

125 

42 

39 

73 

44 

130 

42 

43 

73 

43 

50 

42 

47 

73 

40 

30 

43 

20 

73 

17 

25O 

43 

42 

72 

17 

530 

44 

29 

73 

11 

346 

43 

05 

74 

55 

I185 

43 

00 

75 

20 

II27 

43 

07 

75 

13 

473 

43 

46 

75 

32 

847 

44 

25 

75 

35 

400 

44 

40 

75 

01 

394 

42 

55 

75 

46 

1260 

42 

28 

75 

32 

961 

42 

5& 

76 

05 

1300 

42 

55 

76 

28 

650 

42 

27 

76 

37 

417 

42 

53 

77 

02 

567 

42 

42 

77 

11 

740 

43 

08 

77 

5i 

516 

42 

49 

78 

TO 

800 

42 

26 

79 

24 

710 

Northern  and  Western 


20 

25.04 

55-63 

36.61 

15 

40.36 

19 

35-io 

15 

34-52 

17 

36.48 

28 

31.92 

5°-97 

40.52 

17 

27.50 

44-93 

34-65 

20 

33-31 

15 

3x-52 

19 

3r-65 

55.98 

40.32 

27 

25-45 

49.44 

34-15 

17 

36.45 

19 

56.69 

4r-49 

22 

27-54 

41.14 

22 

33-5° 

24 

15-73 

50.75 

30-I5 

20 

28.63 

25 

45.10 

20 

36.36 

16 

23.21 

45-08 

30.75 

22 

34-42 

19 

34-71 

19 

27.46 

30.87 

3° 

19.66 

44.90 

28  42 

35 

24.97 

43-°3 

32.56 

1 7 

3°-44 

1 6 

36.55 

34-99 

54 


RAINFALL. 


Rainfall  in  the  United  States — ( Continued ). 

GROUP  4. — Upper  Mississippi,  part  of  Iowa,  Minnesota,  and 
Wisconsin. 


Station. 

Lat. 

Long. 

Height 

above 

Sea. 

Years 

of 

Record 

Min. 

Annual 

Rain. 

Max. 

Annual 

Rain. 

Mean 

Annual 

Rain. 

Inches. 

Inches. 

Inches . 

Fort  Ripley,  Minn 

46° 19' 

94°I9/ 

1130 

17 

12.06 

36.14 

25.11 

Fort  Snelling,  “ 

44  53 

93  10 

820 

22 

15.07 

49.69 

25.82 

Dubuque,  Iowa 

42  3° 

90  40 

666 

15 

25.07 

47.19 

33-47 

Milwaukee,  Wis 

43  03 

87  55 

591 

23 

20.54 

44.86 

30.40 

Muscatine,  Iowa 

41  26 

91  °5 

586 

19 

23.66 

74.20 

42.88 

Fort  Madison,  “ 

40  37 

91  28 

600 

18 

27-54 

54*H 

41.96 

33*27 

GROUP  S.— Ohio  River  Valley,  Western 

Missouri. 

Pennsylvania  to  Eastern 

Alleghany  Arsenal,  Penn 

4°°32' 

8o°o2/ 

704 

23 

25.62 

47-79 

35.23 

Steubenville,  Ohio 

40  25 

80  41 

670 

37 

28.02 

57.28 

41.48 

Marietta,  “ 

39  25 

81  29 

580 

48 

32.46 

53*54 

42.70 

Cincinnati,  “ 

39 06 

84  25 

582 

31 

25-49 

65.18 

44.87 

Portsmouth,  “ 

38  42 

82  53 

468 

26 

25.50 

56.79 

38.33 

Athens,  111 

39  52 

89  56 

800 

16 

25.12 

48.17 

39.62 

St.  Louis  Arsenal,  Mo 

38  40 

90  10 

450 

19 

24.08 

7X*54 

42.63 

St.  Louis,  “ 

38  37 

90  16 

481 

28 

27.00 

68.83 

42.18 

Jefferson  Barracks,  “ 

38  28 

9°  *5 

472 

21 

29.18 

55*13 

40.88 

d.0.88 

GROUP  6.— Indian  Territory  and  Western  Arkansas. 


Fort  Gibson,  Ind.  Ter.. 

Fort  Smith.  Ark 

Fort  Washita,  Ind.  Ter. 


3S°48' 
35  23 
34  14 


95°°3 
94  29 
96  38 


560 

460 

645 


20 

22 


l6 


18.84 

24-34 

21.81 


55-82 

61.03 

64.29 


3G37 

40.36 

38.04 


38.25 


GROUP  7.— Lower  Mississippi  and  Red  Rivers  ; 


part  of  Kentucky. 


Springdale,  Ken.. 
Washington,  Ark. 
Vicksburg,  Miss.. 
Natchez,  “ . 


38^07' 

85W 

570 

33  44 

93  41 

660 

32  23 

90  56 

350 

31  34 

91  25 

264 

24 

30-91 

67.10 

48.58 

22 

41.40 

70.40 

54*5° 

16 

37.21 

60.28 

49*30 

18 

31.09 

78*73 

53-55 

51.48 

GROUP  8.— Mississippi  Delta,  and  Coast  of  Mississippi  and  Alabama. 


New  Orleans,  La 

Mt.  V ernon  Arsenal,  Ala 

Baton  Rouge,  La 


29°57' 

90°02' 

20 

23 

41.92 

67.12 

31  12 

88  02 

200 

u 

51*49 

106.57 

30  26 

91  18 

41 

15 

41*34 

116.40 

51*05 

66.14 
60.  r6 


59*12 


GROUP  9.— Pacific  Coast,  Bay  of  San  Francisco  to  Alaska. 


San  Francisco,  Cal 

37°48' 

I22'26' 

170 

18 

IT*73 

36.03  1 21.69 

Sacramento,  “ 

38  35 

121  28 

82 

18 

n.15 

27.44  19.56 

Fort  Vancouver,  YV.  Ter 

45  4° 

122  30 

50 

l6 

25.91 

56.09  | 38.84 

Fort  Steilacoom,  “ 

47  IO 

122  2q 

300 

l6 

25-75 

70.21  | 43.98 

Sitka,  Alaska 

57  03 

135  18 

20 

l6 

58.6s 

95.81  1 83.39 

41.49 

Fig.  3. 


No.  1* 

1.90  ' 

1.80 

1.70 

1.60 

i-5o 

1.40 

1.30 

1.20 

1. 10 

1 

.90 
.80 
.70 
.60  „ 

No.  8. 


Atlantic  sea-coast,  Virginia  to  Florida. 


56 


RAINFALL. 


34.  Monthly  Fluctuations  in  Rainfall. — Our  gener- 
alizations tlius  far  have  referred  to  the  mean  annual  rainfall 
over  large  sections.  There  is  a large  range  of  fluctuation  in 
the  average  amount  of  precipitation  through  the  different 
seasons  of  the  year,  in  different  sections  of  the  United 
States.  It  will  he  of  interest  to  follow  out  this  phase  of  the 
question  in  diagrams  3 and  4,  in  which  type  curves  * of 
monthly  means  are  drawn  about  a line  of  annual  mean 
covering  a series  of  years,  in  no  case  less  than  fifteen. 

The  letters  J,  F,  M,  &c.,  at  the  heads  of  the  diagrams, 
are  the  initials  of  the  months.  The  heavy  horizontal  lines 
represent  means  for  the  year,  which  are  taken  as  unity. 
Their  true  values  may  he  found  at  the  foot  of  their  respect- 
ive groups  in  the  above  table.  About  this  line  of  annual 
mean  is  drawn  by  free-hand  the  type  curve  of  mean  rain- 
fall through  the  successive  months,  showing  for  each  month 
its  percentage  of  the  annual  mean. 

Each  type  curve  relates  to  a section  of  country  having 
uniform  characteristics  in  its  annual  distribution  of  rain. 

Curve  No.  1.  for  Group  No.  1,  includes  the  section  of 
country  bordering  upon  the  Atlantic  sea-coast  from  Port- 
land to  Washington.  The  average  fluctuation  of  the  year 
in  this  section  is  forty  per  cent.  Its  maximum  rainfall 
occurs  oftenest  in  August,  and  its  minimum  oftenest  in 
January  or  February. 

Curve  No.  £,  for  Group  No.  2,  includes  the  Atlantic 
coast  border  from  Virginia  to  Florida.  The  average  fluc- 
tuation of  the  year  is  one  hundred  and  ninety-eight  per 
cent.  Its  maximum  rainfall  occurs  oftenest  about  the  first 
of  August,  and  nearly  equal  minima  in  April  and  October. 

* Reduced  from  a diagram  by  Chas.  Schott,  C.  E.,  Smithsonian  Contribu 
tion,  Vol.  XVIII,  p.  16.  The  tables  of  American  rainfall  arranged  by  Mr. 
Schott,  and  published  in  the  same  volume,  are  exceedingly  valuable. 


Fig.  4. 


J F ■ M A M .7  J A SO  N D J 


CURVES  OF  ANNUAL  FLUCTUATIONS  IN  RAINFALL* 


Indian  Territory  and  Western  ’ Upper  Miss.,  parts  of  Iowa,  Minnesota, 


58 


RAINFALL. 


Curve  No.  3,  for  Group  No.  3,  includes  the  upper  Hud- 
son River  valley,  and  northern  and  western  New  York. 
The  average  fluctuation  of  the  year  is  sixty-six  per  cent. 
Its  maximum  rainfall  occurs  oftenest  near  the  first  of  July 
and  its  minimum  oftenest  about  the  first  of  February. 

Curve  No.  J,  for  Group  No.  4,  includes  a part  of  Iowa, 
central  Minnesota,  and  part  of  Wisconsin,  in  the  upper 
Mississippi  valley.  The  average  fluctuation  of  the  year  is 
one  hundred  and  nine  per  cent.  Its  maximum  rainfall 
occurs  oftenest  in  the  latter  part  of  June  and  its  minimum 
oftenest  about  the  first  of  February. 

Curve  No.  5,  for  Group  No.  5,  includes  the  Ohio  River 
valley,  from  western  Pennsylvania  to  eastern  Missouri. 
The  average  fluctuation  of  the  year  is  seventy-three  per 
cent.  Its  maximum  rainfall  occurs  oftenest  about  the  first 
of  June  and  its  minimum  oftenest  in  the  latter  part  of 
January. 

Curve  No.  6 , for  Group  No.  6,  includes  the  Indian  Ter- 
ritory and  Western  Arkansas.  The  average  fluctuation  of 
the  year  is  ninety-one  per  cent.  Its  maximum  rainfall 
occurs  oftenest  about  the  first  of  May  and  its  minimum 
oftenest  at  the  opening  of  the  year. 

Curve  No.  8 , for  Group  No.  8,  includes  the  Mississippi 
Delta  and  Gulf  coast  of  Alabama  and  Mississippi.  The 
average  fluctuation  of  the  year  is  seventy -five  per  cent.  Its 
maximum  rainfall  occurs  oftenest  in  the  latter  part  of  July 
and  its  minimum  oftenest  early  in  October. 

A similar  type  curve  for  Group  No.  9,  the  region  border- 
ing upon  the  Pacific  coast  from  the  Bay  of  San  Francisco 
to  Puget’s  Sound,  would  show  an  average  annual  fluctua- 
tion through  the  seasons  of  two  hundred  and  thirty -two 
per  cent.  The  fluctuations  here  have  nothing  in  common 
with  the  Mississippi  and  Atlantic  types.  The  maximum 


Fig.  5. 


CURVES  OF  SECULAR  FLUCTUATIONS  IN  RAINFALL. 


60 


RAINFALL. 


rainfall  here  occurs  oftenest  in  December  and  the  minimum 
oftenest  in  July. 

85.  Secular  Fluctuations  in  Rainfall. — Diagram  5 
illustrates  the  secular  fluctuations  in  the  rainfall  through  a 
long  series  of  years  in  the  Atlantic  system  and  in  the  central 
Mississippi  system.  It  presents  the  successions  of  wet  and 
dry  periods  as  they  vibrate  back  and  forth  about  the  mean 
of  the  whole  period. 

The  extreme  fluctuation  is  in  the  first  case  twenty-eight 
per  cent.,  and  in  the  second  case  thirty  per  cent. 

36.  Focal,  Physical,  anti  Meteorological  Influ- 
ences.— The  above  statistics  give  sufficient  data  for  deter- 
mining approximately  the  general  average  rainfall  in  any 
one  of  the  principal  river-basins  of  the  States. 

There  are  local  influences  operating  in  most  of  the  main 
physical  divisions,  analogous  to  those  governing  rainfall  in 
the  grand  atmospheric  systems. 

Referring  to  any  local  watershed,  and  the  detailed  study 
of  such  is  oftenest  that  of  a limited  gathering  ground  tribu- 
tary to  some  river,  we  have  to  note  especially  the  mean 
temperature  and  capacity  of  the  atmosphere  to  bear  vapor, 
the  source  from  which  the  chief  saturation  of  the  atmos- 
phere is  derived,  the  prevailing  winds  at  the  different  sea- 
sons, whether  in  harmony  with  or  opposition  to  the  direction 
of  this  source,  and  if  any  high  lands  that  will  act  as  con- 
densers of  the  moisture  lie  in  its  path  and  filch  its  vapors, 
or  if  guiding  ridges  converge  the  summer  showers  in  more 
than  due  proportion  in  a favored  valley.  A careful  study 
of  the  local,  physical,  and  meteorological  influences  will 
usually  indicate  quite  unmistakably  if  the  mean  rainfall  of 
a subordinate  watershed  is  greater  or  less  than  that  of  the 
main  basin  to  which  its  streams  are  tributary.  There  is 
rarely  a sudden  change  of  mean  precipitation,  except  at  the 


GREAT  RAIN  STORMS. 


61 


crest  of  an  elevated  ridge  or  tlie  brink  of  a deep  and  narrow 
ravine. 

37.  Uniform  Effects  of  Natural  Laws.  — When 
studies  of  local  rain-alls  are  confined  to  mean  results, 
neglecting  the  occasional  wide  departures  from  tlie  influence 
of  the  general  controlling  atmospheric  laws,  the  actions  of 
nature  seem  precise  and  regular  in  their  successions,  and  in 
fact  we  find  that  the  governing  forces  hold  results  with  a 
firm  bearing  close  upon  their  appointed  line. 

But  occasionally  they  break  out  from  their  accustomed 
course  as  with  a convulsive  leap,  and  a storm  rages  as 
though  the  windows  of  heaven  had  burst,  and  floods  sweep 
down  the  water-courses,  almost  irresistible  in  their  fury. 
If  hydraulic  constructions  are  not  built  as  firm  as  the  ever- 
lasting hills,  their  ruins  will  on  such  occasions  be  borne 
along  on  the  flood  toward  the  ocean. 

38.  Great  Rain  Storms. — In  October,  1869,  a great 
storm  moved  up  along  the  Atlantic  coast  from  Virginia  to 
New  York,  and  passed  through  the  heart  of  New  England, 
with  disastrous  effect  along  nearly  its  whole  course.  Its 
rainfall  at  many  points  along  its  central  path  was  from 
eight  to  nine  inches,  and  its  duration  in  New  England  was 
from  forty  to  fifty-nine  hours. 

In  August,  1874,  a short,  heavy  storm  passed  over  east- 
ern Connecticut,  when  there  fell  at  New  London  and  at 
Norwich  twelve  inches*  of  rain  within  forty-eight  hours, 
five  inches  of  which  fell  in  four  hours.  Such  storms  are 
rare  upon  the  Atlantic  coast  and  in  the  Middle  and  'West- 
ern States. 

Short  storms  of  equal  force,  lasting  one  or  two  hours, 
are  more  common,  and  the  flood  effects  from  them,  on  hilly 


* From  data  supplied  by  H.  B.  Winsbip,  Supt.  of  Norwich  Water-works. 


62 


RAINFALL. 


watersheds,  not  exceeding  one  or  two  square  miles  area, 
may  he  equally  disastrous,  and  waterspouts  sometimes 
hurst  in  the  valleys  and  flood  their  streams. 

39.  Maximum  Ratios  of  Floods  to  Rainfalls.— 
When  the  surface  of  a small  watershed  is  generally  rocky, 
or  impervious,  or,  for  instance,  when  the  ground  is  frozen 
and  uncovered  hy  snow,  the  maximum  rate  of  volume  of 
flow  through  the  outlet  channel  may  reach  two-thirds  of  the 
average  rate  of  volume  of  rain  falling  upon  the  gathering- 
ground. 

40.  Volume  of  Water  from  given  Rainfalls. — The 

rates  of  volume  of  water  falling  per  minute,  for  the  rates  of 
rainfall  per  twenty-four  hours,  indicated,  are  given  in  cubic 
feet  per  minute,  per  acre  and  per  square  mile,  in  the  follow- 
ing table : 


TABLE  No.  8. 

Volume  of  Rainfall  per  Minute,  for  given  Inches  per  Twenty- 

four  Hours. 


Rainfall  per 
24  HOURS. 

Volume  per 
Minute  on 
One  Acre. 

V OLUME  per 
Minute  on 
One  Sq.  Mile. 

Rainfall 

per 

24  HOURS. 

Volume  per 
Minute  on 
One  Acre. 

Volume  per 
Minute  on 
One  Sq.  Mile. 

Inches . 

Cu.  feet. 

Cu.  feet. 

Inches . 

Cu.  feet. 

Cu.  feet. 

0.1 

.252 

161.33 

1 

2.521 

I6i3-3I 

.2 

•5°4 

322.67 

2 

5.042 

3226.62 

•3 

•756 

484.01 

3 

7-563 

4840.00 

•4 

1.008 

645-33 

4 

10.084 

6453-25 

•5 

1.264 

806.67 

5 

12.605 

8066.56 

.6 

i-5i5 

968.00 

6 

15.126 

9679.87 

-7 

1-765 

1122.73 

7 

17.647 

1 1293.18 

.8 

2.107 

1390.67 

8 

20.168 

12906.50 

•9 

2.269 

1450.00 

9 

10 

22.689 

25.200 

14529.81 

16133.12 

41.  Gauging  Rainfall. — A pluviometer.  Fig.  6.  is  used 
to  measure  the  amount  of  rain  that  falls  from  the  sky.  It  is 
a deep,  cylindrical,  open-topped  dish  of  brass.  Its  ton 


GAUGING  RAINFALL. 


63 


edge  is  thin,  so  it  will  receive  just  the  rain  due  to  the  sec- 
tional area  of  the  open  top. 

A convenient  size  is  of  two  inches  diameter  at  a,  and  at 
b of  such  diameter  that  its  sectional 
area  is  exactly  one-tentli  the  sec- 
tional area  at  a,  or  a little  more 
than  one-half  inch. 

When  extreme  accuracy  is  re- 
quired, the  diameter  at  a is  made 
ten  inches  and  at  & a little  more 
than  three  inches,  still  maintaining 
the  ratio  of  sectional  areas  ten  to 
one,  the  displacement  of  the  meas- 
uring-rod being  allowed  for. 

This  rain-gauge  should  be  set 
vertically  in  a smooth,  open,  level 
ground,  and  the  grass  around  be 
kept  smoothly  trimmed  in  summer. 

The  top  of  a ten-inch  gauge  is  set 
at  about  one  foot  above  the  surface 
of  the  ground,  and  of  smaller 
gauges,  clear  of  the  grass  surface. 

The  gauge  should  be  placed  sufficiently  apart  from 
buildings,  fences,  trees,  and  shrubs,  so  that  the  volume  of 
rain  gathered  shall  not  be  augmented  or  reduced  by  wind- 
eddies. 

If  such  a situation,  secure  from  interference  by  animals 
or  by  mischievous  persons,  is  not  obtainable,  the  gauge 
may  be  set  upon  the  flat  roof  of  a building,  and  the  height 
above  the  ground  noted. 

The  measuring-rod  for  taking  the  depth  of  rain  in  b is 
graduated  in  inches  and  tenths  of  inches,  so  that  when  the 
sections  of  a and  b are  ten  to  one , ten  inches  upon  the  rod 


64 


RAINFALL. 


corresponds  with  one  inch  of  actual  rainfall,  and  one  inch 
on  the  rod  to  one-tenth  inch  of  rain,  and  one-tenth  on  the 
rod  to  one-lnindredth  of  rain. 

Snow  is  caught  in  a cylindrical,  vertical- sided  dish,  not 
less  than  ten  inches  diameter,  melted,  and  then  measured  as 
rain.  Memorandums  of  d.epths  of  snow  before  melting, 
with  dates,  are  preserved  also. 

It  has  been  observed  at  numerous  places,  that  elevated 
pluviometers  indicated  less  rain  than  those  placed  in  the 
neighboring  ground.  When  there  is  wind  during  a shower, 
the  path  of  the  drops  is  parabolic,  being  much  inclined  in 
the  air  above  and  nearly  vertical  at  the  surface  of  the 
ground.  A circular  rain-gauge,  held  horizontally,  presents 
to  inclined  drops  an  elliptic  section,  and  consequently  less 
effective  area  than  to  vertical  drops. 

The  law  due  to  height  alone  is  not  satisfactorily  estab- 
lished, though  several  formulae  of  correction  have  been 
suggested,  some  of  which  were  very  evidently  based  upon 
erroneous  measures  of  rainfall. 

The  observed  rainfall  at  Greenwich  Observatory,  Eng- 
land, in  the  year  1855,  is  reported,  at  ground  level,  23.8 
inches  depth  ; at  22  feet  higher,  .807  of  that  quantity,  and 
at  50  feet  higher,  .42  of  that  quantity. 

The  observed  rainfall  at  the  Yorkshire  Museum,  Eng- 
land, in  the  years  1832,  1833,  and  1834,  is  reported,  for 
yearly  average,  at  ground  level,  21.477  inches ; at  44  feet 
higher,  .81  as  much,  and  at  213  feet  higher,  .605  as  much. 

Unless  vigilantly  watched  during  storms,  the  gauges  are 
liable  to  overflow,  when  an  accurate  record  becomes  impos- 
sible. Overflow  cups  are  sometimes  joined  to  rain-gauges, 
near  their  tops,  to  catch  the  surplus  water  of  great  storms. 


Pis.  127.  Fig.  128. 


i 


SECTION  AND  PLAN  OF  PUMP-HOUSE. 


CHAPTER  IV. 


FLOW  OF  STREAMS. 

42.  Flood  Volume  Inversely  as  the  Area  of  the 
Basin. — A rain,  falling  at  the  rate  of  one  inch  in  twenty- 
four  hoars,  delivers  upon  each  acre  of  drainage  area  about 
2.5  cubic  feet  of  water  each  minute. 

If  upon  one  square  mile  area,  with  frozen  or  impervious 
surface,  there  falls  twelve  inches  of  rain  in  twenty-four 
hours,  and  two-thirds  of  this  amount  flows  off  in  an  equal 
length  of  time,  then  the  average  rate  of  flow  will  be  215 
cubic  feet  per  second. 

Any  artificial  channel  cut  for  a stream,  or  any  dam 
built  across  it,  must  have  ample  flood-way,  overfall,  or 
waste-sluice  to  pass  the  flood  at  its  maximum  rate. 

The  rate  of  flood  flow  at  the  outlet  of  a watershed  is 
usually  much  less  from  a large  main  basin  than  from  its 
tributary  basins,  because  the  proportion  of  plains,  storage 
ponds,  and  pervious  soils  is  usually  greater  in  large  basins 
than  in  small,  and  the  flood  flow  is  consequently  distrib- 
uted through  a longer  time. 

In  a small  tributary  shed  of  steep  slope  the  period  of 
maximum  flood  flow  may  follow  close  after  the  maximum 
rainfall ; but  in  the  main  channel  of  the  main  basin  the 
maximum  flood  effect  may  not  follow  for  one,  two,  three,  or 
more  days,  or  until  the  storm  upon  its  upper  valley  has 
entirely  ceased. 

43.  Formulae  for  Flood  V olrnnes.— Tlie  recorded  flood 
measurements  of  American  streams  are  few  in  number,  but 

5 


66 


FLOW  OF  STREAMS. 


upon  plotting  sncli  data  as  is  obtained,  we  find  their  mean 
curve  to  follow  very  closely  that  of  the  equation, 

Q = 200  (M)f,  (1) 

in  which  M is  the  area  of  watershed  in  square  miles  and  Q 
the  volume  of  discharge,  in  cubic  feet  per  second,  from  the 
whole  area. 

The  coefficient,  for  ordinary  floods,  for  New  England 
and  Appalachian  watersheds  varies  from  130  to  200,  and 
for  Eastern  Middle-State  watersheds  varies  from  60  to 
100,  and  for  tributaries  to  the  Mississippi,  on  the  west, 
varies  from  12  to  50. 

Among  the  Indian  Professional  Papers  we  find  the  fol- 
lowing formula  for  volume,  in  cubic  feet  per  second  : 

Q = cx27(M)*.  (2) 

in  which  c is  a co-efficient,  to  which  Colonel  Dickens  has 
given  a mean  value  of  8.25  for  East  Indian  practice. 

Testing  this  formula  by  our  American  curve,  we  find  the 
following  values  of  c for  given  areas : 


Area  in  sq.  miles. . . 

I. 

2-  3- 

4- 

6. 

8.  10. 

15* 

20.  30.  | 40. 

5°-  75- 

IOO. 

'Value  of  it 

7.41 

9.33  10.68 

11.76 

13.46 

14.83  rs.ge 

l8.26 

20.11  23.02  25.33 

27.28  31.26 

34-3® 

Mr.  Dredge  suggests,  also  in  Indian  Professional  Papers, 
the  following  formula : 

M 

Q = 1300  (3) 


in  which  L is  the  length  of  the  watershed,  and  M the  area 
in  square  miles. 

Our  formula,  modified  as  follows,  gives  an  approximate 
flood  volume  per  square  mile,  in  cubic  feet  per  second  : 


Q = 


200  (M)t 

M 


(4) 


TABLE  OF  FLOOD  VOLUMES. 


67 


in  which  M is  the  area  of  the  given  watershed  in  square 
miles. 

44.  Table  of  Flood  Volumes. — Upon  the  average 
New  England  and  Appalachian  basins,  maximum  floods 
may  be  anticipated  with  rates  of  flow,  as  per  the  following- 
table:  (See  §386,  page  381,  Waste-Weirs.) 

TABLE  No.  9. 

Flood  Volumes  from  given  Watersheds. 


Area  of  Water- 
shed. 

M. 


Sq.  Miles. 

°-5 

1 

2 

3 

4 
6 
8 

io 

15 

20 

25 

30 

40 

5o 

75 

IOO 

200 

3°° 

400 

5°0 

600 

800 

IOOO 

1500 

2000 

3000 

4000 

5000 


Flood  Discharge 
for  Whole  Area, 
4 

Q = 2<KD  (M)5 


Cu.  Feet  per  Second. 

114.87 

200. 

348- 

482 

606 

839 

1056 
1 262 

1745 

2197 

2627 

3039 

3825 

4573 

6325 

7962 

13863 

19175 

24137 

28854 

33385 

42024 

50238 

69487 

87469 

120984 

152292 

182056 


Flood  Discharge  per 
Square  Mile. 

200  (M)^ 

6 = M 


Cu.  Feet  per  Second. 

229.74 
200. 00 
174.11 
160.54 
I5I-57 
139-77 
I3I-95 
126. 19 
1 16.36 
109. 86 
105.06 
101.29 
95-63 
91.46 
84-34 
79.62 

69.31 
63.92 
60.34 
57-7i 
55-64 
52-53 
50.24 

46.32 
43-73 

40.33 
38.07 
36.41 


Flood  Discharge 
per  Acre. 


Cu.  Feet  per  M inute. 


2 I 

54 

l8 

75 

l6 

32 

J5 

°5 

14 

21 

13 

10 

I 2 

37 

I I 

83 

IO 

9i 

IO 

30 

9 

85 

9 

5° 

8 

97 

8 

57 

7 

9i 

7 

46 

6 

5° 

5 

99 

5 

66 

5 

4i 

5 

22 

4 

92 

4 

7i 

4 

34 

4 

10 

3 

78 

3 

57 

3-4i 

68 


FLOW  OF  STREAMS. 


4 5.  Seasons  of  Floods. — Great  floods  occur  only 
when  peculiar  combinations  of  circumstances  favor  such 
result. 

A knowledge  of  the  magnitude  of  the  floods  upon  any 
river,  and  of  their  usual  season,  is  invaluable  to  the  director 
of  constructions  upon  that  stream,  to  enable  him  to  take  such 
precautionary  measures  as  to  be  always  prepared  for  them. 
Such  knowledge  is  also  requisite  to  enable  him  to  compute 
the  storage  capacity  required  to  save  and  utilize  such  flood, 
or  to  calculate  the  sectional  area  of  waste  weir  required 
upon  dams  to  safely  pass  the  same. 

Long  rivers,  having  their  sources  upon  northern  moun- 
tain slopes,  have  usually  well-known  seasons  of  flood,  de- 
pendent upon  the  melting  of  snows  ; but  small  watersheds 
in  many  sections  of  America  are  subject  to  flood,  alike,  at 
all  seasons. 

40.  Influence  of  Absorption  and  Evaporation 
upon  Flow. — The  rainfall  upon  the  Atlantic  coast  and 
upon  the  Mississippi  valley  appears  comparatively  uniform 
when  noted  in  its  monthly  classification,  but  the  ability  of 
any  one  of  their  watersheds  to  supply,  from  flow  of  stream, 
a domestic  demand  equal  to  its  mean  flow  is  by  no  means 
as  uniform. 

We  have  seen  that,  according  to  the  statistics  quoted, 
the  consumption  of  water  is  not  as  uniform,  when  noted  by 
monthly  classification,  as  is  the  monthly  rainfall.  When 
lesser  classifications  of  rainfall  and  consumption  are  com- 
pared, there  is  scarce  a trace  of  identity  in  their  plotted 
irregular  profiles. 

Evaporation,  though  comparatively  uniform  in  its 
monthly  classification,  is  very  irregular  as  observed  in  its 
lesser  periods. 

In  the  spring  and  early  summer,  when  vegetation  is  in 


CLASSIFICATION  OF  RAINFALL  AVAILABLE  IN  FLOW.  69 


most  thrifty  growth,  the  innumerable  rootlets  of  flowers, 
grasses,  shrubs,  and  forests,  gather  in  a large  proportion  of 
rainfall,  and  pass  it  through  their  arteries  and  back  into 
the  atmosphere  beyond  reach  for  animal  uses. 

47.  Flow  in  Seasons  of  Minimum  Rainfall.— In 
gathering  basins  having  limited  pondage  or  available 
storage  of  rainfall,  the  flow  from  minimum  annual,  and 
minimum  periodic  rainfall  demands  especial  study.  Occa- 
sionally the  annual  rainfall  continues  less  than  the  general 
mean  through  cycles  of  three  or  four  years,  as  is  indicated 
in  the  above  diagram  of  curves  of  secular  rainfall.  The 
mean  rain  of  such  cycles  of  low-rainfall  is  occasionally  less 
than  eight-tenths  of  the  general  mean. 

We  have  selected  for  data  upon  this  point  the  rainfall 
records  of  twenty-one  stations,  of  longest  observation  in  the 
United  States,  at  various  points  from  Maine  to  Louisiana 
and  from  California  to  Sitka.  The  computation  gives  the 
annual  rainfall  of  the  least  three-year  cycle  at  any  one  of 
these  points  as  .67  of  the  general  mean  annual  rain  at  the 
same  point,  and  annual  rainfall  of  the  greatest  three-year 
low  cycle  as  .97  of  the  general  mean  at  the  same  point.  An 
average  of  all  these  stations  gives  the  three-year  low  cycle 
rainfall  as  .81  of  the  average  mean  annual  rainfall. 

48.  Periodic  Classification  of  Rainfall  Available 
in  Flow. — Next,  the  rainfall  and  tire  portion  of  it  that  can 
be  made  available,  demands  especial  study  in  its  monthly, 
or  less  periodic  classification.  It  is  desirable  to  know  the 
ratio  of  each  month’ s average  fall  to  the  mean  monthly  fall 
for  the  year,  and  the  percentage  of  this  fall  that  is  exempted 
from  absorptions  by  vegetation  and  evaporations  into  the 
atmosphere,  and  that  flows  from  springs,  and  in  the  streams, 
since  it  is  ordained  by  Nature  that  the  lily  and  the  oak 
with  their  seed,  shall  first  be  supplied  and  the  atmospheric 


70 


FLOW  OF  STREAMS. 


processes  be  maintained,  and  the  surplus  rain  be  dedicated 
to  the  animal  creation,  as  their  necessities  demand  and 
ingenuities  permit  them  to  make  available. 

49.  Sub-surface  Equalizers  of  Flow. — The  inter- 
stices of  the  soils  and  the  crevices  of  the  rocks  were  filled 
long  ages  ago,  and  now  regularly  aid  in  equalizing  the  flow 
of  the  springs  and  streams  without,  to  any  considerable 
extent,  affecting  the  total  annual  flow,  yet  their  influence  is 
observable  in  cycles  of  droughts  when  the  sub-surface  water 
level  is  drawn  slowly  down. 

The  substructure  of  each  given  watershed  has  its  indi- 
vidual storage  peculiarities  which  may  increase  or  diminish 
the  monthly  flow  and  degree  of  regularity  of  flow  of  its 
streams  to  an  important  extent. 

If  a porous  subsoil  of  great  depth  and  storage  capacity 
is  overlaid  with  a thin  crust  of  soil  through  which  water 
percolates  slowly,  a great  flood-rain  may  fall  suddenly  over 
the  nearly  exhausted  sub-reservoir  and  be  run  off  to  the 
rivers  without  replenishing  appreciably  the  waning  springs, 
or  increasing  tlieir  flow  as  would  an  ordinary  slow  rainfall. 

On  the  other  hand,  if  its  surface  soil  is  open  and  absorb- 
ent, it  may  be  able  to  receive  nearly  the  whole  flood  and 
distribute  it  gradually  from  its  springs. 

The  early  sealing  over  of  the  subsoil  by  winter  frosts 
before  the  usual  subterranean  storage  has  accumulated 
from  winter  storms,  or  a shedding  of  the  melting  snows  in 
spring  by  a like  frost-crust,  may  result  in  a diminished  flow 
of  the  deep  springs  in  the  following  summer. 

Subsoils  that  exhaust  themselves  in  ordinary  seasons 
are  comparatively  valueless  to  sustain  the  flow  in  the  second 
and  third  years  of  cycle  droughts. 

Steep  and  impervious  earths  yield  no  springs,  but  gather 
their  waters  rapidly  in  the  draining  streams. 


SUMMARIES  OF  MONTHLY  FLOW  STATISTICS. 


71 


50.  Flashy  and  Steady  Streams. — Upon  tlie  steep 
and  rocky  watersheds  of  northern  New  Hampshire,  we  find 
extreme  examples  of  “flashy”  streams  that  are  furious  in 
storm  and  vanish  in  droughts. 

Upon  the  saturated  sands  of  Hempstead  Plains  on  Long- 
Island,  N.  Y.,  we  find  an  opposite  extreme  of  constant  and 
even  flow,  where  a great  underground  reservoir  co-extensive 
with  its  supplying  watershed,  feeds  its  streams  with  remark- 
able uniformity. 

Almost  all  degrees  of  constancy  and  fickleness  of  flow 
are  to  be  found  in  the  several  sub-section  streams  of  any 
one  of  our  great  river  basins. 

51.  Peculiar  Watersheds. — The  extremes  or  results 
from  peculiar  watersheds,  are  in  all  cases  to  be  considered 
as  extremes  when  their  individual  merits  and  capacities  of 
supply  are  investigated,  and  the  investigation  may  often 
take  the  direction  of  determining  the  relations  of  its  results 
to  results  from  a general  mean,  or  ordinary  watershed, 
especially  as  respects  its  mean  temperature,  its  mean  hu- 
midity of  atmosphere,  the  direction  from  wdience  its  storms 
come,  the  frequency  of  its  storm  winds,  the  extent  of  its 
storms  in  the  different  seasons,  the  imperviousness  or  the 
porosity  of  its  soils  and  rocks,  the  proportions  of  its  steep, 
gently  undulating,  and  flat  surfaces,  and  also  it  is  to  be 
observed  if  it  can  be  classed  among  those  rare  instances  in 
which  one  watershed  is  tributary  as  giver  to  or  receiver 
from  another  basin,  involving  an  investigation  of  its  geo- 
logical substructure. 

52.  Summaries  of  Monthly  Flow  Statistics. — 

We  have  analyzed  some  valuable  statistics  of  monthly 
rainfalls,  and  measured  flow  of  streams  in  Massachusetts 
and  New  York  State,  which  are  too  voluminous  for  repro- 
duction here,  and  present  the  deduced  results.  The  records 


72 


FLOW  OF  STREAMS. 


are,  first,  from  a report  fay  Jos.  P.  Davis,  C.  E.,  relating  to 
tlie  watershed  of  Cocfaituate  Lake,  which  has  supplied  the 
city  of  Boston  with  -water  until  supplemented  in  1876  from 
the  Sudfaury  River  watershed ; second,  from  a tafale  com- 
piled fay  Jas.  P.  Kirkwood,  C.  E.,  relating  to  the  watershed 
of  Croton  River  above  the  Croton  Dam  ; and  third,  from  a 
paper  read  fay  J.  J.  R.  Croes,  C.  E.,  before  the  American 
Society  of  Civil  Engineers,  July,  1874,  relating  to  the  water- 
shed of  the  West  Branch  of  the  Croton  River. 

Additional  statistics  relating  to  Sudbury  River  are  given 
on  page  83a. 

The  summaries  are  as  follows : 


TAB  L E No.  1 O. 

Summary  of  Rainfall  upon  the  Cochituate  Basin. 

Average  annual,  55.032  inches  ; average  monthly,  4.586  inches. 


c3 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

fcf 

< 

Sept. 

Oct. 

Nov. 

Dec. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

Mean 

3-69 

4-°3 

5-35 

4-58 

5-69 

3.09 

5-23 

4.91 

3.81 

5.86 

5.26 

3-52 

Minimum 

.98 

2.51 

1.94 

2.66 

.58 

1.06 

2.03 

o'64 

1. 19 

2.63 

•45 

Maximum 

7.85 

5.80 

8.44 

ii-34 

8.25 

5.96 

14.12 

12.36 

8.49 

9-5o 

8-54 

5-98 

Ratio  of  monthly 
mean 

.806 

.878 

I.I67 

.998 

1. 241 

•675 

1.141 

1.070 

.831 

1.300 

I*I47 

.768 

TABLE  No.  11. 

Summary  of  Rainfall  upon  the  Croton  Basin. 

Average  annual,  46.497  inches  ; average  monthly,  4.227  inches. 


Jan. 

46 

0 

Mar. 

Apr. 

May. 

June. 

July. 

fci) 

< 

0 

m 

Oct. 

Nov. 

Dec. 

in. 

in. 

in. 

in. 

hi. 

hi. 

in. 

in. 

in. 

in. 

in. 

in. 

Mean 

2-54 

3*I5 

3.16 

3.12 

6.40 

4-58 

4-31 

6.03 

5-3° 

4.70 

3.83 

3.60 

Minimum . 

.96 

1.89 

2.48 

4.78 

2.51 

2.31 

2.30 

2.23 

•74 

3-°9 

1.86 

Maximum . 

4.18 

5-03 

5.64 

4-32 

10.18 

6.19 

8.12 

,9.21 

13*35 

8.74 

5-36 

6.86 

Ratio  of  monthly 
mean 

.625 

•745 

•749 

•739 

1-513 

1.084 

1.020 

1.427 

1.259 

1. 111 

•9°5 

.851 

SUMMARIES  OF  MONTHLY  FLOW  STATISTICS. 


73 


TABLE  No.  12. 

Summary  of  Rainfall  upon  Croton  West-Branch  Basin. 


Average  annual,  44.429  inches  ; average  monthly,  4.039  inches. 


e 

gS 

Feb. 

Mar. 

Apr. 

May.  1 
1 

June. 

July. 

bh 

3 

< 

Sept. 

Oct. 

Nov. 

Dec. 

in. 

in , 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

Mean 

3.16 

3.20 

3-3° 

3-84 

5.08 

4-32 

4-59 

6.59 

2.90 

5-24 

3.10 

3.16 

Minimum 

i-44 

1.22 

2.55 

3-QI 

2.30 

2.06 

3-43 

5.10 

1.44 

2.15 

2-43 

1.49 

Maximum 

4-5i 

6.40 

4.27 

5-45 

8.79 

5-73 

5-52 

10.04 

3-69 

9.46 

4-35 

5.96 

Ratio  of  monthly 
mean 

•783 

.767 

1.296 

.718 

1.633 

1.136 

1.070 

1.257 

•951 

.818 

•793 

•783 

TAB  L E No.  13. 

Summary  of  Percentage  of  Rainfall  Flowing  from  the  Cochit- 

uate  Basin. 


Average  percentage  of  average  annual  rainfall  flowing  off,  45.6. 


fl 

cS 

rQ 

O 

Mar. 

Apr. 

May. 

June. 

July. 

bio 

3 

cl 

<U 

CO 

Oct. 

Nov. 

Dec. 

Mean 

Minimum 

Maximum 

Ratio  of  monthly 
mean 

in. 

52.5 

33 

79 

in. 

79-7 

26 

159 

in. 

7I*3 

44 

153 

in. 

80.5 

39 

124 

in. 

45-i 

20 

76 

in- 

35-i 

9 

84 

in. 

20.3 

9 

39 

in. 

20.0 

x4 

27 

in. 

24.5 

*3 

39 

in. 

26.5 

10 

80 

in. 

27.8 

20 

42 

in. 

64-3 

24 

261 

i*i5 

I*75 

1.56 

1-77 

•97 

.770 

•44 

.44 

•54 

•58 

.61 

1. 41 

TABLE  No.  14. 

Summary  of  Percentage  of  Rainfall  Flowing  from  the  Croton 

Basin. 


Average  percentage  of  average  annual  rainlall  flowing  off,  57.47. 


fl 

o3 

Feb. 

Mar. 

Apr. 

May.  j 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Mean 

Minimum 

Maximum 

Ratio  of  monthly 
mean ... 

in. 

79.68 

49.0 

123.4 

in. 

75-o 

62.1 

107.0 

in. 

86.72 

21.9 

147-4 

in. 

80.60 

53-5 

125.7 

in. 

48.45 

42.8 

56.4 

in. 

45.02 

18.6 

67.4 

in. 

21.02 

8.5 

29.6 

in. 

T9-45 

8.4 

42.2 

in. 

30.10 

10.2 

92.0 

hi. 

81.13 

7.6 

366.5 

in. 

60.40 

36-3 

94-i 

in. 

62.12 

39-o 

94-5 

1.386 

1-305 

1.509 

1.402 

•843 

•783 

•369 

•338 

.524 

1. 412 

1. 051 

1.081 

74 


FLOW  OF  STREAMS. 


TABLE  No.  15. 

Summary  of  Percentage  of  Rainfall  Flowing  from  the  Croton 
West-Branch  Basin. 


Average  percentage  of  average  annual  rainfall  flowing  off,  70.98. 


Jan. 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

> 

O 

Dec. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

Mean  

102.8 

71. 1 

158.9 

117.2 

80.5 

44.8 

19.0 

24.6 

26.6 

3°-4 

78.9 

97.0 

Minimum. 

17.7 

59-o 

ioq.o 

93-2 

46.7 

17.6 

7-3 

3-4 

3-3 

11. 2 

40.5 

65.6 

Maximum ........ 

186.6 

103.9 

209.1 

158.4 

100.3 

71.2 

3r-4 

53-8 

39.8 

56.3 

1 10.2 

140.8 

Ratio  of  monthly 
mean . , ........ 

1.448 

1. 001 

2.238 

1.651 

.636 

.267 

•347 

•375 

.428 

1.112 

1.367 

TABLE  No.  16. 


Summary  of  Volume  of  Flow  of  Rainfall  from  the  Cochituate 
Basin  (in  cubic  feet  per  minute  per  square  mile). 


G 

ci 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

Aug. 

«T 

C/2 

Oct. 

Nov. 

Dec. 

cu.ft. 

99-17 

37-99 

245.12 

cu./t. 

150.42 

58.29 

301.90 

cu./t. 

174.76 

91.60 

242.52 

cu.ft. 

169.80 

70.44 

369.40 

cu.ft. 
131.80 
67.14 
321. II 

cu.ft. 

44.27 

18.28 

85-49 

cu.ft. 

45-27 

21-34 

154.57 

cu.ft. 

49-15 

21.34 

109.29 

cu.ft. 

42.84 

4.30 

99.48 

cu.ft. 

62.45 

36.43 

123-34 

cu.ft. 

75.90 

47-32 

105-39 

cu.ft. 

78.94 

40.07 

164.98 

Maximum 

Ratio  of  monthly 

1.058 

1.605 

1.865 

1.812 

1.406 

.472 

fO 

00 

•524 

•457 

.666 

.809 

.842 

TABLE  No.  17. 

Summary  of  Volume  of  Flow  of  Rainfall  from  the  Croton 
Basin  (in  cubic  feet  per  minute  per  square  mile). 


Jan. 

Feb. 

s 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

d 

0 

Mean 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft . 

91.48 

147.69 

177.02 

132.63 

164.49ln5.12 

48.37 

70.22 

85-99 

81.08 

124.92 

106.23 

Minimum  

48.08 

40.65 

79-°5 

87.43 

108.25 

34-09 

10.46 

I3-12 

12.91 

18.05 

61.41 

72.08 

Maximum 

127.71 

293.01 

25.709 

188.95 

to 

VO 

00 

224-33 

81.76 

202.19 

275-95 

141-14 

201.30 

146.24 

Ratio  of  monthly 
mean 

.816 

1-347 

4-579 

1.183 

4-467 

1.027 

•434 

.627 

.767 

.723 

1.114 

.948 

SECTIONS  OF  CROTON  NEW  AQUEDUCT, 


I 


t 


MINIMUM,  MEAN,  AND  FLOOD  FLOW  OF  STREAMS.  75 


TAB  LE  No.  1 8. 


Summary  of  Volume  of  Flow  of  Rainfall  from  the  Croton 
West-Branch  Basin  (in  cubic  feet  per  minute  per  square  mile). 


fl 

& 

Feb. 

Ih 

*2 

cL 

< 

>> 

s 

[ June. 

' 

>> 

3 

Aug. 

Sept. 

Oct 

Nov. 

Dec. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft- 

cu.ft. 

cu.ft. 

cu.ft. 

Mean 

158.95 

185.19 

290.56 

272.60 

161.60 

103.8  6 

40.02 

103.12 

x47-59 

96.26 

107.85 

164.07 

Minimum ... 

35.08 

47.16 

203.58 

146.04 

26.19 

45.18 

19.26 

9.06 

5-i6 

27.48 

5-92 

50.88 

Maximum 

347.88 

378.90 

39°- 83 

463.98 

394.92 

202.02 

85.56 

281.04 

477-22 

277.26 

203.28 

299.16 

Ratio  of  monthly 

mean. 

1. 04 1 

1-213 

1.904 

1.786 

1.059 

.680 

.262 

.676 

.967 

.631 

.707 

I-°75 

53.  Minimum,  Mean,  and  Flood  Flow  of  Streams. 

— An  analysis  of  the  published  records  of  volumes  of  water 
flowing  in  the  streams  in  all  the  seasons  has  led  to  the  fol- 
lowing approximate  estimate  of  volumes  of  flow  in  the  aver- 
age Atlantic  coast  basins : 

The  minimum  refers  to  a fifteen  days’  period  of  least 
summer  flow. 

The  mean  refers  to  a one  hundred  and  twenty  days’ 
period,  covering  usually  July,  August,  September,  and 
October,  beginning  sometimes  earlier,  in  June,  and  ending 
sometimes  later,  in  November. 

The  maximum  refers  to  flood  volumes. 

TABLE  No.  19. 


Estimates  of  Minimum,  Mean,  and  Maximum  Flow  of  Streams. 


Min.  in  cu.  ft.  per 
sec.  per  sq.  mi. 

Mean  in  cu.  ft.  per 
sec.  per  sq.  mi. 

Max.  in  cu  ft.  per 
sec.  per  sq.  mi. 

Area  of  watershed,  1 

sq.  mi. 

00 

O 

I. OO 

200 

tt  tt  a 

IO 

it 

.1 

.99 

136 

it  it  tt 

25 

tt 

.11 

.98 

117 

5° 

.14 

•97 

104 

it  it  it 

100 

tt 

.18 

•95 

93 

tt  it  it 

250 

it 

•25 

.90 

80 

it  u a 

5°° 

a 

•3° 

.87 

71 

a a tt 

1000 

a 

•35 

.82 

63 

it  a a 

1500 

a 

.38 

.80 

59 

a a a 

2000 

a 

.41 

•79 

56 

76 


FLOW  OF  STREAMS. 


This  table  refers  to  streams  of  average  natural  pondage 
and  retentiveness  of  soil,  but  excludes  effects  of  artificial 
storage.  The  fluctuations  of  streams  will  be  greater  than 
indicated  by  the  table  when  prevailing  slopes  are  steep  and 
rocks  impervious,  and  less  in  rolling  country  with  pervious 
soils. 

54.  Ratios  of  Monthly  Flow  in  Streams. — A care- 
ful analysis  of  the  published  records  of  monthly  flow  of  the 
average  Atlantic  coast  streams  leads  to  the  following  ap- 
proximate estimate  of  the  ratio  of  the  monthly  mean  rain- 
fall that  flows  down  the  streams  in  each  given  month  of  the 
year,  in  which  due  consideration  of  the  evaporation  from 
soils  and  foliage  in  very  dry  seasons  has  not  been  neglected. 


TABLE  No.  20. 
Monthly  Ratios  of  Flow  of  Streams. 


Jan. 

Feb. 

March. 

April. 

May. 

June. 

July- 

fch 

D 

< 

Sept. 

Oct. 

Nov. 

(5 

Q 

Ratio  of  flow . 

1.65 

1-50 

1.65 

i-45 

•85 

•75 

•35 

•25 

.30 

•45 

1.20 

1.60 

Here  unity  equals  the  mean  monthly  flow,  or  one-twelfth 
the  mean  annual  flow. 

To  compute,  approximately,  the  inches  depth  of  rain 
flowing  in  the  streams  each  month,  one-twelftli  the  mean 
annual  rain,  at  the  given  locality,  may  be  multiplied  by  the 
ratios  in  the  following  table.  For  illustration,  a mean 
annual  rain  of  40  inches  depth,  giving  3.333  inches  mean 
monthly  depth,  is  assumed,  and  the  available  flow  of  stream 
expressed  in  inches  depth  of  rain  is  added  after  the  ratios. 


MEAN  ANNUAL  FLOW  OF  STREAMS. 


77 


TABLE  No.  21. 


Ratios  of  Mean  Monthly  Rain,  and  Inches  of  Rain  Flowing. 

each  Month. 


Jan. 

Feb. 

Mar. 

Apr. 

May.  j 

June,  j 

1 

July. 

Aug. 

Sept. 

O 

O 

1 

Dec. 

Ratios  of  mean 
monthly  rain 

.825 

•75  0 

.825 

.725 

■425 

•375 

•i75 

.125 

.150 

.225 

• 600 

.800 

inches  of  rain 

flowing 

2.75 

2.50 

2-75 

2.41 

1.41 

1.25 

o-59 

O.4I 

O.5O 

0.75 

2.00 

2.66 

Eight  - tenths 

0.60 

X.60 

of  same . . . 

2.20 

2.00 

2.20 

*•93 

I,I3 

1. 00 

0.47 

o-33 

O.4O 

2.13 

For  low-cycle  years,  use  eiglit-tentlis  (§  47)  the  available 
monthly  depth  of  rain  flowing. 

55.  Mean  Annual  Flow  of  Streams. — When  month- 
ly data  of  the  flow  of  any  given  stream  is  not  obtainable,  it 
may  ordinarily  be  taken  upon  average  drainage  areas,  for 
an  annual  flow,  as  equal  to  fifty  per  cent,  of  the  annual 
rainfall. 

Or,  for  different  surfaces,  its  ratio  of  the  annual  rain, 
including  floods  and  flow  of  springs,  is  more  approximately 
as  follows : 


From  mountain  slopes,  or  steep  rocky  hills 8o  to  .90 

Wooded,  swampy  lands  60  to  .80 

Undulating  pasture  and  woodland 50  to  .70 

Flat  cultivated  lands  and  prairie 45  to  .60 


Since  stations  for  meteorological  observations  are  now 
established  in  or  near  almost  all  the  populous  neighbor- 
hoods, and  some  of  the  stations  have  already  been  estab- 
lished more  than  a quarter  of  a century,  it  is  easier  to  obtain 
data  relating  to  rainfall  than  to  the  flow  of  streams.  In 
fact,  the  required  data  relating  to  a given  stream  is  rarely 
obtainable,  and  the  estimates  relating  to  the  capacity  and 


78 


FLOW  OF  STREAMS. 


reliability  of  the  stream  to  furnish  a given  water-supply 
must  necessarily  be  quite  speculative. 

56.  Estimates  of  Flow  of  Streams. — In  such  case, 
an  estimate  of  the  capacity  of  a stream  to  deliver  into  a 
reservoir,  conduit,  or  pump-well  is  computed  according  to 
some  scheme  suggested  by  extended  observations  and  study 
of  streams  and  their  watersheds,  and  long  experience  in  the 
construction  of  water  supplies. 

The  first  reconnoissance  of  a given  watershed  by  an  ex- 
pert in  hydrology  will  ordinarily  enable  him  to  judge  veiy 
closely  of  its  capacity  to  yield  an  available  and  suitable 
water  supply ; for  his  comprehension  at  once  grasps  its 
geological  structure,  its  physical  features  and  its  usual 
meteorological  phenomena,  and  his  educated  judgment 
supplies  the  necessary  data,  as  it  were,  instinctively. 

If  the  estimate  of  flow  of  a stream  must  be  worked  up 
from  a survey  of  the  watershed  area  and  the  mean  annual 
rainfall,  as  the  principal  data,  then  recourse  may  be  had  to 
the  data  and  estimates  given  above,  relating  to  the  question, 
for  average  upland  basins  of  one  hundred  or  less  square 
miles  area. 

In  illustration,  let  us  assume  a basin  of  one  square  mile 
area,  having  a forty-inch  average  annual  rainfall,  and  then 
proceed  with  a computation.  This  is  a convenient  unit  of 
area  upon  which  to  base  computations  for  larger  areas. 

The  ratios  of  the  three-year  low  rain  cycles  gives  their 
mean  rainfall  as  about  eight-tenths  of  the  general  mean 
rainfall.  We  assume  it  to  be  eighty  per  cent.  The  mean 
annual  flow  of  the  stream  we  assume  to  be  fifty  per  cent,  of 
the  annual  rainfall.  Eight-tenths  of  fifty  per  cent,  gives 
forty  per  cent,  of  the  annual  rainfall  as  the  annual  available 
flow  of  the  stream,  and  forty  per  cent,  of  the  forty  inches 
rainfall  gives  an  equivalent  of  sixteen  inches  of  rainfall 


ESTIMATES  OF  FLOW  OF  STREAMS. 


79 


flowing  down  tlie  stream  annually.  The  monthly  average 
flow  is  then  taken  as  one-twelfth  of  sixteen,  or  one  and  one- 
third  inches.  Our  estimated  monthly  percentage  of  mean 
flow,  as  given  above  (§  54),  is  sometimes  much  in  excess 
and  sometimes  less  than  the  monthly  average.  Flows  less 
than  the  mean  are  to  be  compensated  for  by  a proportion- 
ate increase  of  storage  above  the  mean  storage  required. 

The  monthly  computations  are  as  follows : 

40  inches  x 50  per  cent,  x .8 
Monthly  mean  = 12  months = 1333 

inches  average  available  rain  monthly.  This  average  mul- 
tiplied by  the  respective  ratios  of  flow  in  each  month  gives 
the  inches  depth  of  available  rain  flowing  in  the  respective 
months,  thus : 


January..  . . 

Mean  Monthly 
Rainfall. 

1-333 

X 

Respective 

Ratios. 

I.65 

Inches  Depth  op 
Available  Rain 
Flowing  eac* 
Month. 

2.20 

February  . . . 

(t 

X 

1-50 

= 

2.00 

March 

i< 

X 

1.65 

= 

2.20 

April 

li 

X 

i-45 

= 

i-93 

May 

M 

X 

.85 

= 

113 

June 

ii 

X 

•75 

= 

I. OO 

July 

a 

X 

•35 

= 

•47 

August 

u 

X 

•25 

= 

•33 

September. . 

u 

X 

•30 

= 

.40 

October  .... 

it 

X 

•45 

= 

.60 

November. . 

« 

X 

1.20 

- 

1.60 

December  . . 

<« 

X 

1.60 

— 

2.14 

Again,  uniting  the  constants, 

we  have 

.8 

x .50 
12  ~ 

0333 

which,  multiplied  by  the  respective  ratios  of  monthly  flow, 
thus  : Jan.,  .0333  x 1.65  = .055,  etc.,  gives  directly  the  mean 
ratio  of  the  low  cycle  annual  rainfall  that  is  available  in  the 
stream  each  month. 


80 


FLOW  OF  STREAMS. 


F LOW  IK  Cu.  F T.  PFTS 
Minute  per  Sq.  Ml 
in  each  Month. 


Jan 

. 40  inches 

X 

•055 

2.20 

inches  depth 

= 

116.60 

Feb 

(( 

X 

.050 

= 

2.00 

it 

— 

106.00 

March. . 

U 

X 

•055 

2.20 

ii 

= 

ir6.6o 

April  . . 

ii 

X 

.0483 

= 

i-93 

it 

= 

102.29 

May. . . . 

ii 

X 

.0283 

= 

1. 13 

it 

— 

59-89 

June.. .. 

it 

X 

.025 

— 

I. OO 

ii 

= 

53-oo 

July.... 

a 

X 

.012 

= 

•47 

<( 

- 

24.91 

Aug.. . . 

a 

X 

.0083 

= 

•33 

It 

17.49 

Sept. . . . 

<( 

X 

.OIO 

= 

.40 

a 

21.20 

Oct 

a 

X 

.015 

= 

.60 

tt 

: - 

31.80 

Nov. . . . 

it 

X 

.040 

= 

1.60 

ft 

= 

84.80 

Dec 

u 

X 

■0533 

= 

2.14 

a 

= 

113.42 

Total,  16.00  inches.  Mean,  70.67  cu.  ft 


57.  Ordinary  Flow  of  Streams. — Mr.  Leslie  has 
proposed*  an  arbitrary  rule  for  computing  the  “average 
summer  discharge”  or  “ordinary”  flow  of  a stream,  from 
the  daily  gaugings,  as  follows : 

“ Range  the  discharges  as  observed  daily  in  their  order 
of  magnitude. 

“Divide  the  list  thus  arranged  into  an  upper  quarter,  a 
middle  half,  and  a lower  quarter. 

“The  discharges  in  the  upper  quarter  of  the  list  are  to  be 
considered  as  floods , and  in  the  lower  quarter  as  minimum 
flows. 

“For  each  of  the  gaugings  exceeding  the  average  of  the 
middle  half,  including  flood  gaugings,  substitute  the  average 
of  the  middle  half  of  the  list,  and  take  the  mean  of  the 
whole  list,  as  thus  modified,  for  the  ordinary  or  average 
discharge , exclusive  of  flood- waters.” 

This  rule  applied  to  a number  of  examples  of  actual 
measurements  of  streams  in  hilly  English  districts  gave 
computed  ordinary  discharges  ranging  from  one-fourth  to 


* Minutes  of  Proceedings  of  Institution  of  Civil  Engineers,  Yol.  X,  p 327. 


TABLES  OF  FLOW. 


81 


one-third  of  the  measured  mean  discharge , including 
floods. 

The  ordinary  flow  of  New  England  streams  is,  at  an 
average,  equivalent  to  about  one  million  gallons  per  day 
per  square  mile  of  drainage  area,  which  expressed  in  cubic 
feet,  .equals  about  ninety -two  cubic  feet  per  minute  per 
square  mile. 

The  above  computation  for  the  average  flow  in  low  cycle 
years  gives  a little  less  than  eight-tenths  of  this  amount,  or 
seventy-one  cubic  feet  per  minute  per  square  mile  as  the 
average  flow  throughout  the  year,  and  a little  less  than  one- 
fourtli  this  amount  as  the  minimum  monthly  flow.* 

58.  Tables  of  Flow  Equivalent  to  Given  Depths 
of  Rain. — To  facilitate  calculations,  tables  giving  the 
equivalents  of  various  depths  of  monthly  and  annual  rain- 
falls, in  even  continuous  flow,  in  cubic  feet  per  minute  per 
acre,  and  per  square  mile,  are  here  inserted. 

Greater  or  less  numbers  than  those  given  in  Tables  22 
and  28  may  be  found  by  addition,  or  by  moving  the  decimal 
point ; thus,  from  Table  22,  for  40.362  inches  depth,  take 
Depth,  30  inches  = 1590.204  cu.  ft. 


IO 

66 

— S3°.°68 

66 

•3 

66 

= IS-9°2 

66 

.06 

66 

= 3.180 

66 

.002 

66 

: : .106 

66 

40.362  inches  = 2139.460  cu.  ft. 


To  reduce  the  flows  in  the  two  tables  to  equivalent  vol- 
umes of  flow  for  like  depths  of  rain  in  ohe  day,  divide  the 
flows  in  Table  22  by  30.4369  (log.  = 1.483400),  and  divide 
the  flows  in  Table  23  by  365.2417  (log.  = 2.562581). 

* Some  useful  data  relating  to  the  flow  of  certain  British  and  Continental 
streams  may  be  found  in  Beardmore’s  “ Manual  of  Hydrology,”  p.  149  (Lon- 
don, 1862). 


82 


FLOW  OF  STREAMS. 


TABLE  No.  2 2. 

Equivalent  Volumes  of  Flow,  for  given  Depths  of  Rain  in 

One  Month.* 


Depths  of  Rain 
in  One  Month. 

Equivalent  Flow  in 
Cubic  Feet  per 
Minute  per  Acre. 

Equivalent  Flow  in  Cu- 
bic Feet  per  Minute 
per  Square  Mile. 

Equivalent  Flow  in  Cu- 
bic Feet  per  Month  per 
Square  Mile. 

Inches . 

.OI 

.00083 

•530 

23*232 

.02 

.00166 

1.060 

46,464 

•03 

.00248 

I-59° 

69,696 

.04 

.00331 

2.120 

92,928 

•°5 

.00414 

2.650 

1 16, 160 

.06 

.00497 

3-i8° 

139*392 

.07 

.00580 

3-7io 

162,624 

.08 

.00662 

4.240 

185,856 

.09 

.00745 

4.770 

209,088 

.1 

.00828 

5-3007 

232,320 

.2 

.01656 

10.6014 

464,640 

•3 

.02484 

15.9020  * 

696,960 

•4 

•°3312 

21.2027 

929,280 

•5 

.04140 

26.5034 

1, 161,600 

.6 

.04968 

31.8041 

1,393,920 

•7 

.05796 

37.1048 

1,626,240 

.8 

.06624 

42.4054 

1,858.560 

•9 

•07452 

47.7061 

2,090,880 

1.0 

.0828 

53.0068 

2*323*200 

2 

.1656 

106.0136 

4,646,400 

3 

.2484 

159.0204 

6,969,600 

4 

•3312 

212.0272 

9,292,800 

5 

.4140 

265.0340 

11,616,000 

6 

.4968 

318.0408 

13*939*200 

7 

.5796 

371.0476 

16,262,400 

8 

.6624 

424.0544 

18,585,600 

9 

•7452 

477.0612 

20,908,800 

10 

.828 

530.068 

23,232,000 

20 

1.656 

1060.136 

46,464,000 

3° 

2.484 

1590.204 

69,696,000 

* One  month  is  taken  equal  to  30.4869  days. 


TABLES  OF  FLOW. 


83 


TABLE  No.  2 3. 

Equivalent  Volume  of  Flow,  for  given  Depths  of  Rain  in 

One  Year.* 


Depths  of  Rain 
in  One  Year. 

Equivalent  Flow  in 
Cubic  Feet  per 
Minute  per  Acre. 

Equivalent  Flow  in  Cu- 
bic Feet  per  Minute 
per  Square  Mile. 

Equivalent  Flow  in  Cu- 
bic Feet  per  Year  per 
Square  Mile. 

Inches * 

.OI 

.000069 

.0442 

23,232 

.02 

.000x38 

.0883 

46,464 

•°3 

.000207 

•1325 

69,696 

.04 

.000276 

.1767 

92,928 

.05 

.000345 

.2209 

x 16, 160 

.06 

.000414 

.2650 

I39,392 

.07 

.000483 

.3092 

162,624 

.08 

.000552 

•3534 

185,856 

.09 

.000621 

•3976 

209,088 

.1 

.00069 

.4417 

232,320 

.2 

.00138 

.8834 

464,640 

•3 

.00207 

I-3252 

696,960 

•4 

.00276 

1.7669 

929,280 

•5 

•00345 

2.2086 

1, 161,600 

.6 

.00414 

2.6503 

I>393>92° 

•7 

.00483 

3.0921 

1,626,240 

.8 

.00552 

3-5338 

^858,560 

•9 

.00621 

3-9755 

2,090,880 

1.0 

.0069 

4.4172 

2,323,200 

2 

.0138 

8.8345 

4,646,400 

3 

.0207 

13-2517 

6,969,600 

4 

.0276 

17.6689 

9,292,800 

5 

•0345 

22.0862 

1 1,616,000 

6 

.0414 

26.5034 

I3>939?2oo 

7 

.0483 

30.9206 

16,262,400 

8 

•°552 

35-3379 

18,585,600 

9 

.0621 

39-755 1 

20,908,800 

10 

.069 

44.1723 

23,232,000 

20 

.138 

88.3447 

46,464,000 

30 

.207 

132.517° 

69,696,000 

40 

.276 

176.6894 

92,928,000 

5° 

•345 

220.8617 

1 16, 160,000 

60 

.414 

265.0340 

I39>392,°oo 

* One  year  is  taken,  equal  to  365  days,  5 hours,  49  minutes. 


83a 


FLOW  OF  STREAMS, 


TABLE  No.  23  a. 

Statistics  of  Flow  of  Sudbury  River,  Mass. 
1875  to  1894. 

Area  of  Watershed  75.2  Square  Miles. 


Mean. 


Min. 


Max. 


Rainfall,  inches  per  year,  (74  years), 

Monthly  flow,  cubic  feet  per  second  per  square  mile, 

Percentage  of  yearly  rain  flowing,  

Inches  of  rain  flowing,  yearly  (74  years), 

Minimum  flow  in  any  week,  cubic  feet  per  second  per  sq.  mile, 
Maximum  flow  in  any  day,  do.  do.  do. 

Rate  of  flow  in  August,  September,  and  October,  cubic  feet, 

per  second  per  square  mile, 

Annual  evaporation  from  water  surface,  inches  depth, 
Maximum  evaporation  in  any  month,  inches  depth, 

Millions  of  gallons,  per  square  mile  per  day, 


47.00 

1-637 

48.23 

22.67 


536 

20 

058 


27.20 
.068 
3i-9 
11. 19 
.036 


.068 

34-05 

-044 


do. 

do. 

do. 

in  May, 

do. 

do. 

do. 

in  June,  . 

do. 

do. 

do. 

in  July, 

do. 

do. 

do. 

in  August, 

do. 

do. 

do. 

in  September, 

do. 

do. 

do. 

in  October, 

do. 

do. 

do. 

in  November, 

1. 174 

•5H 

.488 

•x75 

.185 

.062 

.289 

.055 

.247 

.044 

•503 

.071 

.859 

•175 

67.72 

7.448 

62.2 

35-75 


43.00 

3-515 

43-63 

7-50 

4.814 

2.883 

^338 

•634 

.476 
1. 155 
2.272 

2758 


TABLE  No.  23b. 

Percentage  of  Rainfall  flowing  from  the  Sudbury  Basin. 


Year. 

January. 

February. 

March. 

April. 

May. 

June. 

July. 

August. 

September. 

October. 

November. 

December. 

1875 

7.60 

76.54 

76-52 

162.94 

59-52 

24.05 

16.05 

12.77 

10.44 

23.75 

46.54 

110.74 

1876 

62.68 

54.20 

106.47 

135-41 

73-51 

18.77 

3-57 

42.03 

6.89 

18.61 

32-58 

22.35 

1877 

36.50 

206.90 

102.74 

120.29 

67.04 

42.52 

12.20 

5-87 

31  -89 

13-24 

42.17 

264 -37 

1878 

57-32 

66 . 50 

x33-42 

48.48 

250.15 

22.48 

7-7x 

12.22 

21.46 

x4-35 

41.60 

89.01 

1879 

50.40 

77-37 

80.86 

II4.06 

125.84 

18.82 

7.14 

10.83 

12.94 

x5  -57 

13.24 

18.99 

l88o 

57-43 

76.82 

75.80 

66.62 

51 .22 

X4-52 

5 • x4 

5-42 

8.86 

4-97 

20.35 

11  -33 

Mean  

45-32 

93.06 

95-97 

IO7.96 

106.21 

23.58 

8.64 

14.86 

15-41 

15.08 

32.75 

86. 13 

Minimum 

7 60 

54.20 

75.80 

48.48 

51.22 

14.52 

3-57 

5-42 

6.89 

4-97 

13-24 

”•33 

Maximum 

Ratio  of  monthly 

62.68 

206.90 

133-42 

162.94 

260. 15 

42.52 

16.05 

42.03,31.89 

23-75 

46.54 

26437 

mean 

0.84 

x-73 

1.79 

2.02 

1.98 

0-44 

0. 16 

0.28 

0.29 

0.2S 

0.61 

1 60 

TABLES  OF  FLOW, 


83 1 


TABLE  No.  23c. 

Run-off  of  the  Sudbury  River  Watershed,*  1875  to  1899. 

(Area  of  Watershed  75.2  Square  Miles  and  6.5  per  cent.  Water  Surface  in  1899.) 

CUBIC  FEET  PER  SECOND  PER  SQUARE  MILE. 


Year. 

January. 

February. 

March. 

April. 

May. 

June. 

July, 

August. 

September. 

October. 

November. 

| December. 

Av.  Mo. 

1875 

0.159 

2-3!5 

2.482 

CO 

1.838 

1.346 

O.497 

0.612 

0.321 

I .OOO 

2.015 

0.903 

1.504 

I876 

0-995 

2.116 

6.862 

5-°94 

I.761 

o-343 

0.283 

O.627 

O.285 

0.361 

1.683 

0.702 

1-756 

1877 

I. OI9 

1-469 

7 '448 

3-703 

2.153 

0.924 

0.312 

O.187 

0.092 

O.Q77 

2.193 

I-995 

1.878 

1878 

2.800 

3-814 

5.426 

2.516 

2.158 

0.782 

0.199 

0.736 

0.249 

0-799 

2.619 

4.916 

2.246 

1879 

1.083 

2.647 

3.605 

4.821 

1.723 

0.640 

O.243 

0.6ll 

0.218 

0.109 

0.318 

0.716 

1-383 

1880 

1-733 

2.765 

2. 126 

1.808 

O.  796 

0.271 

0.273 

O.184 

0.124 

0.157 

0.318 

0.271 

0.895 

l88l 

0. 642 

2.392 

6.195 

2.392 

1-493 

2.070 

O.428 

0.229 

0.305 

O.287 

0.611 

I-I99 

1515 

l882 

1.920 

3.718 

4-392 

1.342 

1.998 

0.818 

0.133 

0.086 

O.474 

0.463 

0-324 

0.487 

*•334 

1883 

0.518 

1.598 

2.492 

2.088 

1.450 

0.464 

O.I78 

0.122 

O.I4I 

0.288 

0.317 

0.299 

1.824 

1884 

1 -54° 

4-397 

5-857 

4-4*5 

i-594 

0.644 

0.346 

0-397 

0.068 

0.129 

0.271 

I-43I 

x-747 

1885 

I.QIO 

2.095 

2-433 

2.808 

2.067 

0.659 

O.O96 

O.372 

O.187 

O.5I9 

1.822 

1. 816 

*•393 

l886 

2.260 

7.428 

3-185 

3- 01 3 

1.114 

0.314 

0.179 

O.I46 

0.182 

0.225 

1. 04 1 

1-578 

1.682 

1887 

4.006 

.4-377 

4-437 

4-053 

1.561 

0.640 

O.  I78 

0-331 

O.I72 

0.294 

0.570 

o-995 

1-785 

1888 

I.629 

3. 011 

5.009 

4-°93 

2.526 

0.652 

O.  l82 

0-587 

I.786 

3-093 

4.267 

4.708 

2.626 

I889 

4-305 

1.850 

2.071 

2. 182 

1.361 

1. on 

O.980 

2.216 

I.274 

I.9O3 

3-003 

3-467 

2.140 

I89O 

1. 94 1 

2.366 

5-636 

2.900 

2.114 

0.878 

O.  l66 

0.204 

O.708 

3-515 

1.879 

I-54X 

1.989 

189I 

4.669 

5-393 

6.891 

3- 7°9 

0.901 

0.639 

O.23I 

0.252 

O.3I4 

0.325 

0.472 

O.842 

2.034 

1892 

2.893 

i-459 

3.025 

1.348 

1.947 

0.662 

c-331 

o-433 

0-355 

O.I95 

1.079 

0.750 

1.209 

1893 

O.67I 

2.386 

5.021 

3.288 

4.461 

0.680 

0.244 

0.280 

O.167 

0-343 

0-493 

1.232 

1.604 

1894 

I.O72 

1 533 

3-463 

2-538 

1.299 

0.648 

0.249 

0.324 

0.231 

o-579 

1.293 

I .108 

1. 192 

1895 

1.600 

0.837 

3-728 

3.892 

0.984 

0.269 

0-357 

0-354 

0.138 

2-134 

4.296 

2-757 

1.782 

I896 

1.677 

4.140 

5-933 

2.312 

0-557 

0.617 

o-i47 

0.088 

0.600 

0.916 

1 .020 

1.017 

1-576 

1897 

I-3°7 

1.651 

3.968 

2-344 

1.416 

1.488 

1. 018 

0.914 

0.282 

0.145 

1.407 

2-451 

t-533 

I898 

2-535 

4.676 

4.029 

2.831 

1.927 

0.820 

o.357 

1. 712 

0.571 

i-795 

3-073 

2.783 

2.244 

1899 

3-54i 

2.137 

6.507 

3.900 

0.790 

0.102 

0.030 

-•054 

O.I45 

0.179 

0-474 

0.340 

1.506 

Average 

i-937 

2.904 

4.489 

3.124 

1.680 

o-735 

0.305 

0.478 

0.376 

0.829 

1.474 

1.612 

1-655 

Max. 

4.669 

7.428 

7.448 

5-094 

4.461 

2.070 

1. 018 

2.216 

I.786 

3-515 

4.296 

4.916 

2.626 

Min. 

0.159 

0.837 

2.071 

1.342 

0-557 

O.  102 

0.030 

0. 

0.068 

0.109 

0.271 

0.271 

0.824 

* Boston,  F.  P.  Stearns,  Chief  Engineer  Metropolitan  Water  Board. 

The  Water  surfaces  were  increased  from  time  to  time,  from  1.9  per  cent,  in  1875  to  6.5  per 
cent,  in  1899. 


CHAPTER  Y. 

STORAGE  AND  EVAPORATION  OF  WATER 
STORAGE. 

59.  Artificial  Storage. — The  fluctuations  of  tlie  rain- 
fall, flow  of  streams,  and  consumption  of  water  in  the  differ- 
ent seasons  of  the  year,  require  almost  invariably  that,  for 
gravitation  and  hydraulic  power  pumping  supplies , there 
shall  be  artificial  storage  of  the  surplus  waters  of  the  sea- 
sons of  maximum  flow,  to  provide  for  the  draught  during 
the  seasons  of  minimum  flow.  A grand  exception  to  this 
general  rule  is  that  of  the  natural  storage  of  the  chain  of 
great  lakes  that  equalizes  the  flow  of  the  St.  Laurence 
River,  which  furnishes  the  domestic  water  supply  of  the 
City  of  Montreal  and  the  hydraulic  power  to  pump  the  same 
to  the  reservoir  on  the  mountain. 

When  the  mean  annual  consumption,  whether  for  do- 
mestic use,  or  for  power  and  domestic  use  combined  is 
nearly  equal  to  the  mean  annual  flow  of  the  supplying 
watershed,  the  question  of  ample  storage  becomes  of  su- 
preme importance.  The  cliief  river  basins  of  Maine  present 
remarkable  examples  of  natural  storage  facilities,  since 
they  have  from  six  to  thirteen  per  cent.,  respectively,  of 
their  large  watershed  areas  in  pond  and  lake  surfaces. 

60.  Losses  Incident  to  Storage. — There  are  losses 
incident  to  artificial  storage  that  must  not  be  overlooked ; 
for  instance,  the  percolation  into  the  earth  and  through  the 
embankment,  evaporation  from  the  reservoir  surface  and 
from  the  saturated  borders,  and  in  some  instances  constant 
draught  of  the  share  of  riparian  owners. 


EMBANKMENT:  IMPOUNDING  AND  DISTRIBUTING  RESERVOIR,  NORWICH,  CONN. 


SUDBURY  DAM,  BOSTON,  W.  W„  Page  84^ 


RIGHTS  OF  RIPARIAN  OWNERS. 


85 


61.  Sub-strata  of  the  Storage  Basin. — The  structure 
of  the  impounding  basin,  especially  when  the  water  is  to 
fill  it  to  great  height  above  the  old  bed,  is  to  be  minutely 
examined,  as  the  water  at  its  new  level  may  cover  the  edges 
of  porous  strata  cropping  out  above  the  channel,  or  may 
find  access  to  fissured  rocks,  either  of  which  may  lead  the 
storage  by  subterranean  paths  along  the  valley  and  deliver 
it,  possibly,  a long  distance  down  the  stream,  or  in  a mul- 
titude of  springs  beyond  the  impounding  dam.  If  the 
water  carries  but  little  sediment  of  a silting  nature,  this 
trouble  will  be  difficult  to  remedy,  and  liable  to  be  serious- 
ly chronic. 

62.  Percolation  from  Storage  Basins.— Percolation 
through  the  retaining  embankment  is  a result  of  slighted  or 
unintelligent  construction,  and  will  be  discussed  when  con- 
structive features  are  hereafter  considered.  (See  Reservoir 
Embankments.) 

63.  Rights  of  Riparian  Owners.  — The  rights  of 
riparian  owners,  ancient  as  the  riparian  settlements,  to  the 
use  of  the  water  that  flows,  and  its  most  favored  piscatory 
produce,  is  often  as  a thorn  in  the  impounder’s  side.  What 
are  those  rights  ? The  Courts  and  Legislatures  of  the  man- 
ufacturing States  have  wrestled  with  this  question,  their 
judges  have  grown  hoary  while  they  pondered  it,  and  their 
attorneys  have  prospered,  and  yet  who  shall  say  what 
riparian  rights  shall  be,  until  the  Court  has  considered  all 
anew. 

Beloe  mentions*  that  it  is  a “common  (British)  rule  in 
the  manufacturing  districts  to  deduct  one-sixth  the  average 
rainfall  for  loss  by  floods,  in  addition  to  the  absorption  and 
evaporation,  and  then  allow  one-third  of  the  remainder  to 


* Beloe  on  Reservoirs,  p.  12.  London,  1872. 


86 


STORAGE  AND  EVAPORATION  OF  WATER. 


the  riparian  owners,  leaving  two-thirds  to  the  impounders. 
In  some  instances  this  is  varied  to  the  proportion  of  one- 
quarter  to  the  former  and  three-quarters  to  the  latter.” 

The  question  can  only  be  settled  equitably  upon  the 
basis  of  daily  gaugings  of  How,  through  a long  series  of 
years.  A theoretical  consideration  involves  a thorough 
investigation  of  its  geological,  physical,  and  meteorological 
features.  There  is  no  more  constancy  in  natural  flow  at  any 
season  than  in  the  density  of  the  thermometer’s  mercury. 
The  flow  increases  as  the  storms  are  gathered  into  the  chan- 
nel, it  decreases  when  the  bow  has  appeared  in  the  heavens  ; 
it  increases  when  the  moist  clouds  sweep  low  iu  the  valleys, 
it  decreases  under  the  noonday  sun  ; it  increases  when  the 
shadows  of  evening  fall  across  the  banks,  it  decreases  when 
the  sharp  frosts  congeal  the  streams  among  the  hills. 

64.  Periodical  Classification  of  Riparian  Rights. 
— The  riparian  rights  subject  to  curtailment  by  storage 
might  be  classified  by  periods  not  greater  than  monthly, 
though  this  is  rarely  desirable  for  either  party  in  interest, 
but  they  should  be  based  upon  the  most  reliable  statistics 
of  monthly  rainfall,  evaporation,  and  flow,  as  analyzed  and 
applied  with  disciplined  judgment  to  the  particular  locality 
in  question. 

65.  Compensations. — In  the  absence  of  local  statistics 
of  flow,  it  may  become  necessary,  in  settling  questions  of 
riparian  rights,  or  adjusting  compensation  therefor,  to  esti- 
mate the  periodic  flow  of  a stream  by  some  such  method  as 
is  suggested  above  iu  the  general  discussion  upon  the  flow 
of  streams,  after  which  it  remains  for  the  Court  to  fix  the 
proportion  of  the  flow  that  the  impounders  may  manipulate 
for  their  own  convenience  in  the  successive  seasons,  and  the 
proportion  that  is  to  be  passed  down  the  stream  regularly 
or  periodically. 


EVAPORATION  PHENOMENA. 


87 


EVAPORATION. 

66.  Loss  from  Reservoir  by  Evaporation.— Losses 
by  evaporations  from  the  surfaces  of  shallow  storage  reser- 
voirs, lakes  and  ponds  are,  in  many  localities,  so  great  in  the 
summer  and  autumn  that  their  areas  are  omitted  in  compu- 
tations of  water  derivable  from  their  watersheds.  This  is  a 
safe  practice  in  dry,  warm  climates,  in  which  the  evapora- 
tions from  shallow  ponds  may  nearly  or  quite  equal  the 
volume  of  rain  that  falls  directly  into  the  ponds.  Marshy 
margins  of  ponds  are  profligate  dispensers  of  vapor  to  the 
atmosphere,  usually  exceeding  in  this  respect  the  water 
surfaces  themselves. 

67.  Evaporation  Phenomena.  — The  measure  of 
evaporation  from  a water  surface  is  the  resultant  of  forces 
of  vaporiza  tion  acting  upon  the  water  and  upon  the  moisture 
in  the  air  near  the  water.  The  constituents  of  water  may, 
with  certain  changes  of  temperature,  change  their  state  of 
existence  from  that  of  liquid  to  vapor,  vapor  to  liquid  or 
liquid  to  solid,  and  solid  to  vapor. 

Each  new  increment  of  heat  entering  the  particles  of 
mist  in  the  atmosphere  or  liquid  in  the  lake  increases  their 
gaseous  activities  and  diffusive  powers,  and  the  rapidities 
of  vaporizations  of  liquid,  snow,  ice,  and  the  moisture  of 
the  air  depends  upon  their  respective  absorption  rates  of 
heat.  The  volume  of  vapor  diffused  from  water  surfaces 
into  the  air  greatly  exceeds,  usually,  the  diffusion  from  the 
adjacent  air  and  condensation  into  the  water,  not  including 
the  depositions  of  showers.  This  difference,  the  net  loss  of 
the  water,  is  the  rate  or  volume  of  evaporation  from  the 
water.  The  resultant  varies  in  weight  with  the  difference 
between  the  dynamical  force  of  the  vapor  in  the  water  and 
the  like  force  of  the  vapor  in  the  air,  due  to  their  respec- 


88 


STORAGE  AND  EVAPORATION  OF  WATER. 


tive  temperatures,  and  further  to  the  relative  dryness  and 
motion  of  the  receptive  air  sweeping  across  the  water. 

The  atmosphere  lias,  however,  for  each  given  tempera- 
ture a limit  of  power  to  retain  vapor.  When  winds  blow 
briskly  across  a reservoir,  large  volumes  of  un  saturated  air 
may  be  presented  to  receive  the  diffused  vapor  from  the 
water,  while  the  wave  agitation  aids  at  the  same  time  the 
escape  of  vapor  from  the  ruffled  water  surface,  giving  a 
large  rate  of  net  evaporation. 

68.  Evaporation  from  Water. — Mr.  Fitzgerald’s 
careful  experimental  measures*  of  evaporation  from  water 
surfaces  at  Chestnut  Hill  reservoir  in  Boston,  was  as  follows : 


TABLE  No.  2 4. 

Experimental  and  Estimated  Monthly  Evaporation. 


£ 

Feb. 

Mar.  1 

1 

April. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

> 

z 

Dec. 

Total. 

Measured  evaporation  in 
inches 

o.  90 

1.20 

1.80 

3.10 

4.61 

5.86 

6.28 

5-49 

4.09 

2.95 

1.63 

1.20 

39- 11 

Theoretical  mean  evapor- 

3.82 

ation  in  inches 

0.98 

I. OI 

i-45 

2.39 

5-34 

6.21 

5-97 

4.S6 

3-47 

2.24 

i-38 

39.12 

Percentage  of  theoretical 
mean  per  cent 

2.51 

2.58 

3-71 

6.11 

9.76 

13-65 

15.87 

15.26 

12.42 

8.87 

5-73 

3-53 

100.00 

Theoretical  mean  daily, 

inches 

.0316 

.0361 

.0467 

.0796 

.1232 

.1980 

.2003 

.1926 

.1620 

. III9 

.O747 

•0445 

39.12 

Mr.  Fitzgerald’s  maximum  recorded  daily  evaporation 
from  the  reservoir  surface  was  on  June  23, 1885,  when  from 
tanks  Nos.  1,  2,  and  3,  the  evaporations  were  0.57,  0.64, 
and  0.58  inches  respectively,  the  mean  temperatures  of  the 
waters  being  nearly  70°  Fah. 


Evaporation,  Trans.  Am.  Soc.  Civ.  Engrs.,  Vol.  XV.,  p.  581. 


EVAPORATION  FROM  EARTH. 


89 


TABLE  No.  24. 

Evaporation  from  Water  at  Emdrup,  Denmark. 

N.  Lat.  55°4i"  ; E.  Long  i2034"  from  Greenwich. 


Year. 

Jan. 

Feb. 

£ 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

> 

0 

Dec. 

Total. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

1849 

1. 1 

o-3 

1.8 

2.5 

4.1 

5-8 

4-7 

4.0 

2.6 

1. 1 

0.9 

0.6 

29-5 

1850 

1. 1 

o-3 

1.2 

1-7 

4-5 

5-6 

4.8 

4.8 

2.4 

1.6 

0.9 

0.2 

29.1 

1851 

o-S 

0.4 

O.7 

i-7 

4.2 

4.8 

5-7 

5-i 

2.7 

>•5 

0.6 

o-5 

28.4 

1852 

O.7 

°-5 

0.8 

2.4 

3.8 

4.6 

6.4 

4-5 

2.7 

i-7 

0.8 

o-5 

29.4 

1853 

0.5 

0.1 

0.7 

1.0 

4*1 

6.2 

5-i 

4.2 

2.8 

1. 1 

0.6 

o-5 

26.9 

1854 

o-5 

0.9 

0.9 

3-2 

3-3 

4-5 

5-2 

4-3 

2.6 

1.2 

°*7 

0.6 

27.9 

1855 

1.0 

1. 1 

o-5 

1.2 

2.6 

4.1 

4-7 

4.1 

2.8 

1.4 

°-9 

0.7 

25-1 

1856 

o-5 

o-5 

1.2 

2.1 

2.8 

4.6 

4-3 

4.0 

2.0 

0.9 

0.6 

o-5 

24.0 

1857 

0.7 

0.6 

0.6 

i-4 

4-1 

6.6 

5-9 

4-3 

3-2 

x-4 

0.7 

0.4 

29.9 

1858 

0.4 

0.7 

1.2 

3-i 

5-1 

6.1 

4.9 

5-6 

2.8 

1.6 

0.7 

0.4 

30.6 

1859 

o-3 

o-5 

0.7 

1.9 

4-3 

5-8 

5-3 

3.8 

1.8 

1.0 

0.7 

o-3 

26.4 

Mean  . . 

0.7 

0.5 

o-9 

2.0 

3-9 

5-3 

5-2 

4.4 

2.6 

i-3 

0.7 

o-5 

27.9 

Ratio  . . 

•3QI 

.215 

•387 

.860 

• I*592 

2.323 

2.237 

1.892 

1.118 

•559 

.301 

.215 

Mean  Evaporation  from  Short  Grass,  1852  to  1859  inclusive. 

Mean.. | 0.7  | 0.8  | 1.2  | 2.6  | 4.1  | 5.5  | 5.2  | 4.7  | 2.8  | 1.3  | 0.7  | 0.5  | 30.1 

Mean  Evaporation  from  Long  Grass,  1849  t0  *856  inclusive. 

Mean..)  0.9  | 0.6  | 1.4  | 2.6  | 4.7  | 6.7  | 9.3  | 7.9  | 5.2  | 2.9  | 1.3  | 0.5  | 44.0 


Mean  Rainfall  at  same  Station,  1848  to  1859  inclusive. 
Mean..!  1.5  I 1.7  l 1.0  I 1.6  I 1.5  I 2.2  I 2.4  I 2.4  I 2.0  I 2.3  I 1.8 


TABLE  No.  2 5. 

69.  Evaporation  from  Earth. — Mean  Evaporation  from 
Earth,  at  Bolton  Le  Moors,*  Lancashire,  Eng.,  1844  to 

1853,  INCLUSIVE. 

Lat.  53°3o"  N. ; Height  above  the  Sea,  320  Feet. 


c 

c 3 

Feb. 

c3 

S 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Total. 

Mean  . . 
Ratio. . . 

O.64 

.299 

o-95 

•444 

1.59 

•739 

2 59 

1. 212 

4-38 

2.049 

3-84 

1.796 

4.02 

I.887 

3.06 

I-43I 

2.02 

•945 

1.28 

•599 

0.8l 

•379 

O.47 

.220 

25-65 

Mean  Rainfall  at  same  Station,  1844  to  1853  inclusive. 

Mean..  I 4.63  | 4.03  j 2.25  | 2.22  | 2.23  1 4 07  | 4.32  | 4.77  | 3.79  | 5.07  | 4.64  | 3.94  | 45.96 


* Beardmore’s  Hydrology,  p.  325. 


90 


STORAGE  AND  EVAPORATION  OF  WATER. 


Mean  Evaporation  from  Earth,  at  Whitehaven,  Cumberland, 
Eng.,  1844  to  1853  inclusive. 

Lat.  54  30"  N.  ; Height  above  the  Sea,  90  feet. 


Jan. 

Feb. 

Mar. 

a 

<5 

May. 

June. 

July. 

Aug. 

1 Sept. 

1 

Oct. 

Nov. 

Dec. 

Total.  ' 

1 

Mean. 
Ratio  . . 

0.95 

•390 

I. OI 

•415 

i-77 

.727 

2.71 

1.113 

4.II 

I.689 

4.25 

1.746 

4.13 

1.697 

3*29 

1-352 

2.96 

I.2l6 

I.76 

•723 

1-25 

•513 

1.02 

.419 

29.21 

Mean  Rainfall. at  same  Station,  1844  to  1853  inclusive. 

Mean..  | 5.1  | 3.4  | 2.5  j 2.2  | 1.9  | 3-*  [ 4-3  | 4-3  | 3-i  1 5-3  : 4-5  [ 3-8  | 43-5 


70.  Examples  of  Evaporation.— Charles  Greaves, 
Esq.,  conducted  a series  of  experiments  upon  percolation 
and  evaporation,  at  Lee  Bridge,  in  England,  continuously 
from  1860  to  1873,  and  lias  given  the  results  * to  the  Insti- 
tution of  Civil  Engineers.  The  experiments  were  on  a large 
scale,  and  the  very  complete  record  is  apparently  worthy 
of  full  confidence. 

The  evaporation  boxes  were  one  yard  square  at  the  sur- 
face and  one  yard  deep.  Those  for  earth  were  sunk  nearly 
hush  in  the  ground,  and  that  for  water  floated  in  the 
river  Lee.  The  mean  annual  rainfall  during  the  time  was 
27.7  inches.  The  annual  evaporations  from  soil  were,  mini- 
mum 12.067  inches ; maximum  25.141  inches ; and  mean 
19.534  inches: — from  sand , minimum  1.425  inches;  maxi- 
mum 9.102  inches;  and  mean  4.648  inches: — from  water , 
minimum  17.332  inches ; maximum  26.933  inches ; and 
mean  22.2  inches. 

Some  experimental  evaporators  were  constructed  at 
Dijon  on  the  Burgundy  canal,  and  are  described  in  Annales 
des  Ponts  et  Cliausses.  They  are  masonry  tanks  lined 
with  zinc,  eight  feet  square  and  one  and  one-third  feet  deep, 


* Trans.  Inst.  Civil  Engineers,  1876,  Vol.  XLV,  p.  33. 


RATIOS  OF  EVAPORATION. 


91 


and  are  sunk  in  the  ground.  From  1846  to  1852,  there  was 
a mean  annual  evaporation  of  26.1  inches  from  their  water 
surfaces  against  a rainfall  of  26.9  inches.  At  the  same  time 
a.  small  evaporator,  one  foot  square,  placed  near  the  larger, 
gave  results  fifty  per  cent,  greater. 

Observations  of  evaporation  from  a water  surface  at  the 
receiving  reservoir  in  New  York  indicated  the  mean  annual 
evaporation  from  1864  to  1870  inclusive  as  39.21  inches, 
which  equaled  81  per  cent,  of  the  rainfall. 

On  the  West  Branch  of  the  Croton  River,  an  apparatus* 
was  arranged  for  the  purpose  of  measuring  the  evaporation 
from  water  surface,  consisting  of  a box  four  feet  square  and 
three  feet  deep,  sunk  in  the  earth  in  an  exposed  situation 
and  filled  with  water.  The  mean  annual  evaporation  was 
found  to  be  24.15  inches,  or  about  fifty  per  cent,  of  the 
rainfall.  The  observations  were  made  twice  a day  with 
care.  The  maximum  annual  evaporation  was  28  inches. 

Evaporations  from  the  surface  of  water  in  shallow  tanks 
are  variously  reported  as  follows  : 


At 

Cambridge,  Mass., 

one  year, 

56.00 

inches  depth, 

66 

Salem,  “ 

tt  it 

56.00 

66 

66 

66 

Syracuse,  N.  Y., 

ti  It 

50.20 

66 

66 

66 

Ogdensburgh,  N.  Y., 

tt  tt 

49-37 

66 

66 

u 

Dorset,  England, 

three  “ 

25.92 

66 

66 

u 

Oxford,  “ 

five  “ 

3I>04 

66 

66 

u 

Demerara, 

three  “ 

35-12 

66 

66 

u 

Bombay, 

five  “ 

82.28 

66 

66 

71,  Ratios  of  Evaporation. — In  the  eastern  and  mid- 
dle United  States,  the  evaporation  from  storage  reservoirs, 
having  an  average  depth  of  at  least  ten  feet,  will  rarely 
exceed  eighty  per  cent,  of  the  rainfall  upon  their  surface 

* Vide  paper  on  “ Flow  of  the  VVest^Branch  of  the  Croton  River,”  by  J.  Jas 
R.  Croes.  Trans.  Am.  Soc.  Civ.  Engrs.,  July,  1874,  p 83. 


92 


STORAGE  AND  EVAPORATION  OF  WATER. 


The  ratio  of  evaporation  in  each  month  to  the  monthly  aver- 
age evaporation,  or  one-twelfth  the  annual  depth,  is  esti- 
mated to  be,  for  an  average,  approximately  as  follows  : 


TABLE  No.  2 6. 

Monthly  Ratios  of  Evaporation  from  Reservoirs. 


c 

•—i 

Feb. 

Mar. 

Apr. 

May. 

June. 

>> 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Mean  ratio .... 

• 3°° 

•3^8 

.426 

•732 

1.128 

I-53° 

I.83O 

1.952 

i-793 

1.055 

•558 

.378 

The  following  ratios  of  the  annual  evaporation  from 
water  surfaces  are  equivalent  to  the  above  monthly  ratios, 
and  may  be  used  as  multipliers  directly  into  the  annual 
evaporation  to  compute  an  equivalent  depth  of  rain  in 
inches  upon  the  given  surface  in  action.  Beneath  the  ratios 
are  given  the  equivalent  depths  for  each  month  of  40  inches 
annual  rain,  assuming  the  annual  evaporation  to  equal 
eighty  per  cent,  of  the  rainfall,  or  32  inches  depth. 


TABLE  No.  27. 

Multipliers  for  Equivalent  Inches  of  Rain  Evaporated. 


Jan. 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Total. 

Ratio  ot  annual  evapora- 

.0265 

.85 

•0355 

m3 

.0610 

.0988 

301 

•1273 

4.08 

. 1 525 

.1625 

.1495 

.0880 

.0465 

•03x5 

Equivalent  depth  of  rain 
— inches 

.80 

1.95 

4.88 

5 20 

4.78 

2.85 

1.49 

1. 01 

32 

72.  Resultant  Effect  of  Rain  and  Evaporation.— 

For  the  purpose  of  comparing  the  effects  upon  a reservoir 
replenished  by  rain  only,  let  us  assume  the  available  rain- 
fall to  be  eight-tenths  of  40  inches  per  annum,  and  the 
ratios  of  mean  monthly  rain,  and  the  ratios  of  annual  rain 
in  inches  depth,  to  be  as  per  the  following  table  : 


PRACTICAL  EFFECT  UPON  STORAGE. 


93 


d 

P-* 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Ratio  of  aver, 
monthly  rain 

•75 

.83 

.90 

I. IO 

1.30 

1.08 

1. 12 

1.20 

I. OO 

•95 

•93 

.84 

Ratio  of  .8  of 

annual  rain. 

.0625 

.0692 

.0750 

.O9I7 

.1083 

.0900 

.0933 

.IOOO 

.0833 

.0792 

•°775 

.0700 

Equiv.  inches 

2.67 

2.48 

ol  rain ...... 

2.00 

2.21 

2.40 

2.93 

3-47 

2.88 

2.99 

3.20 

2-53 

2 24 

Comparing,  in  the  two  last  tables,  and  their  lowest 
columns,  the  inches  of  gain  by  rainfall  upon  the  reservoir, 
supposing  the  sides  of  the  reservoir  to  be  perpendicular,  and 
the  inches  of  loss  from  the  same  reservoir  by  evaporation, 
we  note  that  the  gain  preponderates  until  June,  then  the 
loss  preponderates  until  in  November. 

73.  Practical  Effect  upon  Storage. — Since  the  prac- 
tical value  of  storage  is  ordinarily  realized  between  May 
and  November,  the  excess  of  loss  during  that  term  is, 
practically  considered,  the  annual  deficiency  from  the  reser- 
voir' chargeable  to  evaporation.  We  compute  its  maximum 
in  the  following  table,  commencing  the  summation  in  June, 
all  the  quantities  being  in  inches  depth  of  rain. 


d 

Feb. 

' 

Mar. 

Apr. 

May. 

June. 

July. 

Aug. 

a 

m 

Oct. 

Nov. 

Dec. 

Total. ' 

Gain  by  rain- 
inches  

2.00 

2.21 

2 40 

2-93 

3-47 

2.88 

2.99 

3.20 

2.67 

2-53 

2.48 

2.24 

32 

Loss  by  evapo- 
ration— inches 

.80 

■85 

I*I3 

1.95 

3.01 

-e- 

b 

00 

4-88 

5.20 

4.78 

2.82 

1.49 

1. 01 

32 

D ifference  — 
inches 

+ 1.20 

+ i-36 

+ 127 

+ 0.98 

+0.46 

— 1.20 

— I.89 

— 2.00 

— 2. 11 

0.29 

+0.99 

+1.23 

Max.  deficiency 
after  June  — 
inches 

— 1.20 

— 3-°9 

-5.09 

— 7.20 

-7-49 

—6.50 

— 5-2  7 

If  the  classification  is  reduced  to  daily  periods  instead 
of  monthly,  the  maximum  deficiency,  according  to  the 
above  basis,  will  in  a majority  of  years  exceed  eight  inches. 


93a 


STORAGE  AND  EVAPORATION  OF  WATER. 


The  following  table,  No.  27a,  is  quoted  from  the 
“Monthly  Weather  Review,”  for  September,  1888,  and  is 
by  T.  Russell,  Asst.  Prof.  U.  S.  Signal  Service.  It  is  the 
result  of  one  year’s  observations  at  the  signal  stations 
named,  the  evaporations  being  reduced  from  measures 
taken  with  a Piche  evaprometer.  Mr.  Russell  says,  “It  is 
believed  that  these  figures  represent  approximately,  the 
monthly  and  annual  evaporations  that  take  place  from  the 
surface  of  ponds,  rivers,  reservoirs,  and  lakes  in  the  vicinity 
of  the  respective  Signal  Service  stations  named.” 


TABLE  No.  2 7 a. 

Computed  Relative  Monthly  Evaporations  in  America. 


Stations  and  Districts. 

Jan.  1888. 

Feb.  1888. 

00 

00 

00 

Irt 

rt 

a 

April,  1888. 

May,  1888. 

| June,  1888. 

CO 

00 

tv. 

00 

00 

to 

< 

Sept.  1887. 

Oct.  1887. 

Nov.  1887. 

CO 

0 

0 

G 

i2  Months’ 
Evaporation. 

Precipitation 
in  1888. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

New  England. 

Portland 

1.0 

1.2 

1.8 

2.6 

1.8 

3-3 

3-8 

3-9 

3-4 

3° 

2-5 

1.4 

29.7 

59-24 

Manchester  

o.q 

1.6 

2.2 

3-3 

3-8 

5-o 

4.1 

3-3 

2-5 

2.8 

2.4 

1.4 

33-3 

46.81 

Northfield 

0.8 

1.0 

i-5 

2-3 

2-5 

3-4 

3-5 

2.7 

2-3 

1.8 

1. 1 

1.0 

23.9 

45.89 

Boston 

1.2 

1.6 

2.2 

3-4 

3-i 

4-7 

4.4 

4.0 

3-5 

2-7 

2.2 

1.4 

34-4 

45.89 

Nantucket 

1. 1 

1. 1 

1.2 

i-5 

1.8 

2.1 

3-3 

3-8 

3-4 

2.7 

1.8 

1.8 

25.6 

45-71 

New  Haven 

1. 1 

1.6 

1.8 

2.7 

2.7 

4-i 

3 7 

3-8 

31 

3.2 

2.4 

1.6 

31.8 

60.26 

New  London 

i-5 

‘•3 

i-5 

2.6 

2.8 

4.0 

3-4 

3-9 

3-2 

3-1 

2.4 

2.1 

31.8 

45.61 

Middle  Atlantic  States. 

Albany  

o.q 

1.2 

1.6 

3-3 

3-9 

4-5 

5-o 

4-7 

3-2 

3-o 

2.1 

1.4 

34-8 

44.66 

New  York  City 

i.8 

I.4 

2.0 

3-4 

3-3 

4.6 

5° 

5-2 

4-3 

4-1 

3-3 

2.2 

40.6 

52.95 

Philadelphia 

i.6 

2.  I 

2-5 

4.4 

4.0 

5-7 

5-7 

5-2 

4-3 

4.0 

3-3 

2.2 

45-o 

44.06 

Atlantic  City 

1.2 

1.6 

i-5 

2.4 

1.8 

3 b 

2.9 

3-3 

2.4 

1.8 

1.2 

*•5 

25.2 

44.14 

Baltimore  

2.0 

2.2 

2.8 

5-i 

4-7 

5-9 

6.0 

5 0 

4.4 

4-3 

3-6 

2.4 

48.1 

43-53 

Washington  City  

1.8 

i-7 

2-5 

4.2 

3-8 

6.0 

5-4 

4-9 

4- 1 

4.2 

4-5 

2-5 

45.6 

45-05 

Norfolk  

1.8 

1.6 

2-3 

3-5 

3-2 

4.2 

4.6 

3-7 

3-7 

2.9 

2-3 

1.8 

35-6 

56.64 

South  Atlantic  States. 

Charlotte 

2.6 

2.6 

4-3 

6.4 

4-5 

5-8 

4.0 

4.0 

4.6 

4.0 

3-6 

2.6 

49.0 

52.61 

Hatteras  

i.8 

1.6 

i.6 

2-5 

2.2 

3-° 

3-3 

4.1 

3-8 

3-2 

2.6 

1.6 

3T-3 

59-73 

Wilmington 

2.4 

2.2 

2-7 

3-3 

33 

4-3 

4-3 

3-i 

3-9 

3-4 

2.8 

2-7 

38.4 

55-07 

Charleston  

2-5 

2-5 

3-5 

3-7 

3-9 

4-4 

4-5 

4.8 

4.2 

4.0 

3-2 

2.5 

43-7 

49-40 

Augusta 

3*o 

2.6 

3-4 

5-3 

^.8 

5-0 

4.8 

4-5 

5-i 

4.1 

3.6 

3-i 

49  3 

49. 88 

Savannah 

3-3 

2.8 

4- 1 

4-7 

4-3 

4.6 

4.2 

4-7 

3-4 

3-9 

3-5 

2.8 

46.0 

47.06 

Jacksonville 

2.9 

2.6 

3.8 

4-3 

4.6 

5-3 

5° 

4-7 

3.8 

3-9 

3.0 

2.1 

45-7 

53-  x3 

Florida  Peninsula. 

Titusville 

3-5 

2.6 

3-3 

3-8 

3-8 

4-3 

3-8 

4-3 

4.0 

4.1 

3.6 

3-i 

44.2 

59-96 

Cedar  Keys 

3-3 

2.8 

4.0 

4.6 

4-5 

5-i 

5-0 

5-5 

4-5 

4.1 

3-5 

2.6 

49-5 

43- 13 

Key  West 

3.8 

3-7 

3-8 

4-5 

4.4 

4.8 

5-i 

5- 1 

4-7 

4-3 

3-8 

3-6 

51-6 

35-58 

Eastern  Gulf  States. 

Atlanta  

2.7 

2.6 

4.0 

6.2 

4-7 

5-o 

4-5 

4-7 

5-8 

4.6 

4-2 

2-5 

5i-5 

64.98 

Mobile 

2.6 

2-5 

2.8 

3-5 

3-7 

4.0 

4.1 

4.6 

4.6 

4.1 

3-4 

2.2 

42.1 

75-59 

Montgomery 

3-5 

3-3 

S.I 

b-5 

5-9 

5.8 

4-3 

4-5 

5-7 

4.6 

4-3 

3- 1 

56.6 

61.39 

Vicksburg 

2.1 

2-5 

3-6 

5-i 

5 7 

4.8 

4.0 

5-o 

4-7 

3-4 

4.0 

2.2 

47.1 

4S-47 

New  Orleans 

2.8 

2.8 

4.1 

3.8 

4-2 

4.1 

4.1 

4-3 

4.4 

4.6 

3-7 

2-5 

45-4 

— 

STORAGE  AND  EVAPORATION  OF  WATER. 


935 


T A BL  E N o.  2 7 a. — ( Continued .) 


Stations  and  Districts. 

Jan.  1888. 

00 

CO 

CO 

-d 

V 

ta 

Mar.  1888. 

April,  1888. 

CO 

00 

CO 

£ 

s 

June,  1888. 

July,  1887.  | 

Aug.  1887. 

Sept.  1887. 

CO 

CO 

0 

Nov.  1887. 

Dec.  1887. 

12  months’ 
Evaporation. 

Precipitation 
in  1888. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

Western  Gulf  States. 

Fort  Smith 

2.2 

2.7 

3-5 

5*3 

4.4 

4.6 

5.6 

4.6 

4-7 

5-9 

3-9 

2.2 

49.6 

50.97 

Little  Rock 

2.1 

2.8 

3-5 

5-5 

4.8 

4-i 

5-4 

5-9 

5.8 

5-2 

4-3 

2-3 

51-7 

57-55 

Galveston 

i.6 

2.8 

3.2 

2.9 

4-3 

4.2 

3-3 

5-2 

5-2 

4-7 

4.2 

2.4 

46.0 

65.88 

San  Antonio 

2.4 

3-3 

4-i 

3.8 

4.0 

4-5 

6.6 

5-8 

5-2 

5-4 

4.2 

3-1 

52.4 

40-55 

Rio  Grande  Valley. 

Rio  Grande  City ..... 

2.7 

3-5 

3-5 

3-6 

4-5 

4.6 

6.9 

7.0 

5-2 

4.9 

3-6 

3-i 

53- 1 

22.74 

Brownsville 

1.8 

2.6 

2.9 

3-o 

3-5 

3-9 

4-0 

4.1 

3-3 

3.0 

2.6 

2-3 

37-o 

32.58 

Ohio  Valley  and  Tennessee. 

Chattanooga  

2.0 

3-3 

3-3 

5-3 

3-7 

4-3 

4-3 

5.0 

5-4 

4.0 

3-9 

1.9 

46.4 

54-87 

Knoxville 

2.4 

2.6 

3-4 

5-o 

3-5 

4.2 

4-9 

5-o 

4-9 

4.1 

3-8 

2.1 

45-9 

53-03 

Memphis 

2.1 

2.3 

3-1 

5-9 

5-3 

4-8 

4.9 

5-4 

5-5 

4.2 

4.1 

2.4 

50.0 

46.82 

Nashville  

1.9 

2.1 

3-2 

5-9 

5-o 

5-1 

5-5 

9-3 

5-9 

4.0 

3-3 

1,9 

50.1 

50.49 

Louisville 

i-7 

2.1 

2.8 

5-b 

5-4 

5-8 

6.8 

7-4 

6.4 

4.9 

3-8 

2.1 

54.8 

Indianapolis 

i-3 

1.4 

2.2 

4.6 

4.8 

3-7 

7-7 

■6.9 

3-2 

4.1 

3-i 

1.6 

48.6 

41.36 

Cincinnati 

1.8 

1.8 

2.6 

4.9 

S*  2 

6.4 

6.3 

6.6 

6.1 

4-7 

3-3 

2.1 

52.0 

34.88 

Columbus  

1.6 

2.0 

2-3 

4-5 

4.8 

5-8 

6.9 

6.4 

5-i 

4.0 

2.6 

1.8 

47.8 

35.06 

Pittsburg 

r.4 

1.9 

2.2 

3-8 

4.2 

5-4 

6.6 

5-6 

4.9 

3-4 

2.8 

2-3 

44-5 

39.89 

Lower  Lake  Region. 

Buffalo 

0.8 

1. 1 

1-3 

2.2 

3-3 

3-9 

4.9 

5-2 

3-9 

2.8 

1.9 

1.6 

32.9 

33-87 

Oswego 

0.6 

1.0 

1. 1 

2.2 

2.8 

3-8 

3-9 

4.0 

3-h 

2.7 

2.2 

1.0 

28.9 

32-79 

Rochester 

0.5 

1. 1 

°-9 

2.6 

3-8 

4.9 

4.6 

4.1 

3-8 

2.6 

2.2 

i-3 

32-4 

27.76 

Cleveland 

1. 1 

I.4 

I-  5 

2.9 

3-3 

4 4 

5-2 

4.9 

3-8 

3-4 

2.4 

1.4 

35.7 

32.57 

Sandusky 

0.8 

1.4 

i-5 

3.2 

3-7 

4.6 

5-4 

5-4 

3-7 

3-4 

2.2 

i-3 

36.6 

26.45 

Toledo 

°.o 

1. 1 

i-5 

3-5 

3-8 

4.6 

6.0 

6.4 

3-7 

3-4 

2.4 

i-3 

38.6 

25.86 

Detroit 

0.0 

1. 1 

1.6 

3° 

4 1 

4.8 

5-9 

5-2 

3-4 

2.8 

2.0 

i-3 

36.0 

29.02 

Upper  Lake  Region. 

Grand  Haven  

0-5 

O.7 

i-3 

2.6 

3-i 

3-8 

4-7 

3.8 

2.7 

2.6 

i-7 

I.  I 

28.6 

25.96 

Marquette 

0.8 

0.8 

°-9 

i-7 

2.4 

3-3 

3-4 

3-3 

3-1 

2.2 

i-3 

*-3 

24-5 

35.40 

Port  Huron 

0.6 

1.0 

I.  I 

2.6 

3-o 

38 

4.6 

4.2 

3-2 

2-5 

i-7 

1.0 

29-3 

24-33 

Chicago 

1.0 

1.2 

1.8 

3-2 

3-3 

4.8 

5-4 

5-3 

4.1 

3.2 

2-3 

1.2 

39-8 

30.86 

Milwaukee 

o-5 

1.0 

I.  I 

2.4 

2.6 

3.8 

4.8 

3-7 

3-4 

2.9 

1.9 

0.9 

29.O 

23-49 

Duluth 

o-5 

o-5 

0.6 

i-5 

2.4 

2-5 

3-9 

3-4 

3° 

2-5 

1.2 

1.0 

23.0 

27.31 

Extreme  Northwest. 

Moorhead  

0.2 

1.4 

o-5 

2.1 

3-6 

3.8 

3-7 

3-3 

3-5 

2.4 

i-3 

0.5 

26.3 

16.50 

Saint  Vincent 

o*3 

o-3 

o-5 

1.8 

3.8 

3-9 

3-1 

2.6 

2.6 

2.0 

0.9 

°-3 

22.1 

17.22 

Bismark 

0.4 

0.6 

0.6 

3-o 

4-3 

4- 1 

5-6 

4.2 

4.0 

2.6 

1.2 

0.4 

31.0 

16.51 

Fort  Buford 

1.4 

0.7 

0.6 

3-o 

4-7 

S.o 

6.2 

4.9 

4.8 

3-0 

1-7 

0.5 

35-5 

14.70 

Fort  Totton 

0.2 

o-3 

0.4 

2.2 

4-6 

3-8 

4.2 

3-7 

3-7 

2-3 

1.4 

0.4 

27.2 

16. 13 

Upper  Mississippi  Valley. 

Saint  Paul 

0.7 

0.7 

2.2 

2.0 

2-3 

4.1 

5-o 

3-7 

2.8 

2.4 

1-5 

0.7 

28.1 

25.86 

Davenport  

0.5 

1.0 

1.8 

3-8 

3-4 

4.6 

6.Q 

6.2 

4.4 

3-o 

2.3 

1. 1 

39- 0 

40.49 

Des  Moines 

0.6 

1.0 

i-5 

3-7 

3-i 

4.2 

6.6 

4-7 

4.1 

3-3 

2.3 

0.9 

36.0 

Keokuk 

0.8 

1. 1 

2.1 

4.2 

3-7 

4-3 

7.0 

6.8 

3.0 

3-8 

2.9 

1.2 

42.9 

35-79 

S-8 

4.4 

4-3 

5-6 

6.5 

4-5 

3.8 

Springfield,  111 

0.8 

1. 1 

2.0 

4.6 

3-8 

4-3 

5-4 

6-5 

4-5 

3-5 

2.9 

1.4 

40.8 

41.90 

Saint  Louis 

i-3 

1.6 

2-5 

5-5 

4-7 

5-o 

7-5 

8.0 

5-9 

4.9 

3-9 

i-4 

52.2 

41.17 

Missouri  Valley. 

Lamar 

I. I 

1.6 

2.4 

4.4 

3-8 

4.0 

6.0 

4.6 

3-7 

3-6 

2.9 

i-5 

39.6 

42.91 

Springfield,  Mo 

I.  I 

i-7 

2-4 

5-o 

4.8 

4.0 

5-o 

3-4 

3-4 

3-5 

3-1 

1.4 

38- 3 

42.12 

Leavenworth 

0.9 

i-5 

2.3 

4.6 

4-3 

5-o 

6-3 

4-5 

4.0 

3-9 

2-7 

1.4 

41.6 

47-21 

Omaha 

0.8 

i-5 

T-4 

4-4, 

3-8 

5-2 

6.2 

5-2 

4-3 

4-3 

3-0 

1.4 

41.7 

24.22 

Crete  

0.7 

1. 1 

1.2 

3-5 

3-3 

4-5 

5-6 

4-7 

3-8 

3-9 

2.4 

I.I 

35-5 

23-34 

Fort  Sulley 

0.6 

0.9 

i-3 

4.4 

4.1 

5-2 

7-7 

4-9 

5-7 

3.9 

2.8 

0.7 

41.9 

T4-  77 

Huron  

°-3 

0.7 

0.8 

3-7 

3-7 

4- 1 

3-7 

4.2 

4.1 

3-1 

2.4 

O.7 

33-o 

17-05 

Yankton 

0.4 

i-4 

1.2 

3-3 

3-i 

4.4 

4.6 

3-7 

2.9 

3° 

2.2 

0.8 

310 

20.89 

93c 


STORAGE  AND  EVAPORATION  OF  WATER. 


TABLE  No.  27  a. — ( Continued .) 


Stations  and  Districts. 

00 

CO 

00 

c 
1 — 1 

00 

00 

00 

V 

£ 

Mar.  1888. 

April,  1888. 

May,  1888. 

00 

00 

c 

00 

00 

j-f 

•—I 

Aug.  1887. 

Sept.  1887. 

Oct.  1887. 

Nov.  1887. 

Dec.  1887. 

12  months’ 
Evaporation. 

Precipitation 
in  1888.  1 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

Northern  Slope. 

Fort  Assiniboine 

o.8 

1.2 

1.2 

3.8 

4* 1 

4.2 

6.8 

5-5 

4.8 

3-5 

2-5 

1. 1 

39-5 

*3-99 

Fort  Custer 

o.6 

i-5 

i-3 

5-4 

6.8 

4.9 

9.6 

8.0 

6.1 

3-4 

2-9 

i-5 

52.0 

13.98 

Helena 

1. 1 

3-6 

2.1 

6. 1 

4-3 

5-5 

7.2 

7-7 

6.4 

4-3 

3-0 

2.1 

53-4 

10. 14 

Cheyenne 

3-3 

5-7 

4-0 

8.2 

5-2 

10-4 

8.0 

7-7 

8.6 

5-8 

6.1 

3-5 

76.5 

J4-5i 

North  Platte  

o.8 

1.8 

1.8 

5-4 

3-9 

6.9 

6.0 

4.8 

3-7 

2.8 

2-3 

1. 1 

4«-3 

17.46 

Middle  Slope. 

Denver  

2.8 

3-7 

3-5 

7.6 

5.8 

10.5 

8.3 

8.5 

6.1 

4-9 

4.2 

3-i 

69.O 

9-51 

Dodge  City 

1.4 

2-4 

2.8 

4.1 

4.0 

7-4 

8.3 

6.6 

5-5 

5-2 

4.2 

2.1 

54-6 

22.94 

Fort  Elliott 

1-3 

1.9 

3.2 

5-i 

5-4 

8.2 

7.6 

6.2 

5-4 

4-7 

4.2 

2.2 

55-4 

16.51 

Southern  Slope. 

Fort  Sill 

i.6 

2.0 

2.6 

3-8 

4.0 

4.4 

4.8 

7-5 

5-i 

4.2 

4-1 

2.0 

46.I 

35-72 

Fort  Davis 

5-4 

5-7 

6.7 

8-S 

II. O 

12.0 

II. 4 

9.0 

5-9 

5-2 

5 7 

49 

96.4 

18. 11 

Fort  Stanton 

3-9 

3-9 

5-a 

7-3 

9-5 

10.9 

9-4 

11. 6 

3-9 

4.0 

3-6 

3-8 

76.0 

18.04 

Southern  Plateau. 

El  Paso 

4.0 

3-9 

6.0 

8.4 

10.7 

13.6 

9-4 

7-7 

3-6 

5-2 

4.6 

2.9 

82.0 



Santa  F6 

3.0 

3-4 

4.2 

6.8 

8.8 

12.9 

9.2 

9.8 

6.6 

6.7 

5-7 

2-7 

79-8 

12.03 

Fort  Grant 

5-2 

4.8 

6.4 

9.2 

10.2 

13.8 

12.4 

10.5 

9.0 

7-9 

7.2 

4.6 

IOI.2 

14.20 

Yuma 

4.4 

5-2 

6.6 

9.6 

9.6 

12.6 

II. O 

10.2 

8.2 

8.2 

5-5 

4.6 

95-7 

2.95 

Keeler 

3.0 

4.6 

6-3 

8.7 

9-3 

n.9 

12.8 

13.9 

10.6 

8.8 

5-9 

4.8 

100.6 

5.66 

Middle  Plateau. 

Fort  Bid  well  

0.8 

1.8 

1.8 

4.6 

5-2 

4.0 

8.8 

8.1 

5-o 

4.6 

2.4 

i-3 

48.9 



Winnemucca  

°-9 

2.8 

6.2 

9.1 

9-3 

10. 1 

“■5 

12.0 

9.9 

6.6 

3-7 

1.8 

83.9 

4-89 

Salt  Lake  City 

1.8 

2.7 

3-6 

7.2 

6.9 

8.9 

9-2 

10. 7 

9.6 

6-5 

5-o 

2-3 

74-4 

13.62 

Fort  Bridger 

1.6 

2-5 

2.7 

4-3 

4-3 

6.5 

7-7 

6.8 

5-6 

4.2 

5-2 

4-7 

56.1 

— 

Northern  Plateau. 

Boise  City 

1.6 

2-5 

3.8 

6.1 

6-5 

6.6 

10. 0 

9.2 

7-4 

5-2 

3-2 

1.8 

63.9 

11.09 

Spokane  Falls 

0.7 

i-7 

2.7 

4-4 

5-4 

4-4 

7-7 

6.4 

3-8 

2-5 

1-7 

1.4 

42.8 

17.69 

Walla  Walla- 

1. 1 

2.9 

3-6 

6.2 

7-7 

5-7 

9.9 

7-9 

5-i 

3-4 

1.8 

2.4 

57-7 

13-59 

North  Pacific  Coast. 

Olympia 

i-3 

1.2 

1.8 

2-5 

4.1 

3-3 

3-2 

3-i 

2 4 

i-5 

i-3 

1. 1 

26.8 

45-54 

Port  Angeles . . 

1.0 

0.9 

1.8 

1.8 

2-5 

2. 1 

2.1 

1.8 

I-5 

1.2 

i-3 

1. 1 

19. 1 

28.17 

Astoria 

1. 1 

1.0 

1.6 

2.1 

3-o 

2-7 

3-0 

2.9 

2.6 

2.3 

1.8 

1.2 

25-3 

68.73 

Portland  

0.9 

1. 1 

2.4 

3-4 

5-o 

3-2 

5-4 

4.2 

3-4 

2.7 

1.8 

1.2 

34-7 

38.76 

Roseburg 

1.2 

1.6 

2.7 

3-9 

4-7 

3-5 

5-4 

4-7 

5-o 

3-2 

x*7 

1.6 

39-2 

31.19 

Middle  Pacific  Coast. 

Red  Bluff 

3-0 

4.6 

5-4 

6.1 

7.0 

6.9 

11. 0 

10.7 

10. 1 

10.5 

5-9 

3-6 

84.8 

24.94 

Sacramento, 

1.8 

3-' 

3-7 

4-3 

4.2 

5-6 

5-9 

5.6 

6.5 

7-3 

3-9 

2.4 

54-3 

18.46 

San  Francisco 

2.7 

2.7 

3-3 

3-i 

2.8 

3-1 

2.4 

2-5 

3-3 

5.0 

2.8 

3-o 

36-7 

23- 03 

Southern  Pacific  Coast. 

Fresno 

1.8 

2.8 

3.0 

5-6 

6.0 

7.0 

9.1 

10.2 

7-6 

6.7 

3-8 

2.2 

65.8 

8.76 

Los  Angeles 

2-3 

2.0 

2.8 

3-4 

3-o 

3-8 

3-2 

3-5 

3-i 

4.1 

3° 

3-0 

37.2 

21.04 

San  Diego 

2.9 

2.7 

2-5 

2.7 

3-3 

2.8 

3-2 

3-3 

2.9 

4-3 

3-2 

3-7 

37-5 

n-57 

CHAPTER  VI. 


SUPPLYING  CAPACITY  OF  WATERSHEDS. 

74.  Estimate  of  Available  Annual  Flow  of  Streams. 

— Applying  our  calculations  in  the  last  chapter,  of  available 
flow  of  water  from  the  unit  of  watershed,  one  square  mile, 
and  modifying  it  by  the  elements  of  compensation,  storage, 
evaporation,  and  percolation,  we  then  estimate  mean  annual 
quantities  of  low-cycle  years,  applicable  to  domestic  con- 
sumption, as  follows : 


Assumed  mean  annual  rainfall 40  inches. 

Flow  of  stream  available  for  storage,  40  per  cent,  of  mean  rain  = 16  inches  of  rain. 


This  available  rain  is  applied  to  : 

ist.  Compensation  to  riparian  owners,  say  16.8  p.  c.  of  mean  rain  = 6.72  in.  of  rain. 

2d.  Evaporation  from  surface  of  storage  reservoir,  “ 3.2  “ “ “ “ =1.28  “ “ “ 

3d.  Percolation  from  storage  reservoir,  “ 1.6  “ “ “ “ = .64  “ “ “ 

4th.  Balance  available  for  consumption,  18.4  “ “ “ “ = 7.36  “ “ “ 

Total 40  per  cent.  16  inches. 

The  7.36  inches  of  rain  estimated  as  available  from  a 
40-inch  annual  rain  equals  17,098,762  cubic  feet  of  water, 
which  is  equivalent  to  a continuous  supply  of  seven  cubic 
feet  per  day  (=  52.36  gals.)  each,  to  6,692  persons. 

By  applying  to  the  annual  results  the  monthly  ratios, 
and  thus  developing  the  monthly  surpluses  or  deficiencies 
of  flow,  we  shall  have  in  the  algebraic  sum  of  the  deficien- 
cies the  volume  of  storage  necessary  to  make  forty  per  cent, 
of  the  rainfall  available,  and  this  storage  must  ordinarily 
approximate  one-third  of  the  annual  flowT  available  for 
storage. 


s 

< 

Q 

Z 

o 

H 

O 

X 

U 


94 


(Constructed  in  1836.) 


MONTHLY  AVAILABLE  STORAGE  REQUIRED. 


95 


75.  Estimate  of  Monthly  Available  Storage  Re- 
quired.— Computation  of  a supply,  and  the  required 
storage  ; applied  to  one  square  mile  of  watershed  as  a unit 
of  area. 

Assumed  data : Population  to  be  supplied.  6,500  per- 
sons, consuming  7 cubic  feet  per  capita  daily,  each  ; 

Mean  annual  rainfall,  40  inches,  and  eight-tenths  = 
32  inches  of  rain,  in  the  low-cycle  years  ; 

Available  flow  of  stream,  fifty  per  cent,  of  eight-tenths 
of  rain  = 16  inches  ; 

Compensation  each  month,  .168  of  one-twelfth  the  mean 
annual  depth  of  rain  = .56  niches  each  month  uniformly ; 

Evaporation  annually  from  the  reservoir  surface  only, 
eighty  per  cent,  of  the  depth  of  mean  annual  rain,  or  32 
inches;  and  monthly,  eighty  per  cent,  of  one-twelfth  the 
annual  evaporation  = 2§  inches. 

Area  of  storage  reservoir,  .04  square  mile,*  or  25.6  acres, 
with  equivalent  available  draught  of  ten  feet  for  that  sur- 
face. The  evaporation  of  two  inches  from  four  hundredths 
of  a square  mile  = .10667  inch  from  one  square  mile. 

Volume  of  percolation  assumed  to  equal  f volume  of 
evaporation  from  the  reservoir  surface. 

The  monthly  ratios  will  be  multiplied  into 


40  in.  x.8  x -50  p.  c.  _ j ,2333  in.  for  the  monthly  flow. 
12  months 


.168  x 


40  in.  mean  rain 
12  months 


= .56  in.  for  monthly  compensation. 


.04  x 4_°  m-  x 80  p.  c._ -IC,66y  ;n  for  monthly  evap.  from  reservoir. 

12  months 

“ =.0267  in.  for  monthly  percolation  from  reservoir. 

6500  x 7 cu.  ft.  x 30.4369  days  = 1,384,879  cu.  ft.  for  monthly  con- 
sumption. 


* A unit  of  reservoir  area,  for  each  square  mile  unit  of  watershed. 


96 


SUPPLYING  CAPACITY  OF  WATERSHEDS. 


TAB  BE  No.  28. 

Monthly  Supply  to,  and  Draft  from,  a Storage  Reservoir. 


Month. 

Monthly 

Flow. 

cubic  feet. 

Monthly 

Compen- 

sation. 

cubic  feet. 

Monthly 
Evapora- 
tion from 
Reser- 
voir. 

cubic  feet. 

Monthly 
Percola- 
tion from 
Reser- 
voir. 

cubic  Jeet. 

Monthly 

Domestic 

Consump- 

tion. 

cubic  feet. 

Surplus. 
cubic  feet. 

Deficiency. 
cubic  feet. 

Jan.  | 

Gain. 
Ratio,  1.65 
5,111,040 

Loss. 

Ratio,  .168 
1,300,992 

Loss. 
Ratio,  .30 

74»342 

Loss. 

Ratio,  .075 

18,586 

Used. 
Ratio,  1.05 

1,454423 

2,262,997 

Feb.  j 

Ratio,  1.50 
4,646,400 

.168 

1,300,992 

.318 

78,803 

.080 

19,701 

1. 10 

1,523,367 

1,723,537 

Mar.  | 

Ratio,  1.65 
5,111,040 

.l68 

1,300,992 

.426 

105,566 

.106 

26,392 

.90 

1,246,391 

2431,699 

Apr.  | 

Ratio,  1.45 

4,491,520 

.168 

1,300,992 

•732 

181,395 

.183 

45.349 

.85 

1,177447 

1,786,637 

May  j 

Ratio,  .85 
2,632,960 

.l68 

1,300,992 

1.128 

279,528 

.282 

69,882 

.90 

1,246,391 

264,033 

June  j 

Ratio,  .75 
2,323,200 

.l68 

1,300,992 

i-53 

379,146 

•383 

94,786 

1. 00 

1,384,879 

836,603 

July  j 
Aug.  j 

Ratio,  .35 
1,084,160 
Ratio,  .25 

774,400 

.l68 

1,300,992 

.168 

1,300,992 

183 

453.489 

'•95 

483,721 

■457 

113,372 

.488 

120,930 

1.20 

1,661,855 

i. 25 

1, 73  L 099 

2,445,548 

2,762,342 

Sept.  | 

Ratio,  .30 

929,280 

.168 

1,300,992 

1-793 

444,32° 

.448 

1 1 1,080 

1.05 

M54,I23 

2,382,235 

Oct.  -j 

Ratio,  .45 
1,393,920 

.l68 

1,300,992 

1.005 

261,438 

.264 

65,359 

.90 

1,246,391 

1480,260 

Nov.  | 

Ratio,  1.20 
3.717,120 

.168 

1,300.992 

•558 

138,277 

.139 

34,569 

.85 

M77,I47 

1,066,114 

Dec.  | 

Ratio,  1.60 
4,956,160 

.168 

1,300,992 

.373 

93.671 

.095 

23418 

•95 

1,315,635 

2,222444 

Totals 

37,171,200  15,611,904 

2,973,696 

743,424 

16,618,548 

11493428 

10,171,021 

From  certain  localities  no  claim  will  arise  for  diversion 
of  tlie  water,  or  the  diversion  may  be  compensated  for  by 
the  payment  of  a cash  bonus,  in  which  case  the  proportion 
of  rainfall  applicable  to  domestic  consumption  will  be  a 
little  more  than  doubled,  and  approximately  as  follows, 
neglecting  percolation  from  the  storage  reservoir. 


MONTHLY  AVAILABLE  STORAGE  REQUIRED. 


97 


The  monthly  ratios  will  here  be  multiplied  into 

40  in.  x .8  X .50  p.  c.  , .,  a 

5 — £ — = 1.3333  in.  for  the  monthly  now. 

12  months 

04  x — -X  ‘8°  P'—  — .1067  in.  for  monthly  evap.  from  reservoir. 

12  months 

13,500  persons  x 7 cu.  ft.  x 30.4369  days  = 2,876,287  cu.  ft.  foi 
monthly  consumption. 


TABLE  No.  29. 

Monthly  Supply  to,  and  Draft  from,  a Storage  Reservoir 

(without  compensation). 


Month. 

Monthly 

Flow. 

cubic  feet. 

Monthly 
Evaporation  | 

FROM 

Reservoir. 
cubic  feet . 

Monthly 

Domestic 

Consumption. 

cubic  feet. 

Surplus. 
cubic  feet. 

Deficiency. 
cubic  feet . 

Gain. 

Loss. 

Used. 

Jan.  ] 

Ratio,  1.65 

5,111,040 

Ratio,  .30 

74.342 

Ratio,  1.05 
3,020,101 

2,016,597 

Feb.  ] 

Ratio,  1.50 

4,646,400 

.318 

78,803 

1. 10 

3>l63,9i6 

1,403,681 

Mar.  | 

Ratio,  1.65 

.426 

105,566 

.90 

2,588,658 

2,416,816 

• 

Apr.  | 

Ratio,  1.45 

4,491,520 

•732 

181,395 

.85 

2,444,844 

1,865,281 

May  j 

Ratio,  .85 
2,632,960 

1.128 

279,528 

.90 

2,588,658 

235,226 

June  j 

Ratio,  .75 

2,323.200 

i-53° 

379.146 

I. OO 

2,876,287 

932,233 

July  j 

Ratio,  .35 

1,084,160 

I.83O 

453.489 

1.20 

3,451,544 

2,824,873 

Aug.  ] 

Ratio,  .25 
734,400 

1.952 

483,721 

1-25 

3^595,359 

3,344,680 

Sept.  \ 

Ratio,  .30 

929,280 

1-793 
444, 32° 

1.05 

3,020,101 

2,535>!4i 

Oct.  | 

Ratio,  .45 
1,393,920 

1.005 

261,438 

.90 

2,588,656 

1,556,174 

Nov.  | 

1,133,999 

Ratio,  1.20 
3,7I7,I20 

.558 

138,277 

■ 85 

2,444,844 

Dec.  | 

Ratio,  1.60 
4,956,160 

.378 

93,671 

■95 

2,732,472 

2,826,143 

Tbtals, 

37,171,200 

2,973,696 

34,515,442 

11,662,517 

11,428,327 

7 


98 


SUPPLYING  CAPACITY  OF  WATERSHEDS. 


76.  Additional  Storage  Required.  — Forty  inches 
of  rainfall  on  one  square  mile  equals  a volume  of  92,928,000 
cubic  feet.  The  deficiency  as  above  computed  is  nearly 
twelve  per  cent,  of  this  quantity,  and  calls  for  an  available 
volume  of  water  in  store  early  in  May,  or  at  the  beginning 
of  a drought,  equal  to  about  one-eighth  the  mean  annual 
rainfall. 

The  calculations  of  supply  and  draught  in  the  two 
monthly  tables  given  above  refer  to  mean  quantities  of  low- 
cycle  years,  and  not  to  extreme  minimums.  The  seasons  of 
minimum  flow,  which  are  also,  usually,  the  seasons  of 
maximum  evaporation  from  the  storage  reservoirs  and  of 
maximum  domestic  consumption,  are  in  the  calculations 
supposed  to  be  tided  over  by  a surplus  of  storage  provided 
in  addition  to  the  mean  storage  required  for  the  series  of 
low-cycle  years.  The  storage  should  therefore  be  in  excess 
of  the  mean  deficiency  as  above  computed  at  least  twenty- 
five  per  cent.,  or  should  equal  at  least  fifteen  per  cent,  of  the 
mean  annual  rainfall. 

If  the  storage  is  less  than  fifteen  per  cent.,  the  safe 
available  supply  is  liable  to  be  less  than  the  calculations 
given. 

If  the  area  of  the  storage  reservoir  is  greater  per  square 
mile  of  watershed  than  assumed  above,  the  loss  by  evapo- 
ration from  the  water  surface  will  be  proportionately  in- 
creased, and  must  be  compensated  for  by  increased  storage. 

77.  Utilization  of  Flood  Flows. — The  calculations 
as  above  assume  that  fifty  per  cent,  of  the  annual  rainfall 
is  the  available  annual  flow  in  the  stream.  The  remaining 
fifty  per  cent,  is  assumed  to  be  lost  through  the  various 
processes  of  nature  and  by  floods.  If  the  storage  is  still 
further  increased,  an  additional  portion  of  the  flood  flow 
can  be  utilized,  and  sometimes  fifty  per  cent,  or  even  sixty 


INFLUENCE  OF  STORAGE. 


99 


per  cent,  of  the  annual  rainfall  utilized  for  domestic  con- 
sumption, or  made  applicable  at  the  outlet  of  the  reservoir 
for  power.  Hence,  when  it  is  desired  to  utilize  the  greatest 
possible  portion  of  the  flow,  the  storage  should  equal  twenty 
or  twenty-five  per  cent,  of  the  mean  annual  rainfall. 

78.  Qualification  of  Deduced  Ratios. — The  ratios 
of  flow,  evaporation,  and  consumption,  as  above  used  iu 
the  calculations,  are  not  assumed  to  be  universally  appli- 
cable, but  are  taken  as  safe  general  average  ratios  for  the 
Atlantic  Coast  and  Middle  States.  The  winter  consump- 
tion will  be  less  in  the  lower  Middle  and  Southern  States, 
and  also  in  very  efficiently  managed  wTorks  of  Northern 
States ; but  the  summer  consumption  tends  to  be  greater  in 
the  lower  Middle  and  Southern  States,  where  the  evapora- 
tion and  rainfall  are  greater  also. 

The  results  upon  the  Pacific  slope  can  scarcely  be  gen- 
eralized to  any  profit,  since  within  a few  hundred  miles  it 
presents  extremes,  from  rainless  desert  to  the  maximum 
rainfall  of  the  continent,  and  from  vaporless  atmosphere  to 
constant  excessive  humidity. 

79.  Influence  of  Storage  upon  a Continuous 
Supply. — A safe  general  estimate  of  the  maximum  contin- 
uous supply  of  water  to  be  obtained  from  forty  inches  of 
annual  rain  upon  one  square  mile  of  watershed,  provided 
the  storage  equals  at  least  fifteen  per  cent,  of  the  rainfall, 
gives  7 cubic  feet  (=52.36  gals.)  per  capita  daily,  to  from 
13000  to  15000  persons,  dependent  upon  the  amount  of 
available  storage  of  winter  and  flood  flows ; or  say,  three- 
quarters  of  a million  gallons  of  water  daily. 

The  same  area  and  rain,  with  but  one  month’ s deficiency 
storage,  can  be  safely  counted  upon  to  supply  but  about 
3,000  persons  with  an  equal  daily  consumption,  or  157,000 
gallons  of  water  daily.  From  the  same  area  and  rain,  with 


100 


SUPPLYING  CAPACITY  OF  WATERSHEDS. 


no  storage , a flashy  stream  may  fail  to  supply  1.000  persons 
to  the  full  average  demand  in  seasons  of  severe  drought. 

Hence  the  importance  of  the  storage  factor  in  the  calcu- 
lation. 

The  above  estimates  are  based  upon  mean  rainfalls  of 
low-cycle  (§  47)  years ; therefore  the  results  may  be  ex- 
pected to  be  twenty  per  cent,  greater  in  years  of  general 
average  rainfall. 

80.  Artificial  Gathering  Areas. — When  resort  is 
necessarily  had  to  impervious  artificial  collecting  areas  for 
a domestic  water  supply,  as  when  dwellings  are  located 
upon  vegetable  moulds  or  low  marsh  areas,  bituminous 
rock  surfaces,  limestone  surfaces,  or,  as  in  Venice,  where 
the  sheltering  roofs  are  the  gathering  areas  of  the  house- 
holds, the  proportion  of  the  rainfall  that  may  be  run  into 
cisterns  is  very  large.  If  such  cisterns  are  of  sufficient 
capacity  and  their  waters  protected  from  evaporation,  eighty 
per  cent,  of  the  rainfall  upon  the  gathering  areas  may  thus 
be  made  available,  though  special  provisions  for  its  clarifi- 
cation will  be  indispensable. 

In  such  case,  a roof  area  equivalent  to  25  feet  by  100 
feet  might  furnish  from  a forty-inch  rainfall  a continuous 
supply  of  3 cubic  feet  (—  22.44  gallons)  per  day  to  six  per- 
sons, which  would  be  abundant  for  the  household  uses  for 
that  number  of  persons. 

81.  Recapitulation  of  Rainfall  Ratios. — Recapitu- 
lating, in  the  form  of  general  average  annual  ratios,  relating 
to  the  mean  rainfall  upon  undulating  crystalline  or  diluvial 
surface  strata,  as  unity,  we  have : 


Ratio  of  mean  annual  rainfall i.oo 

Ratio  of  mean  rainfall  of  lowest  three-year  cycles So 

Ratio  of  minimum  annual  rainfall 70 

Ratio  of  mean  annual  flow  in  stream  (of  the  given  year’s  rain) 60 


RAINFALL  RATIOS. 


101 


Ratio  of  mean  summer  flow  in  stream  (of  the  given  year’s  rain) 25 

Ratio  of  low  summer  flow  in  stream  “ “ “ 05 

Ratio  of  annual  available  flow  in  stream  “ “ 50 

Ratio  of  storage  necessary  to  make  available  50  per  cent,  of  annual  rain.  .15 
Ratio  of  general  evaporation  from  earths,  and  consumption  by  the  pro- 
cesses of  vegetation 40 

Ratio  of  percolation  through  the  earth  (included  also  in  the  flow  of 

streams) 25 

Ratio  of  mean  rainfall  collectible  upon  impervious  artificial  or  primary 

rock  surfaces 80 


The  monthly  ratios  of  these  annual  ratios  are  to  be  taken 
in-  ordinary  calculations  of  water  supplies,  and  each  annual 
ratio  to  be  subjected  to  the  proper  modification  adapting  it 
to  a special  local  application. 


TABLE  No-  30. 

Ratios  of  Monthly  Rain,  Flow,  Evaporation,  and  Consumption. 


c 

03 

Feb. 

n 

s 

a 

< 

cT 

June. 

_>> 

3 

1 — 1 

fci) 

3 

< 

0. 

c n 

0 

Nov. 

Dec. 

Ratios  of  average  monthly  rain 

•75 

■83 

,qo 

1 . 10 

1.30 

I .08 

I . 12 

1 . 20 

1 .00 

-95 

-93 

.84 

Ratios  of  av.  monthly  flow  of  streams 

i.b5 

1.50 

1.65 

i-45 

•85 

-75 

• 35 

•25 

•30 

•45 

1 . 20 

1.60 

Ratios  of  av.  monthly  evap  from  water 
Ratios  of  average  monthly  consumption 

•3° 

.32 

•43 

•73 

1 • 53 

1 83 

1.95 

1 • 79 

1.05 

•56 

.38 

of  water 

1.05 

I . IO 

.90 

•85 

.90 

I .OO 

1 . 20 

1.25 

1 05 

.90 

•85 

■95 

TABLE  No.  30a. 

Example  of  an  Estimate  of  Collectable  Rainfall.* 


j Assumed  annual  rainfall  40  in.  1 
"j  Average  available  monthly  flow  f 
1.667 

c 

a 

Feb. 
j March. 

April. 

cS 

June. 

fci 

< 

Sept. 

O 

O 

Nov. 

Dec. 

Total. 

Ratio  of  monthly  mean  available  flow 

1.65 

1.50  1.65 

1-45 

.85 

•75 

■35 

•25 

•30 

•45 

1.20 

t . 60 

12.00 

Equivalent  inches  ol  monthly  avail- 

able  flow 

2-75 

2.50  2.75 

2.42 

I.42 

125 

.58 

•4i 

•50 

75 

2.00 

2.67 

20.00 

Eight-tenths  of  do 

Inches  of  rain  monthly  to  satisfy 

2.20 

2.00  2.20 

1 

i-93 

1. 13 

1 .00 

•47 

■33 

.40 

.60 

I.60 

2. 13 

16.00 

riparian  rights 

•56 

■561  -56 

■56 

.56 

.56 

•47 

•33 

.40 

•56 

•56 

•56 

6.25 

Inches  ot  rain  collectable  monthlv, 

for  storage 

1 .64 

I.44  I.64 

i-37 

■ 57 

•44 

.00 

.00 

.OO 

.04 

I.04 

i-57 

9-75 

The  inches  of  rainfall  flowing  monthly,  here  assigned  as  a riparian  right,  are  found  by 
taking  the  mean  of  flows  from  June  to  October  inclusive,  thus: 

1. 00  -f-  .47  -f-  .33  -}-  .40  -f-  .60  inches  . , c 

— -t'— ! — f — = .56  inches  of  rain. 

5 months 

This  allows  to  riparian  rights  the  entire  low  water  flow  of  summer,  and  allows  for  losses 
of  rainfall  approximately  as  follows:  Loss  by  evaporation  and  absorption,  12  in.;  loss  by 

floods,  8 in.;  reduced  flow  in  dry  seasons,  4 in.;  remaining  available  flow,  16  in. 


* Relating  to  the  Adirondack  water  shed  of  Hudson  River.  From  “ Report  on  a Water 
Supply  for  New  York  and  other  Cities  of  the  Hudson  Valley,  by  J.  T.  Fanning.  N.  Y.  1881. 


CHAPTER  VII. 


SPRINGS  AND  WELLS. 

82.  Subterranean  Waters. — A portion  of  tlie  rain, 
perhaps  one-fourth  part  of  the  whole,  distilled  upon  the 
surface  of  the  earth,  penetrates  its  soils,  the  interstices  of 
the  porous  strata,  the  crevices  of  the  rocks,  and  is  gathered 
in  the  hidden  recesses.  These  subterranean  reservoirs  were 
filled  in  the  unexplored  past,  and  their  flow  continues  in 
the  present  as  they  are  replenished  by  new  rainfalls. 

83.  Tlieir  Source  the  Atmosphere. — AVe  find  no 
reason  to  suppose  that  Nature  duplicates  her  laboratory  of 
the  atmosphere  in  the  hidden  recesses  of  the  earth,  from 
whence  to  decant  the  sparkling  springs  that  issue  along  the 
valleys.  On  the  other  hand,  we  are  often  able  to  trace  the 
course  of  the  waters  from  the  storm-clouds,  into  and  through 
the  earth  until  they  issue  again  as  plashing  fountains  and 
flow  down  to  the  ocean. 

The  clouds  are  the  immediate  and  only  source  of  supply 
to  the  subterranean  watercourses,  as  they  are  to  the  sur- 
face streams  we  have  just  passed  in  review. 

The  subterranean  supplies  are  subject  indirectly  to  at- 
mospheric phenomena,  temperatures  of  the  seasons,  surface 
evaporations,  varying  rainfalls,  physical  features  of  the 
surface,  and  porosity  of  the  soils.  Especially  are  the  shal- 
low wells  and  springs  sensitively  subject  to  these  influences. 

84.  Porosity  of  Earths  and  Rocks. — Respecting  the 
porosity  and  absorptive  qualities  of  different  earths,  it  may 
be  observed  that  clean  silicious  sand,  when  thrown  loosely 
together,  has  voids  between  its  particles  equal  to  nearly 


Fir.  131 


INTERCEPTING  WELL,  PROSPECT  PARK,  BROOKLYN. 


THEIR  SOURCE  THE  ATMOSPHERE. 


103 


one-third  its  volume  of  cubical  measure  ; that  is,  if  a tank 
of  one  cubic  yard  capacity  is  filled  with  quartzoid  sand, 
then  from  tliirty-to  thirty-five  per  cent,  of  a cubic  yard  of 
water  can  be  poured  into  the  tank  with  the  sand  without 
overflowing. 

Gravel,  consisting  of  small  water- worn  stones  or  pebbles, 
intermixed  with  grains  of  sand,  has  ordinarily  twenty  to 
twenty-five  per  cent,  of  voids. 

Marl,  consisting  of  limestone  grains,  clays,  and  silicious 
sands,  has  from  ten  to  twenty  per  cent,  of  voids,  according 
to  the  proportions  and  thoroughness  of  admixture  of  its 
Eonstituents. 

Pure  clays  have  innumerable  interstices,  not  easily 
measured,  but  capable  of  absorbing,  after  thorough  drying, 
from  eight  to  fifteen  per  cent,  of  an  equal  volume  of  water. 

The  water  contained  in  clays  is  so  fully  subject  to  laws 
of  molecular  attraction,  owing  to  the  minuteness  of  the 
individual  interstices,  that  great  pressure  is  required  to  give 
it  appreciable  flow. 

Water  flows  with  some  degree  of  freedom  through  sand- 
stones, limestones,  and  chalks,  according  to  their  textures, 
and  they  are  capable  of  absorbing  from  ten  to  twenty  per 
cent,  of  their  equal  volumes  of  water. 

The  primary  and  secondary  formations,  according  to 
geological  classification,  as  for  instance,  granites,  serpen- 
tines, trappeans,  gneisses,  mica-slates,  and  argillaceous 
schists,  are  classed  as  impervious  rocks,  as  are,  usually, 
the  several  strata  of  pure  clays  that  have  been  subjected  to 
great  superincumbent  weight. 

The  crevices  in  the  impervious  rocks,  resulting  from 
rupture,  may,  however,  gather  and  lead  away,  as  natural 
drams,  large  volumes  of  the  water  of  percolation. 

The  free  flow  of  the  percolating  water  toward  wells  or 


104 


SPRINGS  AND  WELLS. 


spring,  is  limited  and  controlled,  not  only  by  the  porosity 
of  the  strata  which  it  enters,  bat  also  by  their  inclination, 
curvature,  and  continuous  extent,  and  by  the  impervious- 
ness  of  the  underlying  stratum,  or  plutonic  rock. 

85.  Percolations  in  the  Upper  Strata. — Shallow 
well  and  spring  supplies  are,  usually,  yields  of  water  from 
the  drift  formation  alone.  Them  temperatures  may  be  va- 
riable, rising  and  falling  gradually  with  the  mean  tempera- 
tures of  the  surface  soils  in  the  circuits  of  the  seasons,  and 
they  may  not  be  wholly  freed  from  the  influence  of  the 
decomposed  organic  surface  soils.  Their  flow  is  abundant 
when  evaporation  upon  the  surface  is  light,  though  slack- 
ened when  the  surface  is  sealed  by  frost. 

A variable  spring,  and  it  is  the  stream  at  its  issue  that 
we  term  a spring,  indicates,  usually,  a flow  from  a shallow, 
porous  surface  stratum,  say,  not  exceeding  50  feet  in  depth, 
though  occasionally  its  variableness  is  due  to  peculiar 
causes,  as  the  melting  of  glaciers  in  elevated  regions,  and 
atmospheric  pressure  upon  sources  of  intermittent  springs. 

Porous  strata  of  one  hundred  feet  in  depth  or  more  give 
comparatively  uniform  flow  and  temperature  to  springs. 

86.  The  Courses  of  Percolation — Gravitation  tends 
to  draw  the  particles  of  water  that  enter  the  earth  directly 
toward  the  center  of  the  earth,  and  they  percolate  in  that 
direction  until  they  meet  an  impervious  strata,  as  clay, 
when  they  are  forced  to  change  their  direction  and  follow 
along  the  impervious  surface  toward  an  outlet  in  a valley, 
and  possibly  to  find  an  exit  beneath  a lake  or  the  ocean. 

When  the  underlying  impervious  strata  has  considerable 
average  depth,  it  may  have  been  unevenly  deposited  in 
consequence  of  eddies  in  the  depositing  stream,  or  crowded 
into  ridges  by  floating  icebergs,  or  it  may  have  been  wojt 
into  valleys  by  flowing  water.  Subsequent  deposits  of 


SUBTERRANEAN  RESERVOIRS. 


105 


sand  and  gravel  would  tend  to  fill  up  the  concavities  and 
to  even  the  new  surface,  hiding  the  irregularities  of  the 
lower  strata  surface. 

The  irregularities  of  the  impervious  surface  would  not 
be  concealed  from  the  percolating  waters,  and  their  flow 
would  obey  the  rigid  laws  of  gravitation  as  unswervingly 
as  do  the  showers  upon  the  surface,  that  gather  in  the  chan- 
nels of  the  rocky  hills. 

Springs  will  appear  where  such  subterranean  channels 
intercept  the  surface  valleys.  The  magnitude  of  a spring 
will  be  a measure  of  the  magnitude  of  its  subterranean 
gathering  valley. 

87.  Deep  Percolations. — The  deep  flow  supplies  of 
wells  and  springs  are  derived,  usually,  from  the  older 
porous  stratifications  lying  below  the  drift  and  recent  clays. 
The  stratified  rocks  yielding  such  supplies  have  in  most 
instances  been  disturbed  since  their  original  depositions, 
and  they  are  found  inclined,  bent,  or  contorted,  and  some- 
times rent  asunder  with  many  fissures,  and  often  intercepted 
by  dykes. 

88.  Subterranean  Reservoirs. — Subterranean  basins 
store  up  the  waters  of  the  great  rain  percolations  and 
deliver  them  to  the  springs  or  wells  in  constant  flow,  as 
surface  lakes  gather  the  floods  and  feed  the  streams  with 
even,  continuous  delivery.  A concave  dip  of  a porous 
stratum  lying  between  two  impervious  strata  presents  favor- 
able conditions  for  an  “artesian”  well,  especially  if  the 
porous  stratum  reaches  the  surface  in  a broad,  concentric 
plane  of  great  circumference,  around  the  dip,  forming  an 
extensive  gathering  area. 

Waters  are  sometimes  gathered  through  inclined  strata 
from  very  distant  watersheds,  and  sometimes  their  course 


106 


SPRINGS  AND  WELLS. 


leads  under  considerable  bills  of  more  recent  deposit  than 
the  stratum  in  which  the  water  is  flowing. 

The  chalks  and  limestones  do  not  admit  of  free  percola- 
tion, and  are  unreliable  as  conveyers  of  water  from  distant 
gathering  surfaces,  since  their  numerous  fissures,  through 
which  the  water  takes  its  course,  are  neither  continuous  nor 
uniform  in  direction. 

89.  The  Uncertainties  of  Subterranean  Searches. 

— The  conditions  of  the  abundant  saturation  and  scanty 
saturation  of  the  strata,  and  their  abilities  to  supply  water 
continuously,  are  very  varied,  and  may  change  from  the 
first  to  the  second,  and  even  alternate,  with  no  surface  indi- 
cations of  such  result ; and  the  subterranean  flow  may,  in 
many  localities,  be  in  directions  entirely  at  variance  with 
the  surface  slopes  and  flow. 

Predictions  of  an  ample  supply  of  water  from  a given 
subterranean  source  are  always  extremely  hazardous,  until 
a thorough  knowledge  is  obtained  of  the  geological  posi- 
tions, thickness,  porosity,  dip,  and  soundness  of  the  strata, 
over  all  the  extent  that  can  have  influence  upon  the  flow  at 
the  proposed  shaft. 

Experience  demonstrates  that  water  may  be  obtained  in 
liberal  quantity  at  one  point  in  a stratum,  while  a few  rods 
distant  no  water  is  obtainable  in  the  same  stratum,  an 
intervening  “fault”  or  crevice  having  intercepted  the  flow 
and  led  it  in  another  direction.  Sometimes,  by  the  exten- 
sion of  a heading  from  a shaft  in  a water-bearing  stratum, 
to  increase  an  existing  supply,  a fault  is  pierced  and  the 
existing  supply  led  off  into  a new  channel. 

90.  Renowned  Application  of  Geological  Science. 
— Arago’s  prediction  of  a store  of  potable  water  in  the  deep- 
dipping greensand  stratum  beneath  the  city  of  Paris,  was 
one  of  the  most  brilliant  applications  of  geological  science 


INFLUENCE  OF  WELLS  UPON  EACH  OTHER. 


107 


to  useful  purposes.  He  felt  keenly  that  a multitude  of  his 
fellow-citizens  were  suffering  a general  physical  deteriora- 
tion for  want  of  wholesome  water,  for  which  the  splendors 
of  the  magnificent  capital  were  no  antidote.  With  a fore- 
sight and  energy,  such  as  displays  that  kind  of  genius  that 
Cicero  believed  to  be  “in  some  degree  inspired,”  he  pre- 
vailed upon  tlie  public  Minister  to  inaugurate,  in  the  year 
1833,  that  notable  deep  subterranean  exploration  at  Cre- 
nelle. By  his  eloquent  persuasions  he  maintained  and 
defended  the  enterprise,  notwithstanding  the  eight  years  of 
labor  to  successful  issue  were  beset  with  discouragements, 
and  all  manner  of  sarcasms  were  showered  upon  the  pro- 
moters. In  February,  1841,  the  augur,  cutting  an  eight- 
inch  bore,  reached  a depth  of  1806  feet  9 inches,  when  it 
suddenly  fell  eighteen  inches,,  and  a whizzing  sound  an- 
nounced that  a stream  of  water  was  rising,  and  the  well 
soon  overflowed. 

91.  Conditions  of  Overflowing-  Wells.  - An  over- 
flow results  only  when  the  surface  that  supplies  the  water- 
bearing stratum  is  at  an  elevation  superior  to  the  surface  of 
the  ground  where  the  well  is  located,  and  the  water-bearing 
stratum  is  confined  between  impervious  strata.  In  such 
case,  the  hydrostatic  pressure  from  the  higher  source  forces 
the  water  up  to  the  mouth  of  the  bore. 

93.  Influence  of  Wells  upon  Each  Other. — The 
success  of  wells,  penetrating  deep  into  large  subterranean 
basins,  upon  their  first  completion,  has  usually  led  to  their 
duplication  at  other  points  within  the  same  basin,  and  the 
flow  of  the  first  has  often  been  materially  checked  upon  the 
commencement  of  flow  in  the  second,  and  both  again  upon 
the  commencement  of  flow  in  a third,  though  neither  was 
within  one  mile  of  either  of  tlie  others.  The  flow  cf  the 
famous  well  at  Greuelle  was  seriously  checked  by  the  open- 


108 


SPRINGS  AND  WELLS. 


ing  of  another  well  at  more  than  3000  yards,  or  nearly  two 
miles  distant. 

93.  American  Artesian  Wells. — The  snb-stratnm 
which,  in  the  United  States  has  been  most  successfully 
pierced  for  artesian  waters  is  the  coarse  Potsdam  sand- 
stone having  its  northerly  outcrop  in  central  Wisconsin. 
This  stratum  is  now  well  known  as  far  easterly  as  Chi- 
cago and  Milwaukee,  as  far  westerly  as  the  Mississippi 
river,  and  southerly  into  central  Illinois.  The  wells  in  this 
sandstone  for  public  water  supplies  are  numerous  and  the 
water  generally  satisfactory  for  domestic  uses,  but  having 
considerable  mineral  impregnations.  The  granite  outcrop 
in  Wisconsin  extends  from  the  ridge  near  the  southern 
shore  of  Lake  Superior,  southerly  to  the  centre  of  the 
state  and  there  dips.  Southerly  of  the  dip  the  water- 
bearing Potsdam  sandstone  lies  upon  the  granite  and  has 
width  of  outcrop  of  about  sixty  miles  on  a north  and  south 
line  midway  between  lake  and  river,  and  then  glasses  under 
a magnesian  limestone.  Upon  this  limestone  is  a layer  of 
St.  Peter  sandstone,  also  water-bearing,  and  this  last  is 
covered  by  yellow  Galena  and  blue  Trenton  limestones  and 
in  Illinois  by  shales,  with  occasional  lower  coal  measures. 

The  wells  of  this  locality  have  depths  varying  from 
1200  to  2000  feet  usually,  according  to  the  relative  altitudes 
of  the  ground  surface  and  water-bearing  stratum. 

These  wells  are  usually  lined  through  the  upper  strata 
with  six  or  eight  inch  iron  pipes,  and  cost  from  three  to  five 
dollars  per  foot  of  depth. 

These  wells  usually  overflow,  with  a moderate  pressure 
when  first  drilled,  and  give  mean  deliveries  of  from  90.000 
to  350,000  gallons  of  water  per  twenty-four  hours,  but  with 
gradual  decrease  of  flow  at  each  well  as  additional  wells  are 
opened. 


ARTESIAN  WELL  STRATA. 


GEOLOGICAL  SECTION  IN  NORTHERN  ILLINOIS  AND  SOUTHERN  WISCONSIN. 


SPRINGS  AND  WELLS. 


108a 


The  piesometric  slope  of  water  pressure  along  this  north 
and  south  line,  prolonged,  is  about  one  foot  per  mile,  indicat- 
ing a much  fissured  as  well  as  coarse  grained  porous  rock. 

The  well  waters  have  temperatures  of  about  60°  Fall. 

The  next  best  known  artesian  basin  is  beneath  the  James 
River  valley  in  the  Dakotas,  where  many  borings  have  been 
made  for  water  supply  and  irrigation  purposes.  Some  of 
the  wells  opened  in  South  Dakota  have  pressures  equivalent 
to  one  hundred  feet  head  and  upwards,  and  their  waters 
have  been  utilized  for  mechanical  power. 

The  deep  wells  east  of  the  Alleghany  mountains  and 
especially  in  eastern  New  England,  have  not  generally  been 
successes  in  either  quantity  or  quality  of  water. 

Piped  Drift  Wells,  usually  termed  driven  wells,  have 
become  much  used  in  the  sources  of  water  supply  for  small 
towns.  The  best  condition  for  these  is  usually  an  inclined 
thick  stratum  of  course  siliceous  sand  resting  upon  imper- 
vious clay  or  rock  and  covered  with  a stratum  of  imper- 
vious clay.  This  water-bearing  sand  stratum  is  the  counter- 
part of  the  water-bearing  sandrock  stratum  in  the  successful 
deep  artesian  wells,  and  for  continued  success  it  must  have 
a very  large  relative  outcrop  for  a watershed. 

Sometimes  a location  is  found,  where  a former  basin  or 
bay  in  the  land  has  subsequently  been  filled  by  a deposit 
of  gravel  or  sand,  and  this  deposit  gathers  a considerable 
portion  of  the  rain  that  falls  upon  its  surface  and  upon  the 
adjoining  higher  grounds.  In  such  case  the  site,  if  there  are 
not  sanitary  objections,  is  favorable  for  driven  pipe  wells. 
Sometimes  extensive  deposits  of  sand  or  gravel  beside  a 
lake  or  water  course,  or  such  deposits  made  by  ancient 
floods,  present  facilities  for  successful  driven  wells.  The 
cities  of  Brooklyn,  L.  I.,  and  Memphis,  Tenn.,  have  very 
unusual  facilities  of  this  kind. 


1086 


SPRINGS  AND  WELLS. 


The  pipes  of  these  wells  have  now  usually  ingenious 
strainers  at  their  feet,  intended  to  admit  waters  freely  hut 
to  exclude  the  sand.  When  a considerable  quantity  of 
water  is  desired  a group  or  line  of  pipe  is  sunk  at  right 
angles  to  the  line  of  subterranean  flow,  and  if  pumping  is 
necessary  the  tops  of  the  pipes  are  coupled  in  to  one  main 
which  is  connected  with  the  suction  chamber  of  the  pump. 

The  success  of  these  drift  pipe  wells  in  both  quantity 
and  quality  of  water  has  many  uncertainties  until  actual 
test  shows  results,  unless  the  geological  conditions  are  fully 
known,  but  fortunately  the  conditions  of  the  drift  sub-strata 
may  often  be  more  easily  studied  than  can  those  of  the  rock 
sub-strata  for  deep  artesian  wells. 

General  practice  seems  to  sanction  an  ordinary  rate  of 
flow  in  the  well  pipes  about  as  follows,  although  great 
natural  pressures  and  pump  suctions  may  at  times  increase 
these  rates,  when  the  rock  is  so  fissured,  or  the  rock  or  sand 
is  so  coarse,  as  to  permit  an  increased  quantity  of  water  to 
enter  the  bore  in  the  rock,  or  the  pipe  strainer. 


TABLE  No.  3 1 a. 
Ordinary  Rate  of  Flow  in  Well  Pipes. 


Diameter  of  Pipe. 

Cubic  feet  per  minute. 

Gallons  per  24  hours. 

Number  of  Pipes  for 
1 million  Gallons  per  24 
Hours. 

Inches. 

2^ 

2.0 

21,542 

46 

3 , 

3-° 

32.30 

31 

3-8 

40»93i 

25 

4 

5-o 

53.856 

66,781 

19 

4^ 

6.2 

15 

5 

7-8 

84,015 

12 

6 

II. 2 

120,637 

9 

7 

15.0 

161,568 

6 

8 

:9-5 

210,038 

5 

IO 

30.0 

3z3.i36 

3 

94.  Watersheds  of  Wells.— The  watershed  of  a deep 
subterranean  supply  is  not  so  readily  distinguishable  as  is 


WATERSHEDS  OF  WELLS. 


109 


tliat  of  a surface  stream,  that  usually  has  its  limit  upon  the 
crowu  of  the  ridge  sweeping  around  its  upper  area. 

The  subterranean  watershed  may  possibly  lie  in  part 
beyond  the  crowning  ridge,  where  its  form  is  usually  that 
of  a concentric  belt,  of  varying  width  and  of  yarying  sur- 
face inclination.  A careful  examination  of  the  position, 
nature,  and  dip  of  the  strata  only,  can  lead  to  an  accurate 
trace  of  its  outlines. 

The  granular  structure  of  the  water-bearing  stratum,  as 
a vehicle  for  the  transmission  of  the  percolating  water,  is  to 
be  most  carefully  studied  ; the  existence  of  faults  that  may 
divert  the  flow  of  percolation  are  to  be  diligently  sought 
for ; and  the  point  of  lowest  dip  in  a concave  subterranean 
basin  or  the  lowest  channel  line  of  a valley-like  subterra- 
nean formation,  is  to  be  determined  with  care. 

A depressed  subterranean  water  basin,  when  first  dis- 
covered, is  invariably  full  to  its  lip  or  point  of  overflow. 
Its  extent  may  be  comparatively  large,  and  its  watershed 
comparatively  small,  yet  it  will  be  full,  and  many  centuries 
may  have  elapsed  since  it  was  moulded  and  first  began  to 
store  the  precious  showers  of  heaven.  A few  drops  accu- 
mulated from  each  of  the  thousand  showers  of  each  decade, 
may  have  filled  it  to  its  brim  many  generations  since  ; yet 
this  is  no  evidence  that  it  is  inexhaustible.  If  the  perennial 
draught  exceeds  the  amount  the  storms  give  to  its  replen- 
ishment, it  will  surely  cease,  in  time,  to  yield  the  surplus. 

Coarse  sands  will,  when  fully  exposed,  absorb  the 
greater  portion  of  the  showers,  but  such  sands  are  usually 
covered  with  more  or  less  vegetable  soil,  except  in  regions 
where  showers  seldom  fall. 

Fissured  limestones  and  chalks  will  also  absorb  a large 
portion  of  the  storms,  if  exposed,  but  they  are  rarely  en- 
tirely uncovered  except  upon  steep  cliff  faces,  where  there 


110 


SPRINGS  AND  WELLS. 


is  little  opportunity  for  the  storms  that  drive  against  them 
to  secure  lodgement. 

95.  Evaporation  from  Soils.— Vegetable  and  surface 
soils  that  do  not  permit  free  percolation  of  their  waters 
downward  to  a depth  of  at  least  three  feet,  lose  a part  of 
it  by  evaporation.  On  the  other  hand,  evaporation  opens 
the  surface  pores  of  close  soils,  so  that  they  receive  a por- 
tion of  the  rain  freely. 

96.  Supplying-  Capacity  of  Wells  and  Springs.— 

Percolation  in  ordinary  soils  takes  place  in  greatest  part 
in  the  early  spring  and  late  autumn  months,  and  to  a lim- 
ited extent  in  the  hot  months.  In  cold  climates  it  ceases 
almost  entirely  when  the  earth  is  encased  with  frost. 

Permanent  subterranean  well  or  spring  supplies  receive 
rarely  more  than  a very  small  share  of  their  yearly  replen- 
ishment between  each  May  and  October,  then-  continuous 
flow  being  dependent  upon  adequate  subterranean  storage. 

Such  storage  may  be  due  to  collections  in  broad  basins, 
to  collections  in  numerous  fissures  in  the  rocks,  or  to  very 
gradual  flow  long  distances  through  a porous  stratum  where 
it  is  subject  to  all  the  limiting  effects  of  retardation  included 
under  the  general  term,  friction. 

In  the  latter  case  a great  volume  of  earth  is  saturated, 
and  a great  volume  of  water  is  in  course  of  transmission, 
and  the  flow  continues  but  slightly  diminished  until  after 
a drought  upon  the  surface  is  over  and  the  parched  surface 
soils  are  again  saturated  and  tilling  the  interstices  of  perco- 
lation anew. 

For  an  approximate  computation  of  the  volume  of  per- 
colation into  one  square  mile  of  porous  gathering  area, 
covered  with  the  ordinary  superficial  layer  of  vegetable  soil, 
and  under  usual  favorable  conditions  generally,  let  us 
assume  that  the  mean  annual  rainfall  is  40  inches  in  depth, 


SUPPLYING  CAPACITY  OF  WELLS  AND  SPRINGS.  Ill 


and  that  in  the  seasons  of  droughts,  or  the  so-called  dry 
years,  60  per  cent,  of  the  mean  monthly  percolation  will 
take  place. 

TABLE  No.  3 1. 

Percolation  of  Rain  into  One  Square  Mile  of  Porous  Soil. 


Assumed  Mean  Annual  Rain  40  Inches  Depth. 


c 

rt 
•— > 

Feb. 

u 

rt 

Apr. 

ci 

2 

<D 

C 

3 

July. 

bi 

3 

Sept. 

Oct. 

Nov. 

Dec. 

Total.  | 

Ratios  of  TV  of  mean 

annual  rain — 

•737 

.796 

I.070 

.814 

1.462 

.964 

I.O77 

1. 251 

I. 015 

I.O76 

■937 

.801 

Inches  of  rain  each 

month 

2-457 

2 653 

3-567 

2.713 

4.873 

3-2I3 

3-59° 

4,  T7° 

3-383 

3-587 

3-123 

2.67O 

40 

Ratios  of  Percolation . . 

•50 

.40 

•45 

15 

•055 

.02 

.OI 

.ooq 

.OI 

.20 

•50 

.70 

Mean  inches  of  Rain 

Percolating 

1.228 

I. o6l 

1.605 

.407 

.268 

.064 

.O36 

.021 

•034 

.717 

1.561 

1.869 

Sixty  per  cent,  of  do.  in 

.161 

dry  years 

•737 

•637 

.963 

.244 

.038 

.022 

.013 

.020 

•430 

•937 

I.T2I 

f ■*,* 

Volume  ot  Perco-  1 ^ 
lation  in  dry-j 

00 

ON 

00 

ON 

rC 

NO 

CO 

NO* 

(O 

O 

N 

CO 

CO 

O 

N 

O 

0 

•T 

NO 

NO*" 

NO 

C£ 

00 

CO 

00 

ro 

years 3 

CO 

N 

NO 

t-- 

CO 

10 

CO 

•T 

ON 

O 

H 

cT 

cT 

cT 

No.  of  persons  it  would 

supply  at  5 cu.  ft. 

eacli  daily 

11,046 

10,570 

*4,434 

3,779 

2,413 

588 

33° 

195 

310 

6,445 

14,512 

16.802 

From  springs , with  the  aid  of  capacious  storage  reser- 
voirs, it  might  be  possible  to  utilize  fifty  per  cent,  of  the 
above  volume  of  percolation.  From  wells , it  would  rarely 
be  possible  to  utilize  more  than  from  ten  to  twenty  per  cent, 
of  the  volume,  without  tank  storage. 

Fifty  per  cent,  of  the  above  total  estimated  volume  of 
percolation  would  be  equivalent  to  a continuous  supply  of 
5 cubic  feet  per  day  each,  to  3391  persons,  or  126,823  gal- 
lons per  diem  ; and  ten  per  cent,  of  the  same  volume  would 
be  equivalent  to  a like  supply  (37.4  gals,  daily)  to  678 
persons,  or  25,357  gallons  per  diem. 

Wells  sunk  in  a great  sandy  plain  bordering  upon  the 
ocean,  or  bordered  by  a dyke  of  impervious  material,  would 
give  greater  and  more  favorable  results,  for  in  such  case  the 
conditions  of  subterranean  storage  would  be  most  favorable, 
but  such  are  exceptional  cases. 


CHAPTER  Till. 


IMPURITIES  OF  WATER. 

• 97.  The  Composition  of  Water. — If  a quantity  of 

pure  water  is  separated,  chemically,  the  constituent  parts 
will  be  two  in  number,  one  of  which  weighing  one-ninth  as 
much  as  the  whole  will  be  hydrogen,  and  the  other  part 
oxygen  ; or  if  the  parts  of  the  same  quantity  be  designated 
by  volume,  two  parts  will  be  hydrogen  and  one  part  oxygen. 

These  two  gases,  in  just  these  proportions,  had  entered 
simultaneously  into  a wondrous  union,  the  mystery  of 
which  the  human  mind  has  not  yet  fathomed.  In  fact, 
many  years  of  intense  intellectual  labor  of  such  profound 
investigators  as  Cavendish,  Lemery,  Lavoisier,  Volta,  Hum- 
boldt, Gray  Lussac,  and  Dumas  wTere  consumed  before  the 
discovery  of  jLe  proportions  of  the  two  gases  that  were 
capable  of  entering  into  this  mystic  union. 

98.  Solutions  in  Water. — If  two  volumes  of  oxygen 
are  presented  to  two  volumes  of  hydrogen,  one  only  of  the 
oxygen  volumes  will  be  capable  of  entering  the  union,  and 
the  other  can  only  be  diffused  through  the  compound,  water. 

> When  alcohol  is  poured  into  water  it  does  not  become 
a part  of  the  water,  but  is  diffused  through  it. 

This  we  are  assured  of,  since  by  an  ingenious  operation 
we  are  able  to  syphon  the  alcohol  out  of  the  water  by  a 
method  entirely  mechanical.  If  we  put  some  sugar,  or 
alum,  or  carbonate  of  soda  into  water,  the  water  will  cause 
the  crystals  to  separate  and  be  diffused  throughout  the 
liquid,  but  they  will  not  be  a part  of  the  water.  The  water 


HORIZONTAL  TURBINES  AND  PUMPS.  To  face  P.  112. 

Wilxim antic  Water  Works.  Conn. 


PROPERTIES  OF  WATER. 


113 


might  be  evaporated  away,  when  the  sugar,  or  alum,  or 
soda  would  have  returned  to  its  crystalline  state.  In  these 
cases,  the  surplus  hydrogen,  the  alcohol,  and  the  constitu- 
ents of  the  crystalline  ingredient  are  diffused  through  the 
water  as  impurities. 

If  in  a running  brook  a lump  of  rock  salt  is  placed,  the 
current  will  flow  around  it,  and  the  water  attack  it,  and  will 
dissolve  some  of  its  particles,  and  they  will  be  diffused 
through  the  whole  stream  below.  A like  effect  results  when 
a streamlet  fl  ows  across  a vein  of  salt  in  the  earth.  In  like 
manner,  if  water  meets  in  its  passage  over  or  through  the 
earth,  magnesium,  potassium,  aluminium,  iron,  arsenic,  or 
other  of  the  metallic  elements,  it  dissolves  a part  of  them, 
and  they  are  diffused  through  it  as  impurities.  In  like 
manner,  if  water  in  its  passage  through  the  air,  as  in 
showers,  meets  nitrogen,  carbonic  acid,  or  other  gases, 
they  are  absorbed  and  are  diffused  through  it  as  impurities. 

99.  Properties  of  Water. — Both  oxygen  gas  and 
hydrogen  gas,  when  pure,  are  colorless,  and  have  neither 
taste  nor  smell.  Water,  a result  of  their  combination,  when 
pure,  is  transparent,  tasteless,  inodorous,  and  colorless, 
except  when  seen  in  considerable  depth. 

The  solvent  powers  of  water  exceed  those  of  any  other 
liquid  known  to  chemists,  and  it  has  an  extensive  range  of 
affinities.  This  is  why  it  is  almost  impossible  to  secure 
water  free  from  impurities,  and  why  almost  every  substance 
in  nature  enters  into  solution  in  water.  There  is  a property 
in  water  capable  of  overcoming  the  cohesive  force  of  the 
particles  of  matter  in  a great  variety  of  solids  and  liquids, 
and  of  overcoming  the  repulsive  force  in  gases.  The  par- 
ticles are  then  distributed  by  molecular  activities,  and  the 
result  is  termed  solution. 

Some  substances  resist  this  action  of  water  with  a large 


114 


IMPURITIES  OF  WATER. 


degree  of  success,  tliougli  not  perfectly,  as  rock  crystals, 
various  spars  and  gems,  and  vitrified  mineral  substances. 

100.  Physiological  Effects  of  the  Impurities  of 
Water. — When  we  remember  that  seventy-five  per  cent,  of 
our  whole  body  is  constituted  of  the  elements  of  water,  that 
not  less  than  ninety-five  per  cent,  of  our  healthy  blood,  and 
not  less  than  eighty  per  cent,  of  our  food  is  also  of  water, 
we  readily  acknowledge  the  important  part  it  plays  in  our 
very  existence. 

Water  is  directly  and  indirectly  the  agency  that  dissolves 
our  foods  and  separates  them,  and  the  vehicle  by  which  the 
appropriate  parts  are  transmitted  in  the  body,  one  part  to 
the  skin,  one  to  the  finger-nail,  one  to  the  eye-lash,  to  the 
bones  phosphate  of  lime,  to  the  flesh  casein,  to  the  blood 
albumen,  to  the  muscles  fibrin,  etc.  When  the  stomach  is 
in  healthy  condition,  nature  calls  for  water  in  just  the 
required  amount  through  the  sensation,  thirst.  Good 
water  then  regulates  the  digestive  fluids,  and  repairs  the 
losses  from  the  watery  part  of  the  blood  by  evaporation 
and  the  actions  of  the  secreting  and  exhaling  organs. 
Through  the  agency  of  perspiration  it  assists  in  the  regula- 
tion of  heat  in  the  body ; it  cools  a feverish  blood  ; and  it 
allays  a parching  thirst  more  effectually  than  can  any  fer- 
mented liquor.  Water  is  not  less  esseutial  for  the  regula- 
tion of  all  the  organs  of  motion,  of  sight,  of  hearing,  and 
of  reason,  than  is  the  invigorating  atmosphere  that  ever  sur- 
rounds us,  to  the  maintenance  of  the  beating  of  the  heart. 

If  from  a simple  plant  that  may  be  torn  asunder  and  yet 
revive,  or  a hydra  that  may  be  cut  across  the  stomach  or 
turned  wrong  side  out  and  still  retain  its  animal  functions, 
the  water  is  quite  dried  away,  if  but  for  an  instant,  man, 
with  his  wonderful  constructive  ability,  and  reason  almost 


MINERAL  IMPURITIES. 


115 


divine,  cannot  restore  that  water  so  as  to  return  the  activity 
of  life  and  the  power  of  reproduction. 

The  human  stomach  and  constitution  become  toughened 
in  time  so  as  to  resist  obstinately  the  pernicious  effects  of 
certain  of  the  milder  noxious  impurities  in  water,  but  such 
impurities  have  effect  inevitably,  though  sometimes  so  grad- 
ually that  their  real  influence  is  not  recognized  until  the 
whole  constitution  has  suffered,  or  perhaps  until  vigor  is 
almost  destroyed. 

Note  the  effect  of  a few  catnip  leaves  thrown  into  drink- 
ing water,  which  will  act  through  the  water  upon  the  nerves  ; 
or  an  excess  of  magnesia  in  the  water  will  neutralize  the  free 
acids  in  the  stomach,  or  lead  in  the  water  will  act  upon  the 
gums  and  certain  joints  in  the  limbs,  or  alcohol  will  act 
upon  the  brain ; and  so  various  vegetable  and  mineral  solu- 
tions act  upon  various  parts  of  the  body. 

It  would  be  fortunate  if  the  pernicious  impurities  in 
water  affected  only  matured  constitutions,  but  they  act  with 
most  deplorable  effect  in  the  helplessness  of  youth  and  even 
before  the  youth  has  reached  the  light.  These  impurities 
silently  but  steadily  derange  the  digestive  organs,  destroy 
the  healthy  tone  of  the  system,  and  bring  the  living  tissues 
into  a condition  peculiarly  predisposed  to  attack  by  malig- 
nant disease. 

101.  Mineral  Impurities. — The  purest  natural  waters 
found  upon  the  earth  are  usually  those  that  have  come 
down  in  natural  streams  from  granite  hills  ; but  if  a thou- 
sand of  such  streams  are  carefully  analyzed,  not  one  of  them 
will  be  found  to  be  wholly  free  from  some  admixture.  This 
indicates  that  in  the  economy  of  nature  it  has  not  been 
ordained  to  be  best  for  man  to  receive  water  in  the  state 
chemically  called  pure.  A United  States  gallon  of  water 
weighs  sixty  thousand  grains  nearly.  Such  waters  as  phy- 


116 


IMPURITIES  OF  WATER. 


sicians  usually  pronounce  good  potable  waters  have  from 
one  to  eight  of  these  grains  weight,  in  each  gallon,  of  certain 
impurities  diffused  through  them.  'These  impurities  are 
usually  marshalled  into  two  general  classes,  the  one  derived 
more  immediately  from  minerals,  the  other  derived  directly 
or  indirectly  from  living  organisms.  The  first  are  termed 
mineral  impurities,  and  the  other  organic  impurities. 

The  mineral  impurities  may  be  resolved  by  the  chemist 
into  their  original  elementary  forms,  and  they  are  usually 
found  to  be  one  or  more  of  the  most  generally  distributed 
metallic  elements,  as  calcium,  magnesium,  iron,  sodium, 
potassium,  etc.  If  as  extracted  they  are  found  united  with 
carbonic  acid,  they  are  in  this  condition  termed  carbonates  ; 
if  with  sulphuric  acid,  sulphates ; if  with  silicic  acid,  sili- 
cates ; if  with  nitric  acid,  nitrates  ; if  with  phosphoric  acid, 
phosphates , etc. ; if  one  of  these  elements  is  formed  into  a 
compound  with  chlorine,  it  is  termed  a chloride;  if  with 
bromine,  it  is  termed  a bromide , etc.  A few  metallic  ele- 
ments may  thus  be  reported,  in  different  analyses,  under  a 
great  variety  of  conditions. 

102.  Organic  Impurities. — There  are  a few  elements 
that  united  form  organic  matter,  as  carbon,  oxygen,  hydro- 
gen, nitrogen,  sulphur,  phosphorus,  potassium,  calcium, 
sodium,  silicon,  manganese,  magnesium,  chlorine,  iron,  and 
fluorine.  Certain  of  these  enter  into  each  organized  body, 
and  their  mode  of  union  therein  yet  remains  sealed  in  mys- 
tery. In  the  results  we  recognize  all  animated  creations, 
from  the  lowest  order  of  plants  to  the  most  perfect  quadru- 
peds and  the  human  species.  All  organic  bodies  may, 
however,  upon  the  extinction  of  their  vitality,  be  decom- 
posed by  heat  in  the  presence  of  oxygen,  and  by  fermenta- 
tion and  putrefaction. 

The  metallic  elements  are,  in  the  impurities  of  good 


ANALYSES  OF  POTABLE  WATERS. 


117 


potable  waters,  usually  much  in  excess  of  the  organic  ele- 
ments, but  the  contained  nitrogenized  organic  impurities 
indicate  contaminations  likely  to  be  much  more  harmful  to 
the  constitution,  and  especially  if  they  are  products  of  ani- 
mal decompositions. 

103.  Tables  of  Analyses  of  Potable  Waters.— We 

will  quote  here  several  analyses  of  running  and  quiet  waters 
that  have  been  used,  or  were  proposed  for  public  water 
supplies,  indicating  such  impurities  as  are  most  ordinarily 
detected  by  chemists  in  water.  For  condensation  and  for 
convenience  of  comparison  they  are  arranged  in  tabular 
form. 

TABLE  No.  3 2. 


Analysis  of  various  Lake,  Spring,  and  Well  Waters. 


Jamaica  Pond,  near 
Brooklyn,  L.  1. 

Flax  Pond,  near 
Lynn,  Mass. 

Sluice  Pond,  near 
Lynn,  Mass. 

Breeds  Pond,  near 
Lynn,  Mass. 

Reeds’  Lake,  near 
Grand  Rapids,  Mich. 

Lake  Konomac,  near 
New  London,  Conn. 

Loch  Katrine,  near 
Glasgow,  Scotland. 

Soring  Water,  near 
Clapham,  England. 

Well  at  Highgate, 
England. 

Artesian  Well,  at 
Hatton,  (England. 

Artesian  Well,  at 
Colney  Hatch,  England. 

Carbonate  of  Lime 

1.092 

.700 

.400 

.600 

4.65 

.O96 

12.583 

1.768 

5-420 

“ Magnesia . 

.408 

.692 

.32° 

.6l2 

1.13 

.216 

n.658 

•734 

I.IOI 

“ Soda 

12.677 

5-921 

Protocarbonate  ot  Iron. . 

4.00 

Chloride  of  Sodium 

.244 

.612 

.408 

.504 

2.l8 

9-556 

8.032 

7-745 

“ Magnesia  . . . 

.328 

trace 

3-553 

“ Calcium.  . . . 

.120 

.... 

.144 

4.930 

“ Potassium... 

1.62 

Alkaline  Chlorides 

•433 

Sulphate  of  Lime 

.120 

.300 

•3°° 

.270 

1.29 

.381 

12.775 

3.798 

“ Magnesia... 

.288 

.050 

“ Potash 

.064 

.070 

14.217 

trace 

2.160 

“ Potassa 

.080 

.086 

'.880 

5.662 

8.776 

7-935 

8.719 

trace 

Phosphate  of  Lime 

trace 

trace 

Nitrate  of  Lime 

33-457 

“ Magnesia 

14.231 

Oxide  of  Iron 

.044 

.840 

trace 

.O96 

.85 

.035 

trace 

Ammonia 

Silica 

.156 

.144 

.120 

•75 

2-43 

.170 

.200 

•747 

.042 

•559 

Organic  Matter 

.008 

2.208 

1-344 

2.184 

8.75 

1.80 

.900 

3-419 

Total  Solids 

to  1 

b\  | 

5-652 

3.072 

5-3l6 

I7-750 

7-831 

2.244 

64.629 

83-549 

35-685 

27-323 

Soluble  Organic  Matter. 
Hardness,  Degrees  by 

.... 

.392 

Clark’s  Scale 

I 

1 

0.80 

.... 

118 


IMPURITIES  OF  WATER. 


TABLE 

Analysis  of  various 


The  quantities  are  expressed  in 
grains  per  U.  S.  Gallon  ot  231  cubic 
inches,  or  58,3721^0  grains. 

Hudson  River,  above 
Albany,  N.  Y. 

1 Hudson  River,  above 
Poughkeepsie,  N.  Y. 

Connecticut  River, 
above  Holyoke,  Mass. 

Connecticut  River, 
above  Springfield,  Mass. 

0 

0 

<u_cf 
— 22. 

"o 

Vj 

Croton  River,  above 
Croton  Dam,  N.  Y. 

Croton  River  Water  in 
New  York  Pipes,  N.  Y. 

5 

0 

“ CO 
- J) 

S| 

c n £ 

tuS 

(A 

1.059 

.85 

•56 

.90 

.67 

1.56 

.60 

2.67 

1-52 

.84 

1.812 

2.126 

.361 

.161 

.108 

.676 

.72 

.49 

.402 

.480 

.86 

•83 

•75 

.156 

“ “ and  Sodium 

.980 

.090 

.146 

.I58 

.280 

.076 

“ Potassa 

2.785 

•43 

.48 

.179 

.200 

.040 

Silicate  of  Potassa 

•156 

.168 

trace 

trace 

Iron  Alumina  and  Phosphates 

.408 

.699 

ty> 

• i33 
1.680 

•3° 

.46 

I.  104 
2.880 

.776 

I.728 

.67 

2.685 

12.699 

4.408 

6.007 

4.24 

7.719 

6.624 

Soluble  Organic  Matter  

Solid  residue  obtained  on  evaporation. 

Hardness,  Degree  by  Clarke’s  Scale. .. 

3-35 

•43 

•51 

:::: 

:::: 

* Notwithstanding  the  exceeding  importance  of  an  intelligent  microscopi- 
cal examination  of  each  proposed  domestic  water  supply,  in  addition  to  the 
chemical  analysis,  no  record  of  such  examination  is  found  accompanying  the 
reports  upon  the  waters  herein  enumerated.  Lenses  of  the  highest  microscop- 
ical powers  should  he  used  for  such  purpose,  and  immersion  lenses  are  required 
in  many  instances. 

To  obtain  specimens  of  sedimentary  matters,  the  sample  of  water  may  first 


ANALYSIS  OF  POTABLE  WATERS. 


119 


No.  33. 

River  and  Brook  Waters.* 


Chickopee  River,  near 
Springfield,  Mass. 

Mill  River,  near 
Springfield,  Mass. 

Grand  River,  above 
Grand  Rapids,  Mich. 

White  River,  in  Filter 
Wells  on  Bank,  at 
Indianapolis,  Md. 

Fallkill  Creek,  near 
Poughkeepsie,  N.  Y. 

Wapinger’s  Creek,  near 
Poughkeepsie,  N.  Y. 

Lynde  Brook,  near 
Worcester,  Mass. 

Thames  River,  above 
London,  Eng. 

Dee  River,  near 
Aberdeen,  Scotland. 

New  River,  London, 
Eng. 

Hampstead  Water  Co.’s 
Supply,  England. 

Cowley  Brook,  near 
Preston,  Eng. 

Loud  Scales,  Preston, 
England. 

Dutton  Brook,  near 
Preston,  Eng. 

•65 

1.30 

7.l8 

10.02 

.51 

6.221 

•334 

13.13 

.709 

6.521 

4.128 

•575 

6.131 

1-343 

•59 

.87 

I.84 

•05 

.909 

2.944 

■238 

.966 

.217 

.40 

.322 

4-245 

.147 

.242 

.152 

•532 

.865 

4.7O 

1.20 

trace 

1.56 

1.442 

5.662 

-938 

•55o 

.970 

.091 

2-37 

•334 

•3X7 

•75 

.07 

I.38 

1.501 

.64 

.11 

•559 

•13 

.260 

3.00 

2.73 

.101 

2.693 

•175 

.321 

.105 

•394 

.926 

1.167 

.287 

•133 

■ 159 

trace 

.092 

.150 

1.242 

12.625 

.780 

.171 

.093 

•348 

.017 

.058 

trace 

trace 

.72 

1.66 

.851 

.167 

•13 

trace 

trace 

trace 

trace 

.12 

trace 

i-37 

trace 

.05 

.275 

.27 

.417 

.058 

•425 

•334 

.401 

1. 104 

3.864 

18.75 

•50 

•15 

trace 

.417 

2.37 

2.327 

i-535 

4.516 

7-339 

3x-24 

2O.99 

6.74 

11.459 

1.727 

20.19 

16.496 

29.678 

3-3x7 

1-774 

3-912 

I.167 

I. l68 

.785 

16.327 

25.527 

3-5°2 

9.340 

4-x44 

6.037 

5-562 

4-633 

•3° 

•63 

14.5 

14.9 

9.8 

x.25 

12 

1.50 

rest  a day  in  a deep,  narrow  dish,  and  then  have  its  clear  upper  water  syphoned 
off.  The  remainder  of  the  water  may  then  be  poured  into  a conical  glass,  such 
as,  or  similar  to,  the  graduated  glasses  used  by  apothecaries,  and  then  again 
allowed  to  rest  until  the  sediment  is  concentrated,  when  the  greater  part  of  the 
clear  water  may  he  carefully  syphoned  off  and  the  sediment  gathered  and 
transferred  to  a slide,  where  it  should  be  protected  by  a thin  glass  cover. 


120 


IMPURITIES  OF  WATER 


TABLE  No.  34. 

Analysis  of  Streams  in  Massachusetts.* 

(Quantities  in  Grains  per  U.  S.  Gallon.) 


Solid  Residue  of 
Filtered  Water. 

Free 

Ammonia. 

Albuminoid 

Ammonia. 

Inorganic. 

Organic  and 
Volatile. 

Total. 

Chlorine, 

Merrimac  River — Mean  of  n ex- 
aminations above  Lowell 

O.OO27 

0.0066 

1.38 

1 .01 

2.39  | 

0.08 

Merrimac  River— Mean  of  12  ex- 
aminations above  Lawrence 

.0026 

.0064 

1. 41 

.98 

2-39 

.12 

Merrimac  River — Mean  of  11  ex- 
aminations below  Lawrence 

.0018 

.0074 

I.54 

1.05 

2-59 

.11 

Blackstone  River,  near  Quinsig- 
amund  Iron  Works 

.105 

.015 

I.98 

1.98 

3*9^ 

.50 

Blackstone  River,  just  above  Mill- 
bury 

.024 

.012 

2.62 

1 • 75 

4-37 

.» 

Blackstone  River,  below  Black- 
stone   

.004 

.008 

1.66 

1 .21 

2.87 

.21 

Charles  River,  at  Waltham 

.0035 

.0096 

2.26 

1.07 

3-33 

.23 

Sudbury  River,  above  Ashland. . . . 

.0030 

.0107 

1.63 

2.50 

4-13 

.23 

Sudbury  River,  at  Concord 

.0026 

.0115 

2.22 

1 -31 

3-53 

.18 

Concord  River,  at  Concord 

.0047 

.0158; 

1.80 

1.42 

3.22  ! 

.20 

Concord  River,  at  Lowell 

.0027 

.OO97 

2.85 

1.59 

4-44  I 

.26 

Neponset  River,  at  Readville 

.0027 

.0158 

I.4O 

1.98 

3-38  ) 

.29 

Neponset  River,  below  Hyde  Park. 

.0064 

.0175 

2.IO 

1.77 

3-87  1 

.30 

104.  Ratios  of  Standard  Gallons. — A portion  of  tlis 
above  analyses  were  found  with  their  quantities  of  im- 
purities expressed  in  grains  per  imperial  gallon,  a British 
standard  measure  containing  70,000  grains,  and  some  of 
them  expressed  in  parts  per  100,000  parts.  They  have  all 
been,  as  have  those  following,  reduced  to  grains  in  a U.  S. 
standard  gallon,  containing  58372.175  grains. 

The  degrees  of  hardness  are  expressed  by  Clark’s  scale, 
which  refers  to  the  imperial  gallon. 


* Selected  from  the  Fifth  Annual  Report  of  the  Mass.  State  Board  of 
Health. 


ANALYSES  OF  WELL  WATERS. 


121 


The  other  quantities  may  be  easily  reduced  to  equiva- 
lents for  imperial  gallons,  by  aid  of  logarithms  of  the  quan 
tities  or  of  the  ratios : 


Imperial  gallon — No.  of  grains 70000  Logarithm,  4.845098 


U.  S.  gallon — No.  of  grains 58372.175 

Ratio  of  imp.  to  U.  S.  gallon 1.199201 

“ of  U.  S.  to  imperial  gallon 833886 

“ of  cubic  foot  to  one  imp.  gallon. . . 6.23210 

“ “ “ “ “ “ U.  S.  “ . . . 7.48052 

“ “ one  imp.  gall,  to  one  cu.  ft 16046 

“ “ “ U.S.  “ “ “ “ “ 13368 


4. 766206 
0.078892 
1.921108 
0.794634 
0.873932 
1.205367 
1.126066 


The  following  analyses  of  various  well  waters  are  in  a 
more  condensed  form : 


TABLE  No.  35. 

Analyses  of  Water  Supplies  from  Domestic  Wells. 
(Quantities  in  Grains  per  U.  S.  Gallons.) 


Wells. 

Mineral 

Matters. 

Organic 

Matters. 

J £ 
< 2 
h j 
0 C 

He n 

Hardness, 

Clark’s 

Scale. 

Albany,  Capital  Park 

65.20 

“ Lvdius  Street 

19.24 

“ average  of  several 

48.69 

Boston,  Beacon  Hill 

50.00 

“ Tremont  Street 

26.60 

“ Long  Acre 

56.80 

“ average  of  three 

44.46 

“ Old  Artesian 

54-35 

1.85 

55.20 

Brookline,  Mass 

9.89 

4.08 

13-97 

Brookl}-n,  L.  I 

45.40 

“ average  of  several 

48.83 

Charlestown,  Mass 

26.40 

Cape  Cod 

TO. 01 

2.41 

12.42 

Detroit,  Mich 

116.46 

Dayton,  Ohio 

56.50 

Dedham,  Mass.,  Driven  Pipe 

5-12 

1. 12 

6.24 

“ “ Artesian 

4.08 

1 .11 

5.19 

Fall  River,  Mass.,  average  of  seventeen.. 

25.16 

7.00 

32.16 

12.17 

Hartford,  Conn.,  No.  1 

19-33 

8-39 

“ “ No.  2 

32.16 

13-44 

“ “ No.  3 

37-io 

“ “ No.  4 

“ “ No.  5 

43- 60 

69.05 

io-55 

19.22 

122 


IMPURITIES  OF  WATER. 


Analyses  of  Water  Supplies  from  Domestic  Wells — ( Continued ) 


Wells. 

Mineral 

Matters. 

Organic 

Maimers. 

Total 

Solids. 

Hardness, 

Clark's 

Scale. 

Indianapolis,  Ind 

60  OO 

Lowell,  Mass.,  average  of  fifteen 

39-33 

8.71 

London,  Eng.,  Leadenhall  Street 

90.38 

9-59 

99-97 

.... 

“ “ St.  Paul’s  Churchyard. .. . 

62.54 

Lambeth,  “ 

83-39 

Lynn,  Mass 

34.08 

Manhattan,  N.  Y 

104 . 00 

“ average  of  several 

49.00 

New  Haven,  Conn.,  average  of  five 

New  York,  west  of  Central  Park 

38.95 

4-59 

20.32 

43-54 

“ average  of  several 

58.00 

Newark,  N.  J.,  average  of  several 

19.36 

Providence  R.  I.,  average  of  twenty-four. 

24.05 

8.82 

33-02 

IO.87 

“ “ purest  of  “ 

7.76 

3-35 

II.  II 

7.70 

“ “ foulest  of  “ 

56.99 

24.12 

81. 11 

22.26 

Portland,  Me.,  average  of  four 

13-35 

5-13 

18.48 

Pawtucket,  R.  I 

29. 16 

3- 03 

32.19 

“ “ 

25.08 

3-73 

28 . 81 

“ “ 

18.68 

3-62 

22.30 

Paris,  France,  Artesian 

9.86 

Rochester,  N.  Y.,  average  of  General 

30.00 

Rye  Beach,  N.  H 

6.08 

2-43 

8.51 

Springfield,  Mass 

7.82 

2.03 

9-85 

8.81 

2.01 

10.82 

<(  ti 

11-53 

1. 91 

13-44 

It  U 

14-83 

3- 08 

17.91 

Schenectadv,  N.  Y.,  State  Street 

46.88 

2-33 

49.21 

Taunton,  Mass 

20.14 

2.98 

23.12 

“ “ 

39-86 

4.09 

43-95 

Waltham,  “ 

7.68 

4.08 

11.76 

“ “ Pump 

17-79 

7.46 

25.25 

Winchester,  “ 

4.00 

2.40 

6.40 

“ “ 

8.00 

2.40 

10.40 

“ <l  

10.80 

2.04 

13.20 

Woburn,  Mass.,  average  of  four 

51-52 

4.60 

56.12 

105.  Atmospheric  Impurities. — The  constant  disin- 
tegration of  mineral  matters  and  the  constant  dissolutions 
of  organic  matters,  and  their  disseminations  in  the  at- 
mosphere, offer  to  falling  rains  ever-present  sources  of  ad 
mixture,  finely  comminuted  till  just  on  the  verge  of  trans- 
formation into  their  original  elements.  The  force  of  the 
winds,  the  movements  of  animals,  the  actions  of  machines, 


SUB-SURFACE  IMPURITIES. 


123 


are  every  moment  producing  friction  and  rubbing  otf  minute 
particles  of  rocks  and  woods  and  textile  fabrics.  Decaying 
organisms,  breaking  into  fibre,  are  caugbt  up  and  wafted 
and  distributed  hither  and  thither. 

The  atmosphere  is  thus  burdened  with  a mass  of  lifeless 
particles  pulverized  to  transparency. 

■'A  ray  of  strong  light  thrown  through  the  atmosphere  in 
the  night,  or  in  a dark  room,  reveals  by  reflection  this  sea  of 
matter  that  vision  passes  through  in  the  light  of  noon-  day. 
These  matters  the  mists  and  the  showers  absorb,  and  dis- 
solve in  solution. 

The  respirations  of  all  animate  beings,  the  combustions 
of  all  hearth-stones  and  furnaces,  and  the  decaying  dead 
animals  and  vegetables,  continually  evolve  acid  and  sul- 
phurous gases  into  the  atmosphere.  Chief  among  the  del- 
eterious gases  arising  from  decompositions  are  carbonic 
acid,  nitrous  and  nitric  acids,  chlorine,  and  ammonia. 
These  are  all  soluble  in  water,  and  the  mists  and  showers 
absorb  them  freely.  Ehrenberg  states  that,  exclusive  of 
inorganic  substances,  he  has  detected  three  hundred  and 
twenty  species  of  organic  forms  iu  the  dust  of  the  winds. 
Hence  the  so-called  pure  waters  of  heaven  are  fouled,  before 
they  reach  the  earth,  with  the  solids  and  gases  of  earth. 

106.  Sub-surface  Impurities. — The  waters  that  flow 
over  or  through  the  crevices  of  the  granites,  gneisses,  ser- 
pentines, trappeans,  and  mica  slates,  or  the  silicious  sand- 
stones, or  over  the  earths  resulting  from  their  disintegrations, 
are  not  usually  impregnated  with  them  to  a harmful  extent, 
they  being  nearly  insoluble  in  pure  water. 

The  limestones  and  chalks  often  impart  qualities  objec- 
tionable in  potable  waters,  and  troublesome  in  the  house- 
hold uses  and  in  processes  of  art  and  manufacture. 

The  drift  formation,  wherever  it  extends,  if  unpolluted 


124 


IMPURITIES  OF  WATER. 


"by  organic  remains  upon  or  in  its  surface  soil,  usually  sup- 
plies a wholesome  water. 

The  presence  of  carbonic  acid  in  water  adds  materially 
to  its  solvent  power  upon  many  ingredients  of  the  soil  that 
are  often  present  in  the  drift,  such  as  sulphate  of  lime, 
chloride  of  sodium,  aud  magnesian  salts,  and  upon  organic 
matters  of  the  surface.  % 

Carbonic  acid  in  rain-water  that  soaks  through  foul  sur- 
face soils,  gives  the  water  power  to  carry  down  to  the  wells 
a superabundance  of  impurities. 

The  presence  of  ammonia  is  a quite  sure  indication  of 
recent  contamination  with  decaying  organic  matter  capable 
of  yielding  ammonia,  whether  in  spring,  stream,  or  well. 
This  readily  oxidizes,  and  is  thus  converted  into  nitrous 
acid  and  by  longer  exposure  into  nitric  acid. 

These  acids  combine  freely  with  a lime  base,  as  nitrate 
and  nitrite  of  lime. 

Analysts  attach  great  importance  to  the  nature  of  the 
nitrates  and  nitrites  present,  as  indications  of  the  nature  of 
the  contaminations  of  the  water. 

Some  of  the  subterranean  waters  penetrate  occasional 
strata  that  wholly  unfit  them  for  domestic  use.  A portion 
of  the  carboniferous  rocks  are  composed  so  largely  of  min- 
eral salts  that  their  waters  partake  of  the  nature  of  brine,  as 
in  parts  of  Ohio  ; in  the  Kanawha  Valley,  West  Virginia ; 
and  in  parts  of  New  York  State  ; for  instance,  at  Syracuse, 
where  the  manufacture  of  salt  from  sub-surface  water  lias 
assumed  great  commercial  importance.  In  other  sections, 
the  bituminous  limestones  are  saturated  with  coal-oils,  as  in 
the  famous  oil  regions  of  Pennsylvania.  The  dark  waters 
from  the  sulphurous  strata  of  the  Niagara  group  of  the 
Ontario  geological  division  are  frequently  impregnated  with 
sulphuretted  hydrogen. 


HARDENING  IMPURITIES. 


125 


All  along  the  western  flank  of  the  Appalachian  chain, 
from  St.  Albans  and  Saratoga  on  the  north  to  the  White 
Sulphur  Springs  on  the  south,  the  frequent  mineral  springs 
give  evidence  of  the  saline  sub-structure  of  the  lands,  while 
like  evidences  have  recently  become  conspicuous  in  certain 
portions  of  Kentucky,  Arizona,  New  Mexico,  Utah,  Califor- 
nia, and  Oregon. 

107.  Deep-well  Impurities. — Deep  well  and  spring 
waters,  except  those  from  dipping  sand  or  sandstone  strata, 
are  especially  liable  to  impregnations  of  mineral  salts. 

These  impurities  from  deep  and  hidden  sources,  when 
present  in  quantities  that  will  be  harmful  to  the  animal 
constitution,  are  almost  invariably  perceptible  to  the  taste, 
and  are  rejected  instinctively. 

10S.  Hardening-  Impurities. — The  solutions  of  salts 
of  lime  and  magnesia  are  among  the  chief  causes  of  the 
quality  called  hardness  in  water.  Their  carbonates  are 
broken  up  by  boiling,  for  the  heat  dissipates  the  carbonic 
acid,  when  the  insoluble  bases  are  deposited,  and,  with  such 
other  insoluble  matters  as  are  present,  form  incrustations 
such  as  are  seen  in  tea-kettles  and  boilers  where  hard  waters 
have  been  heated.  The  carbonates,  in  moderate  quantities, 
are  less  troublesome  to  human  constitutions  than  to  steam 
users.  The  effects  of  the  carbonates  are  termed  temporary 
hardness.  The  sulphates,  chlorides,  and  nitrates  of  lime 
and  magnesia  are  not  dissipated  by  ordinary  boiling. 
Their  effects  are  therefore  termed  permanent  hardness. 

An  imperial  gallon  of  pure  water  can  take  up  but  about 
two  grains  of  carbonate  of  lime,  when  it  is  said  to  have  two 
degrees  of  hardness ; but  the  presence  of  carbonic  acid  in 
the  water  will  enable  the  same  70,000  grains  of  water  to  dis- 
solve twelve,  sixteen,  or  even  twenty  grains  of  the  carbonate, 
when  it  will  have  twelve,  sixteen,  or  twenty  degrees  of 


126 


IMPURITIES  OF  WATER. 


hardness,  according  to  the  number  of  grains  taken  into 
solution. 

These  salts  of  lime  and  magnesia,  and  of  iron,  in  water, 
have  the  property  of  decomposing  an  equivalent  quantity 
of  soap,  rendering  it  useless  as  a detergent ; thus,  one 
degree  or  grain  of  the  carbonate  neutralizes  ten  grains  of 
soap ; two  degrees,  twenty  grains  of  soap ; three  degrees, 
thirty  grains,  etc. 

This  source  of  waste  from  foul  hard  waters,  which  extends 
to  the  destruction  of  many  valuable  food  properties,  as  well 
as  to  destroying  soap,  is  not  sufficiently  appreciated  by  the 
general  public. 

It  may  be  safely  asserted  that  a foul  hard  well  water 
will  destroy  from  the  family  that  uses  it,  more  value  each 
year  than  would  be  the  cost  in  money  of  an  abundant 
supply  of  water  for  domestic  purposes,  from  an  accessible 
public  water  supply ; and  this  refers  to  purchased  articles 
merely,  and  not  to  destruction  of  human  health  and  energy, 
which  are  beyond  price. 

109.  Temperatures  of  Deep  Sub- surface  Waters. 

— Very  deep  well  and  spring  waters  have,  upon  their  tirst 
issue,  too  high  a temperature  for  drinking  purposes,  as  from 
the  artesian  wells  of  the  Paris  basiu.  which  rise  at  a tem- 
perature of  82°  Fall.,  and  as  from  hot  springs,  among  which, 
for  illustration,  may  be  mentioned  the  Sulphur  Springs, 
Florida,  of  70°  Fall.,  the  Lebanon  Springs,  N.  Y.,  of  73°  F. ; 
and,  as  extremes  of  high  temperature,  the  famous  geysers 
of  the  Yellowstone  Yalley,  at  a boiling  temperature,  and 
the  large  hot  spring  near  the  eastern  base  of  the  Sierra 
Nevadas  and  Pyramid  Lake,  whose  broad  pool  has  a tem- 
perature of  206°,  and  central  issue  212°.  The  springs  at 
Cliaudes  Aigues,  in  France,  have  a temperature  of  176°. 
and  the  renowned  geysers  of  Iceland,  of  212°. 


DECOMPOSING  ORGANIC  IMPURITIES. 


127 


Artesian  wells  have  temperatures  for  given  depths  ap- 
proximately as  follows : 

TABLE  No.  3 6. 


Artesian  Well  Temperatures. 


Depth  in  Feet 

IOO 

500 

1000  1500 

2000 

2500  1 3000 

Temperature,  deg.  Fah 

52 

59 

68  76 

85 

94  102 

110.  Decomposing-  Organic  Impurities.— If  we  re- 
solve, chemically,  a piece  of  stone,  ore,  wood,  fruit,  a cup 
of  water,  or  an  amputated  animal  limb,  into  their  simple 
elements  within  the  limits  of  exact  chemical  investigation, 
we  shall  find  that  their  varied  compositions  and  proper- 
ties are  results  of  combinations,  substantially,  of  the  same 
few  elements  ; and  that  the  organic  substances— that  is,  such 
as  are  the  result  of  growth  under  the  influence  of  their  own 
vitality — are  composed  chiefly  of  carbon,  oxygen,  hydrogen, 
and  nitrogen,  with  spare  proportions  of  a few  metalloids, 
as  above  enumerated.  The  general  order  of  predominance 
of  the  gases  and  metalloids  is  not,  however,  quite  the  same 
in  mineral  as  in  organic  matters.  But  notwithstanding  this 
apparent  similarity  of  chemical  compositions,  there  is  a 
quality  in  organic  substances  accompanying  the  vital  force, 
that  makes  it  as  widely  different  in  essential  characteristics 
from  simple  mineral  compounds  as  life  is  from  death. 

The  mysterious  properties  which  accompany  only  the 
vital  force  do  not  submit  to  analyses  by  human  art.  They 
are  known  only  by  their  results  and  their  effects. 

In  the  natural  decomposition  of  animal  matters,  espe- 
cially in  their  stage  of  putrefaction,  their  elements  are  often 
in  a condition  of  molecular  activity  that  will  not  admit  of 
their  being  safely  brought  into  contact  with  the  human 


128 


IMPURITIES  OF  WATER. 


circulation,  where  they  will  be  liable  to  induce  disturbing 
conditions. 

Witness  the  extreme  danger  to  a surgeon  who  receives 
a minute  quantity  of  animal  fluid  into  a sore  upon  his  hand, 
when  dissecting  a dead  body,  even  though  the  life  has  been 
extinct  but  one  or  two  days. 

The  excreta  of  living  animals  also  passes  through  a 
decomposing  transformation,  in  which  stage  they  cannot 
safely  be  brought  into  contact  with  the  human  circulation, 
however  finely  they  may  be  dissolved  in  water,  when  re- 
ceived. 

The  process  of  decay  in  dead  animal  bodies,  and  of  de- 
composition of  vegetable  substances,  is  quite  rapid  when 
moisture  and  an  abundance  of  atmospheric  air,  or  available 
oxygen  in  any  form,  are  present,  and  a warm  temperature 
promotes  the  activity  of  the  elements  ; hence  the  same  mat- 
ter does  not  long  remain  in  its  most  objectionable  state,  but 
from  the  multiplicity  of  bodies  on  every  hand,  a constant 
source  of  pollution  may  be  maintained. 

Potable  waters,  when  exposed  to  those  organic  matters 
in  process  of  rapid  decay,  meet  perhaps  their  most  fatal 
sources  of  natural  and  microbic  contamination,  that  are 
not  readily  detected  l>y  the  eye  and  tongue. 

111.  Vegetable  Organic  Impurities. — Nature  around 
us  swarms  with  an  abundance  of  both  vegetable  and  ani- 
mal life,  in  air,  in  earth,  hi  stream  and  sea,  and  therefore 
death  is  constantly  on  every  hand,  and  its  dissolutions 
meet  the  waters  wherever  they  fall  or  flow.  There  are 
numerous  plants,  trees,  insects,  and  animals  that  we  recog- 
nize day  by  day,  but  there  are  undoubtedly  species  and 
classes  more  innumerable  above  and  below,  that  we  can  dis- 
cover only  when  our  vision  is  aided  by  magnifying  lenses. 

Upon  the  meadow  pools  and  small  ponds  of  the  swamps, 


VEGETAL  OEGANISMS  IN  WATER-PIPES. 


129 


species  of  microscopic  fungi,  not  unlike  the  mould  upon 
decaying  fruit,  though  less  luxuriant,  are  found  in  abun- 
dance by  searchers  who  suspect  their  presence.  To  the 
general  observer  they  appear  as  dust  upon  the  water  or 
give  to  it  a slight  appearance  of  opaqueness. 

There  are  species  of  fresli-water  algse  that  thrive  in 
abundance,  peculiar  to  all  seasons,  and  they  are  said  to  have 
been  found  in  the  heated  waters  of  boiling  spring  basins, 
and  also  in  healthy  life  within  an  icicle,  and  they  are  the  last 
of  life  high  up  on  the  mountain  slopes,  near  the  borders  of 
eternal  suows.  Ditches,  pools,  springs,  rivers,  lakes,  and 
dripping  grottoes  have  each  their  native  class.  In  stagnant 
waters  abound  the  oscillatorise  of  dull-greenisli  or  dark- 
purplish  or  bluish  color,  forming  dense  slimy  strata,  and 
the  brighter  green  zygenemas  which  float  or  lie  entangled 
among  the  water  plants. 

The  desmids  abound  in  the  early  spring  of  the  year,  and 
various  algse  flourish  in  the  autumn.  A thrifty  fungus  of 
the  genus  Noctos  frequents  the  quiet  waters  of  lower  New 
England  and  the  Middle  States. 

These  plants  at  their  dissolution  often  impart  an  oily 
appearance,  a greenish  or  brownish  color,  and  a somewhat 
offensive  smell  to  the  water.  The  noctos,  while  in  active 
growth,  forms  part  of  the  green  scum  often  seen  upon  the 
surface  of  still  water.  The  fishy  smell  and  the  color  which 
they  impart  to  the  water  in  decomposing  seems  to  be  largely 
due  to  an  essential  oil  which  they  give  out  when  breaking  up. 

112.  Vegetal  Organisms  in  Water-Pipes.  — A 
species  of  confervee  has  been  found  growing  and  multiply- 
ing rapidly  within  water-pipes,  having  taken  root  in  the 
fine  organic  sediment  deposited  from  feeble  currents  of 
water  in  the  dead  ends  or  in  the  large  mains.  These  micro- 
scopic plants,  after  maturing  in  abundance,  are  detached 


130 


IMPURITIES  OF  WATER. 


by  the  current,  decompose,  and  impart  an  appreciable 
amount  of  odor  and  taste  to  the  water,  reduce  its  trans- 
parency and  give  a slight  tinge  of  color. 

112a.  Bacteria. — Bacteria  are  the  smallest  vege- 
table colorless  microcosms  of  the  class  Algse.  The  group 
is  large  and  the  forms  varied,  and  under  favoring  con- 
ditions their  multiplication  is  rapid,  and  their  influence 
upon  the  organic  matter  or  life  with  which  they  come  in 
contact,  and  upon  which  they  thrive,  is  sometimes  most 
momentous  in  its  consequences. 

They  are  widely  diffused  in  nature  wherever  there  is 
both  warmth  and  moisture,  and  multiply  so  rapidly  by 
fission  or  by  spores  that  they  are  almost  omnipresent  in 
water  and  air.  Two  hundred  forms  of  micro-organisms, 
found  in  water,  have  been  described  by  the  Frank! antis. 

A large  majority  of  the  bacteria  are  deemed  to  be  use- 
ful as  scavengers  that  assist  in  reconverting  dead  organic 
matters  in  and  above  the  water  into  new  elements,  and  thus 
promote  the  processes  of  sturdier  green  vegetation  and  the 
purification  of  the  waters.  Such  bacteria  are  termed 
saprophytic,  and  they  are  present  where  there  is  fermen- 
tation and  putrefaction  as  active  agents  in  these  processes. 
There  are  certain  of  the  bacteria  that  thrive  best  on  the 
tissues  of  living  organisms.  Such  are  termed  parasitic, 
and  it  is  these  that  Water  Commissioners,  physicians,  and 
humanity  in  general  fear  most,  for  the  products  of  their 
nutrition  are  poisonous  to  the  tissues  attacked,  and  the 
results  disease  producing,  sometimes  fatal. 

Even  clear  spring  water  contains  usually,  as  it  issues, 
a few  bacterial  plants.  These  waters,  and  filtered  waters 
having  at  first  a few  plants,  may  experience,  within  three 
days  of  the  exposure  of  the  water  to  the  summer  atmos- 
phere, a multiplication  of  the  growths  several  thousand  fold 
Most  waters  of  fresh  ponds  contain  bacteria  in  abundance. 


BACTEEIA. 


130a 


The  waters  of  such  rivers  as  the  Thames  in  England, 
the  Seine,  Marne  and  Oureq  in  France,  and  the  Spree  in 
Germany,  have  been  found  to  contain  ordinarily,  as  the 
seasons  vary,  from  5,000  to  50,000  micro-organisms  per 
cubic  centimeter,  or  nearly  one  tea-spoonful  of  water. 
Sediments  or  the  slimes  on  submerged  surfaces  have  been 
found  to  contain  one  and  one-half  million  organisms  in  a 
like  volume  of  water.  The  faeces  of  a typhoid  patient 
have  been  found  to  contain  one  thousand  million  organ- 
isms in  a like  volume.  The  total  number  in  a single  putre- 
fying carcass  is  inconceivable. 

Crystallization  of  the  water  by  frost  does  not  certainly 
destroy  the  bacteria,  but  their  activities  are  checked  by 
temperatures  less  than  50°  Fahr. 

A warmth  equal  to  the  normal  temperature  of  the 
human  body,  about  100°  Fahr.,  is  favorable  to  their 
growth.  A temperature  of  212°  is  destructive,  if  con- 
tinued a quarter  of  an  hour  or  more. 

Manifestly  it  is  not  in  the  number  alone,  but  in  the 
parasitical  kind  of  microbes  brought  in  our  drinking  water 
that  we  fear  the  origin  of  an  epidemic. 

If  a cistern  or  well  or  stream  has  been  subject  to  drain- 
age affected  by  the  dejecta  of  fever  patients  or  by  any  ani- 
mal evacuations;  if  a stream  is  subject  to  the  disintegra- 
tions of  dead  animal  substances  or  to  sewage  containing  or- 
ganic matter  in  dissolution,  or  even  to  hospital  or  house- 
hold drainage,  the  waters  may  be  stocked  with  parasitic 
germs. 

Hence  there  is  microbial  danger  in  water  supplies 
affected  by  drainage  from  manured  fields,  there  is  danger 
from  infusions  of  even  a relatively  small  amount  of  sew- 
age, there  is  danger  from  infusions  of  any  animal  matters, 
and  hence  there  is  extreme  hazard  to  a community  when 
the  dissolutions  of  a carcass  permeates  its  well  water,  its 


1306 


IMPURITIES  OF  WATER. 


stream  of  water  supply  or  its  reservoir  storage  with  those 
parasitic  microbes  which  thrive  upon  and  destroy  human 
tissues  and  blood. 

113.  Animate  Organic  Impurities. — The  waters 
are  not  less  pregnant  with  animal  than  vegetal  life.  The  mi- 
croscope has  here  extended  our  knowledge  of  varieties  and 
numbers  of  species  also,  especially  in  waters  infused  with 
organic  substances. 

The  tiny  infusoria  were  first  discovered  in  strong  vegeta- 
ble infusions,  hence  the  name  given  to  them ; but  with  the 
extension  of  microscopical  science,  the  class  has  been  ex- 
tended to  include  a variety  of  animate  existences,  from  the 
quiet  fresh  water  sponge  to  the  most  energetic  little  creatures 
that  battle  ferociously  in  a drop  of  water. 

Dr.  Crace  Calvert  has  shown  * that  when  albumen  from 
a new  laid  egg  is  introduced  in  pure  distilled  water  and 
exposed  to  the  atmosphere,  minute  globular  bodies  soon 
appear  having  independent  motion.  These  he  denominated 
monads. 

Their  appearance  was  earlier  in  lake  water  than  in  dis- 
tilled water,  and  earliest  and  most  abundant  in  solutions 
of  largest  exposure  to  the  atmosphere. 

These  monads  have  diameters  of  about  y^sVoo  °f  an 
inch ; in  their  next  successive  stage,  of  about  yowti  an 
inch  ; and  then  of  about  gyVo  of  an  inch.  He  denominates 
them  vibrios  in  the  two  last  stages.  Then  they  change  into 
cells,  having  power  to  pass  over  the  field  of  the  microscope 
rapidly. 

The  albuminous  products  of  decaying  leaves  and  plants 
in  water  also  promote  the  generation  of  aquatic  life,  and 
dead  animal  substances  are  almost  immediately  inhabited 
by  a myriad  of  creatures. 

* Papers  read  before  the  Royal  Society,  London. 


AQUATIC  ORGANISMS. 


131 


The  discussion  upon  the  question  of  spontaneous  gene- 
ration in  progress  at  the  opening  of  our  centennial  year,  is 
adding  many  new  and  interesting  experimental  results  to 
the  researches  of  Pasteur  and  Schroeder,  relating  to  the 
propagation  of  bacterial  life  from  atmospheric  mote  germs, 
and  the  agency  of  germs  in  the  spread  of  epidemic  contagia. 
Prof.  Tyndall  and  Dr.  Bastian,  the  leading  controversialists 
in  this  discussion,  are  agreed  that  both  vegetable  and  animal 
infusions,  if  exposed  to  the  summer  atmosphere,  will,  ordi- 
narily, abound  in  bacterial  life  in  about  three  days. 

There  are  also  in  the  streams  and  lakes  the  larger 
zoophytes,  mollusca,  articulata,  and  Crustacea,  some  of  which 
are  familiar  products  of  the  waters,  and  also  fish  in  great 
variety. 

But  all  of  these  do  not  pass  through  the  objectionable 
putrefactive  stage  described  above.  The  weaker  classes 
are  food  for  the  stronger,  and  the  smaller  of  some  classes 
food  for  the  larger  of  the  same  class.  Of  the  many  that 
come  into  being,  comparatively  few  survive  till  a natural 
death  terminates  their  existence,  but  each  devours  others 
for  a substantial  part  of  its  own  nourishment,  and  hides, 
fights,  or  retreats  to  preserve  its  own  existence. 

114.  Propagation  of  Aquatic  Organisms. — A warm 
temperature  of  both  air  and  water  are  requisite  for  the  abun- 
dant propagation  of  aquatic  life.  The  presence  of  a consid- 
erable amount  of  either  vegetable  or  animal  impurities  in 
the  waters  seems  also  a requisite  for  the  lower  grades  of  life. 

How  far  certain  electrical  influences  in  the  air  and  water 
control  the  results  are  not  yet  determined.  Certain  it  is, 
however,  that  the  microscopic  creatures  sometimes  swarm 
suddenly  in  abundance  in  quiet  lakes  and  pools,  in  a seem- 
ingly unaccountable  manner,  remain  in  abundance  for  a 
few  days,  or  possibly  a few  weeks  in  rare  seasons,  and  then 


132 


IMPURITIES  OF  WATER. 


as  mysteriously  disappear.  There  is  a similar  appearance 
of  microscopic  plants,  when  all  the  natural  conditions  favor- 
able thereto  occur  simultaneously,  but  their  coming  cannot 
always  be  predicted,  neither  can  the  time  of  their  disap- 
pearance be  foretold. 

A very  brief  existence  is  allotted  to  a large  share  of  the 
minute  vegetal  and  animate  aquatic  beings  we  have  had  in 
consideration.  Perhaps  the  greater  share  of  the  animate, 
count  scarce  a single  circuit  of  the  sun  in  their  whole  term  ; 
others  soon  pass  to  a higher  stage  in  them  existence,  and 
are  thereafter  terrestrial  in  their  habits. 

115.  Purifying  Office  of  Aquatic  Life. — One  of  the 
chief  offices  of  the  inferior  inhabitants  of  the  waters  is  to 
aid  in  their  purification  by  devouring  and  assimilating  the 
dead  and  decaying  organic  matters. 

The  infusorial  ani  male  aim  are  undoubtedly  encouraged 
in  their  propagation  by  the  presence  of  impurities  so  far  as 
to  be  an  unmistakable  indication  of  such  impurities ; and 
they,  on  the  other  hand,  attack  and  destroy  such  impurities 
for  their  own  nourishment,  when  they  are  devoured,  and 
their  devourers  devoured  by  higher  existences,  till  the  last 
become  food  for  fish  that  constitutes  a food  for  man. 

Tills,  and  this  only,  is  the  proper  channel  through  which 
the  decomposing  organic  impurities  in  water  should  reach 
the  human  stomach,  having  by  Nature’s  wonderful  pro- 
cesses of  assimilation  been  first  converted  into  superior 
liviug  tissues. 

A great  variety  of  fish  are  daily  consumed  for  our  food, 
also  of  mollusca  from  salt  water,  as  clams,  oysters,  and  mus- 
sels, also  of  Crustacea,  as  lobsters,  crabs,,  shrimp,  etc.;  hence 
we  infer  that  the  higher  orders  of  fresh  water  inhabitants  are 
not  harmful  while  living  therein,  and  are  nourishing  as  food, 
if  consumed  while  the  influence  of  their  vital  force  remains 


ABRASION  IMPURITIES. 


133 


The  action  of  oxygen  upon  organic  bodies  tends  always 
powerfully  to  decomposition,  but  is  counteracted  by  the 
vital  force.  When  the  vital  force  ceases  then  decomposi- 
tion soon  begins,  and  then  the  body  acted  upon  is  unfitted 
for  the  human  digestive  organs. 

11G.  Intimate  Relation  between  Grade  of  Organ- 
isms and  Quality  of  Water. — The  grade  and  character 
of  the  growths  in  fresh  water  are  almost  invariably  reliable 
tests  of  the  quality  of  the  water,  and  if  the  plants  be  fine- 
grained, firm,  and  delicate  in  outline,  or  the  fish  trim  in 
form,  lithe  in  motion,  and  fine  in  flavor,  the  water  is  most 
sure  to  be  good. 

117.  Animate  Organisms  in  Water-Pipes. — Nearly 
all  of  the  animate  aquatic  existences  must  rise  frequently 
to  the  water  surface  to  secure  their  necessary  share  of  at- 
mospheric oxygen.  If  any  of  them,  not  having  tracheal 
gills,  or  their  equivalents,  to  enable  them  to  breathe  a long 
time  under  water,  are  drawn  into  the  pipes,  and  are  thus 
cut  off  from  their  supply  of  oxygen,  they  soon  perish. 
Then,  if  the  water  is  not  of  low  temperature,  their  decom- 
position soon  commences,  and  an  offensive  gas  from  their 
bodies  enters  into  solution  with  the  water. 

118.  Abrasion  Impurities  in  Water.  — The  most 
prominent  sources  of  the  frictional  impurities  are  the  banks 
of  clay  and  sand  bordering  upon  the  running  streams,  and 
the  plowed  fields  of  the  hillside  farms.  The  movement 
of  these  sedimentary  matters  in  suspension  is  dependent 
largely  upon  the  force  of  storms  and  floods,  and  in  the  ma- 
jority of  streams  their  movement  is  rapid  toward  the  sea, 
where  they  are  massed  in  foundations  of  lagoons  and  islands. 

With  them  are  swept  away  a great  bulk  of  the  matured 
products  of  vegetation  that  annually  ripen  in  the  forest,  the 
field,  and  upon  the  banks  of  the  streams. 


134 


IMPURITIES  OF  WATER. 


119.  Agricultural  Impurities. — It  remains  now  to  re- 
view in  outline  the  artificial  impurities,  which  are  always 
to  he  shunned  if  known  to  he  present,  and  are  to  he  sus- 
piciously watched  for,  as  secret  poisons  lurking  in  the  clear 
and  sparkling  water. 

These  are,  it  is  true,  compounds  of  mineral  and  organic 
matters,  similar  in  many  respects  to  those  already  con- 
sidered. 

Nature  provides  prompt  acting  remedies  for  such  nox- 
ious impurities  as  she  presents  to  the  waters,  and  the 
seasons  of  most  rapid  fouling  have  the  most  abundant 
purifying  resources.  But  when  great  hulks  of  decompos- 
ing organic  matters  are  massed  and  are  permitted  to  foul 
the  streams  with  a blackening  flow  of  disease-inducing 
dregs,  such  as  are  washed  from  fertile  gardens,  or  pour 
from  manufactories  and  sewers,  no  adequate,  prompt,  na 
tural  remedy  is  at  hand. 

One  of  the  first  results  of  the  massing  of  people  together 
is  an  increase  in  degree  of  fertilization  of  the  land  of  their 
neighborhood,  and  thus  the  lands  over  and  through  which 
their  waters  flow  are  mixed  with  concentrated  decomposing 
vegetable  and  animal  products. 

120.  Manufacturing  Impurities.  — Manufactories, 
especially  such  as  deal  with  organic  products,  are  prolific 
sources  of  contamination.  Among  then-  operations  and 
refuse  may  he  enumerated  as  prominent  polluters,  washings 
of  wool  and  vegetable  dyes  of  woollen  mills,  washing  of  old 
rags  and  foul  linens  of  paper-mills,  the  hair,  scrapings, 
bark,  and  liquors  of  tanneries,  the  refuse  and  liquors  of 
glue  factories,  bone-boiling  and  soap-works,  pork  render- 
ing and  packing  establishments,  slaughter-houses  and  gas- 
works. 

121.  Sewage  Impurities. — Most  foul  and  fearful  of  all 


IMPURE  ICE  IN  DRINKING  WATER. 


135 


the  artificial  pollutions  which  ignorant  and  careless  human- 
ity permits  to  reach  the  streams  are  the  drainage  of  cesspools, 
sewers,  pig-styes,  and  stable-yards. 

The  man  who  permits  his  family  to  use  waters  impreg- 
nated with  fecal  substances  that  the  bodies  of  other  persons 
or  animals  have  already  excreted,  and  the  authorities  who 
permit  their  citizens  to  use  such  waters,  opens  for  them 
freely  the  gates  to  aches  and  pains,  weaknesses  of  body  and 
mind,  injuries  of  tissues  and  blood,  attacks  of  chronic  dis- 
eases and  epidemics,  and  surely  permits  destruction  of 
their  vigor,  shortens  their  average  life,  and  also  degenerates 
the  entire  existence  of  the  generation  they  are  rearing  to 
succeed  them,  whom  it  is  them  duty  as  well  as  pleasure  to 
cherish  and  protect. 

There  is  no  community,  there  are  very  few  families,  and 
comparatively  few  animals  without  disease.  In  large  com- 
munities there  is  rarely  a time  when  some  virulent  disease 
does  not  exist. 

The  products  of  the  humors  and  fevers  of  each  individual 
in  large  part  escapes  from  the  body  in  the  feces  and  urine. 
If  drinking  water  is  allowed  to  absorb  these  festering  mat- 
ters, either  in  the  ground  or  in  the  stream,  it  transmits  them 
directly  to  the  blood  and  tissues  of  other  individuals,  and  a 
hundred  deaths  may  result  from  the  evacuations  of  a single 
diseased  person. 

122.  Impure  Ice  in  Drinking  Water. — Ice  is  now 

so  generally  used  in  drinking-water  in  summer,  to  cool  it 
immediately  before  drinking,  that  the  people  should  be 
warned  against  such  use  of  ice  gathered  from  water  that 
would  have  been  unfit  for  drinking;  before  freezing.  Chem- 
istry has  fully  demonstrated  that  ice  is  not  entirely  purified 
by  the  process  of  crystallization,  as  has  been  popularly 
believed. 


136 


IMPURITIES  OF  WATER. 


The  impurities  that  are  in  that  portion  of  water  that 
freezes,  some  of  which  have  just  been  brought  from  the 
bottom  by  the  vertical  circulation  that  occurs  when  water 
is  chilled  at  the  surface,  are  caught  among  the  crystals  and 
preserved  there,  as  even  fresh  meats,  and  fruits  might  be 
preserved.  The  process  of  purification  of  the  water  that 
would  have  gone  on  by  the  oxidation  of  the  impurities,  is 
checked  when  they  are  surrounded  by  the  ice  crystals,  and 
proceeds  again  when  the  ice  melts. 

An  instance,  of  much  notoriety,  of  the  effects  of  impure 
ice,  was  that  of  the  sickness  among  the  numerous  guests, 
during  the  season  of  1875,  at  one  of  the  Rye  Beach  hotels, 
a popular  resort  on  the  New  Hampshire  coast. 

The  sickness  here,  confined  to  one  hotel  in  the  early  part 
of  the  season,  was,  after  much  search  by  an  expert  physi- 
cian, traced  unmistakably  to  the  ice,  which  was  gathered 
from  a small  stagnant  pond,  and  all  the  peculiar  unplea- 
sant symptoms  ceased  when  the  source  was  located  and  a 
purer  supply  of  ice  obtained. 

An  analysis  of  the  impure  ice  in  question,  by  Professor 
W.  R.  Nichols,  gave  the  following  result,  by  the  side  of 
which  is  placed  a like  analysis  of  water  from  Cochituate 
Lake,  for  the  purpose  of  comparison  : 


Ice  from  Stagnant 
Pond. 

Water  from 
Cochituate 
Lake. 

Grains  per 

U.  S.  Gal. 

Grains  per 
U.  S.  Gal. 

Unjiltered. 

O.OI2I 

O.O4IO 

4-55 

3.33 

Filtered. 

O.OI24 

.OO96 

4.01 

1.66 

0.0020 

0.006S 

1. 6l 
1. 22 

Albuminoid  Ammonia 

Inorganic  Matter 

Organic  and  Volatile  Matter 

Total  solid  residue  at  2120  Fahrenheit. . 

7.8s 

5-67 

i.SS 

0.495 

2.83 

.18 

Oxygen  required  to  oxidize  organic  matter. 

DEFINITION  OF  POLLUTED  WATER, 


137 


123.  A Scientific  Definition  of  Polluted  Water.— 

Subject,  as  the  sensitive  water  is,  to  innumerable  deteriora- 
ting and  purifying  influences,  in  its  transformations  and 
varied  course  from  the  atmosphere  to  the  household  foun- 
tain, it  becomes  of  the  greatest  sanitary  importance  to  know 
when  the  deteriorating  influences  still  predominate,  and  when 
further  purification  is  essential  for  the  well  being  of  the 
consumers. 

Professor  Frankland,  au  eminent  English  authority  on 
the  quality  of  drinking  water,  has  clearly  defined  a mini 
mum  limit,  when,  in  his  opinion,  water  contains  sufficient 
mechanical  or  chemical  impurities,  in  suspension  or  solu- 
tion, to  entitle  it  to  be  considered  bad,  or  a polluted 
liquid,  viz.  : 

(a.)  Every  liquid  which  has  not  been  submitted  to  pre- 
cipitation produced  by  a perfect  repose  in  reservoirs  of  suf- 
ficient dimensions  during  a period  of  at  least  six  hours ; oi 
which,  having  been  submitted  to  precipitation,  contains  in 
suspension  more  than  one  part  by  weight  of  dry  organic 
matter  in  100,000  parts  of  liquid  ; or  which,  not  having  been 
submitted  to  precipitation,  contains  in  suspension  more 
than  3 parts  by  weight  of  dry  mineral  matter,  or  1 part  by 
weight  of  dry  organic  matter,  in  100,000  parts  of  liquid. 

(b.)  Every  liquid  coutaining  in  solution  more  than  2 
parts  by  weight  of  organic  carbon  or  . 3 parts  of  organic 
nitrogen  in  100,000  parts  of  liquid. 

(c. ) Every  liquid  wdiicli,  when  placed  in  a white  porce- 
lain vessel  to  the  depth  of  one  inch,  exhibits  under  daylight 
a distinct  color. 

(d.)  Every  liquid  which  contains  in  solution,  in  every 
100.000  parts  by  weight,  more  than  2 parts  of  any  metal, 
except  calcium,  magnesium,  potassium,  and  sodium. 

(e.)  Every  liquid  which  iu  every  100,000  parts  by  weight 


138 


IMPURITIES  OF  WATER. 


contains  in  solution,  suspension,  chemical  combination,  or 
otherwise,  more  than  0.05  of  metallic  arsenic. 

(f.)  Every  liquid  which,,  after  the  addition  of  sulphuric 
acid,  contains  in  every  100,000  parts  by  weight  more  than 
1 part  of  free  chlorine. 

(g.)  Every  liquid  which,  in  every  100,000  parts  by 
weight,  contains  more  than  1 part  of  sulphur,  in  the  state 
of  sulphuretted  hydrogen  or  of  a soluble  sulphuret. 

(h.)  Every  liquid  having  an  acidity  superior  to  that  pro- 
duced by  adding  2 parts  by  weight  of  hydrochloric  acid  t^> 

1,000  parts  of  distilled  water. 

(i.)  Every  liquid  having  an  alkalinity  greater  than  that 
produced  by  adding  1 part  by  weight  of  caustic  soda  to 

1.000  parts  of  distilled  water. 

(./.).  Every  liquid  exhibiting  on  its  surface  a film  of 
petroleum  or  hydrocarbon,  or  containing  in  suspension  in 

100.000  parts,  more  than  0.05  of  such  oils. 

The  analytical  examination  of  drinking  water  in  the 
laboratory  should  be  preceded  by  a microscopical  exami- 
nation of  the  water  at  the  source  of  supply,  and  as 
promptly  as  possible  a bacteriological  examination  of 
specimens  of  the  water  taken  in  sterilized  tubes. 

Prof.  Y.  C.  Vaughn’s  standard  of  permissible  impu- 
rities in  drinking  water,  is  quoted  as  follows  : 


Total  residue, 

. 500  parts  per  million. 

Earthy  bases, 

. 200 

4 4 

4 4 4 4 

Sodium  chloride  (about), 

. 10 

cc 

4 4 44 

Sulphates,  .... 

. 100 

44 

44  4* 

Free  ammonia. 

. 0.05 

u 

44  44 

Albuminoid  ammonia,  . 

0.15 

t c 

44  4 4 

Nitrates  .... 

. 0.5 

4 4 

4 4 4 4 

Nitrites,  .... 

0.0 

44 

4 4 4 4 

Reduction  of  j)otassium  and 

per- 

manganate  s 


PUMPING  STATION,  NEW  BEDFORD. 


CHAPTEB  IX. 


t- 


WELL,  SPRING,  LAKE,  AND  RIVER  SUPPLIES. 

It  remains  now  to  add  to  these  general  theories  respect- 
ing the  purity  of  water  some  special  suggestions  relating  to 
the  selection  of  a potable  water. 

WELL  WATER. 

124.  Location  for  Wells. — We  have  seen  that  the 
source  of  water  supply  to  wells  is,  immediately,  the  rain, 
and  that  in  the  vicinity  of  dense  populations  the  rain  reaches 
the  surface  of  the  earth,  already  polluted  by  the  impurities 
of  the  town  atmosphere. 

In  the  open  country,  the  water  reaches  the  ground  in  a 
tolerably  pure  condition,  and  by  judicious  selection  of  a 
site  for  a well,  its  water  may  usually  be  procured  of  excel- 
lent quality.  Country  wells  must,  however,  be  entirely 
separated  from  the  drainage  of  the  stable  yards,  muck 
heaps,  and  house  sewerage,  and  from  soakage  through 
highly  fertilized  gardens. 

In  towns,  surface  soils  are  continually  recipients  of 
household  refuse,  manures,  and  sewer  liquors,  and  of  dead 
and  decaying  animal  matters. 

These  have,  by  abundant  examples,  been  proved  to  be 
the  most  dangerous  of  the  ordinary  contaminations  of  shal- 
low wells. 

The  strictly  mineral  impurities,  to  which  all  wells  are 
to  some  extent  subject,  are  not  usually  injurious  to  human 
constitutions,  though  in  districts  where  lime  is  present  in 


140 


WELL,  SPRING,  LAKE,  AND  RIVER  SUPPLIES. 


tlie  soil  in  considerable  quantity,  tlie  resulting  hardness  is 
inconvenient  and  indirectly  expensive. 

An  intelligent  examination  of  tlie  positions,  dip,  and 
porosity  of  the  earth’s  superstrata  in  the  vicinity  of  a pro- 
posed well  will  be  a more  infallible  guide  to  its  location 
where  it  will  yield  an  unfailing,  abundant,  and  wholesome 
supply,  than  will  reliance  upon  “hazel  forks”  and  “divin- 
ing rods,”  in  which  the  superstitious  have  evinced  faith  and 
by  which  they  have  often  been  deceived. 

125.  Fouling-  of  Old  Wells. — The  table  of  analyses 
of  well-waters  above  presented  (page  121,  et  seq.)  indicates 
that  the  old  wells  of  towns  are  among  the  most  impure 
sources  of  domestic  water  supply. 

The  continued  increase  in  the  hardness  of  well-water  as 
the  population  about  them  becomes  more  dense,  indicates 
that  this  increase  is  due  to  the  salts  of  the  dissolved  organic 
refuse  with  which  the  ground  in  time  becomes  saturated. 

Mr.  E.  Sutton,  an  English  analyst,  states,  that  -‘out  of 
four  hundred  and  twenty-nine  samples  of  water  sent  him 
from  wells  in  country  towns,  lie  was  obliged  to  reject  three 
hundred  and  seven  as  untit  for  drinking.”  Another  Eng- 
lish chemist  states  that  “much  of  tlie  well-water  he  is  called 
upon  to  examine  proves  to  be  more  fit  for  fertilizing  pur- 
poses than  for  human  consumption.” 

Prof.  Chandler,  President  of  the  New  York  City  Board 
of  Health,  and  Professor  of  Chemistry  in  the  School  of 
Mines,  Columbia  College,  remarked  : “In  many  cases,  from 
the  proximity  of  cesspools  and  privy  vaults,  the  well-water 
becomes  contaminated  with  filtered  sewage,  matters  which, 
while  they  hardly  affect  the  taste  or  smell  of  the  water, 
have  nevertheless  the  power  to  create  the  most  deadly  dis- 
turbances in  the  persons  who  use  the  waters.” 

Hall’s  “Journal  of  Health”  remarked  that,  “in  the 


' 


HARMLESS  IMPREGNATIONS.  143 

autumn  many  wells,  which  supply  families  with  drinking 
and  cooking  water,  get  very  low  and  their  bottoms  are  cov- 
ered with  a line  mud,  largely  the  result  of  organic  decom- 
positions, also  containing  poisonous  matters  of  a very  con 
cemrated  character.  The  very  emanations  from  this  well 
mud  are  capable  of  causing  malignant  fevers  in  a few  hours  ; 
hence  many  families  dependent  on  well-waters  are  made 
sick  during  the  fall  of  the  year  by  drinking  these  impreg- 
nated poisons,  and  introducing  them  directly  into  the  circu- 
lation. Many  obscure  ailments  and  ‘dumb  agues’  are 
caused  in  this  way.” 

SPRING  WATERS. 

120.  Harmless  Impregnations. — The  impurities  of 
spring  water  are  chiefly  mineral  in  character,  derived  from 
the  constituents  of  the  earths  through  which  their  waters 
percolate.  Among  the  most  soluble  of  the  earths  are  mag- 
nesium, calcium,  potassium,  and  sodium,  and  these  appear 
in  spring  waters  as  carbonates,  bicarbonates,  chlorides, 
sulphates,  silicates,  phosphates,  and  nitrates,  and  are  usu- 
ally accompanied  by  an  oxide  of  iron  and  a minute  quan- 
tity of  silica. 

The  above  earths  are  harmless,  and  are,  in  fact,  consid- 
ered beneficial  in  drinking  waters,  when  present  in  moderate 
quantities,  or  not  exceeding  eight  or  ten  grains  per  gallon. 
Most  persons  are  familiar  with  the  medicinal  properties  of 
the  carbonate  of  magnesia,  a mild  cathartic,  and  of  its  sul- 
phate (Epsom  salts),  a mild  purgative,  and  with  the  carbon- 
ate and  nitrate  of  potassa  (pearlash  and  saltpetre)  in  the 
arts,  and  with  the  medicinal  properties  of  the  bromide  of 
potassium,  a mild  diuretic. 

Sodium  is  more  familiarly  known  as  common  sea-salt, 
and  calcium  as  common  lime,  of  which  it  is  the  base,  and 


142  WELL,  SPRING,  LAKE,  AND  RIVER  SUPPLIES.  . 

silica  as  tlie  base  of  quartz  or  common  sand.  Spring  waters 
are,  by  their  passage  through  the  earth,  thoroughly  filtered 
and  relieved  of  suspended  impurities,  and  therefore  appear 
as  the  most  clear  and  sparkling  of  all  natural  waters. 

In  the  selection  of  a spring  water,  it  is  to  be  specially 
observed  that  it  is  free  from  impregnation  by  decaying 
organic  matters. 

127.  Mineral  Springs. — In  illustration  of  the  facts 
that  clearness  to  the  eye  is  not  evidence  of  purity,  or  min- 
eral impregnation  of  the  most  usual  character  immediately 
dangerous  to  the  constitution,  we  append  a few  analyses  of 
well-known  mineral  spring  waters,  with  quantities  of  ingre- 
dients expressed  in  grains  per  U.  S.  gallon.  (See  page  143.) 

This  formidable  array  of  chemical  ingredients  indi- 
cates that  the  waters  have  taken  into  solution  the  familiar 
minerals,  magnesia,  common  salt,  lime,  iron,  potash,  sul- 
phur, quartz,  and  clay,  and  the  gases,  oxygen,  hydrogen, 
nitrogen,  and  carbonic  acid. 

It  is  much  to  be  regretted  that  supplies  from  good  springs 
are  usually  so  limited  in  quantity. 

The  water  supply  of  Dubuque,  Iowa,  is  obtained  from 
an  adit  pierced  into  the  bluff  near  the  city.  The  operations 
of  miners  working  in  the  bluff  were  seriously  impeded  by 
water,  and  they  relieved  themselves  by  tunneling  in  horn 
the  face  of  the  bluff,  and  thus  underdraining  the  mine.  In 
so  doing,  they  intercepted  numerous  percolating  streams  of 
water.  This  water  is  now  utilized  for  the  supply  of  the 
city. 

LAKE  WATERS. 

128.  Favorite  Supplies. — Fresh  water  lakes  and  deep 
ponds,  whose  watersheds  have  extents  equal  to  at  least  ten 
times  their  water  surfaces,  are  ordinarily,  of  all  ample 


TABLE  No,  37. — Analyses  of  Mineral  Spring  Waters. 


4^4 

*qd[ns  aiRAi. 

MINERAL  SPRING  WATERS. 

M . CO  . . .VO  « N 'i-  •rco ...  . VO  . . t o 

co  . *n  . . . « O O fi  h ; m * ; in 

1 fc*,CO,!!**’d'd'CO,,*‘' 

143 

1 K. 

•bj  ' 03 
pjojpag 
‘•ads  pjojpog 

8 

W 

o o ::::;  o : o ::::  o o : 

• * CO  ■ M • • * * H 

*no2ajo 

‘Suudg 

vO 

O' 

CO 

0 

co  , n-  . . .■^-ovcn-^-.Ti- I . . . . | 

*3  'N : 4*°3 
gqraooung 
‘sSnudg  hue  y\ 

Q . N , . . N . 0 

♦ 

vq 

*Ax  ‘Snudg 
sjprj  siqg 

co  c**  o Nin  \o  -4- 

M . rj-  . . . q • • • coco  00 -4-  • co  • . 

. 01  , . . fOOO  ...  CO  M . 

■T 

1 

g 

Q ah 

•^inqspoxBH 

‘Suijag 

9^B3qA|^q3 

00  O "4-  Cl  VO  N 

••-^•q-^-.-O'-co-cv-..*  ... 

! ! ^ ’j-  co  ! ! ov  ! co  ! h ; ] | | ] ; ; ; | | | | ; ; ; ; ; 

. r CO  ..  .N.VO 

0)  M 

1 

■4- 

■^N 

SjnqspojBH 

‘Sauag 

3qiAn39J£) 

CO  VO  CO  CO 

CO  • ov  

0 

VC 

£ 

M 

'^A  IS3AV 
'ssnuds 
jnqdpis  anta 

M .to.  . . -4-  w M CO  -+lO t^.  . .CO 

h . o . . . O'  co  o coco  to h ...  o' 

O' 

cl 

O' 

N 'T 

•ba‘‘°3  3oj 
-uoj^  4*jdg 

jnqdins  pan 

N .in '4-10..  VO M 

co.w Min m -r  . . 

■ io ! • 4 I co  *;!*:;  oo  • ; 

CO 

VO 

, . ‘BA 
4,idg  unqv 

aSpijqqoox 

-4- 

q 

vo* 

00 

1 

O.vO.dr-^ , , . lOMCO  , , OVCO  . . . 

M 

A "N  “03 
noisSuiAig 
‘Sauds'uoAy 

• .VO  ...  .00  .CO  N N . . . , ............... 

vo 

qv 

••\d....id*ododco*!  

’A’N  ‘aoj'Eqg 

0 

CO 

••••CO’  • N • N * 

’A  *M  ‘*°3 
9U'eqoq9g 
“idg  uojBqg 

CO 

'4- 

0’ 

00 

N 

, „ 'A  'N 
'ESOJBJ'ES 
‘•jdg  ss3_l2uo3 

32.00 

16.00 
144.00 

434.40 

0 

T 

VO 

Cl 

VO 

Ingredients. 

Carbonate  of  magnesia 

“ u soda 

“ “ lime 

44  44  iron 

Bicarbonate  " magnesia 

“ “ soda 

Chloride  44  magnesium... 

44  41  sodium 

44  “ calcium 

Sulphate  44  magnesia 

“ “ soda 

“ “ lime 

44  41  potash 

Bromide  41  magnesium... 

Iodide  44  magnesium.. 

Muriate  44  magnesia 

“ “ soda 

44  44  lime 

Hydrobromate  “ potassa 

Hydrosulphuret  “ sodium 

44  calcium 

Hydrosulphate  44  magnesia 

44  44  lime 

Carbonic  acid 

Sulphuric  acid 

Silicic  acid 

Hydrosulphuric  acid 

Alumina 

Peroxide  of  iron 

Protoxide  of  iron 

Sulphur  compound 

Sulphuretted  hydrogen  

Nitrogenized  organic  matter 

144 


WELL,  SPRING,  LAKE,  AND  RIVER  SUPPLIES. 


sources,  least  liable  to  objectionable  impregnation  in  harm- 
ful quantity.  When  such  waters  have  been  imprisoned  in 
their  flow,  by  the  uplifting  of  the  rock  foundations  of  the 
hills  across  some  resulting  valley,  or  by  more  recent  crowd- 
ing by  ice-fields  of  masses  of  rock  and  earth  debris  into  a 
moraine  dam,  they  are  bright  and  lovely  features  in  their 
landscapes,  and  favorite  sources  of  water-supplies. 

The  accomplishments  of  scientific  attainments  are  not 
requisite  to  enable  the  intelligent  populations  to  discover 
in  these  waters  wholesomeness  for  human  draughts  and 
adaptability  to  quench  thirsts. 

When  such  waters  are  deep,  and  have  a broad  expanse 
and  bold  shores,  nature  is  ever  at  work  with  rain  and  wind 
and  sunshine,  maintaining  their  natural  purity  and  sparkle. 

129.  Chief  Requisites. — The  prime  requisites  in  lakes, 
when  to  be  used  for  domestic  supplies,  are  abundant  in- 
flow and  outflow , that  will  induce  a.  general  circulation ; 
abundant  depth , that  will  maintain  the  water  cool  through 
the  heats  ot  summer  and  hinder  organic  growth ; and  a 
broad  surface , which  the  wind  can  press  upou,  and  roll, 
and  thus  stir  the  water  to  its  greatest  depths. 

These  are  features  opposed  to  quietude,  shallowness, 
and  warmth,  which  we  have  seen  (§  114)  to  be  promoters  of 
excesses  of  vegetal  and  animal  life,  accompanied  by  a very 
objectionable  mass  of  vegetable  decay  and  animal  decom- 
position. Fortunately,  the  shallow  waters  are  oftenest  at 
the  upper  ends,  opposite  to  the  usual  points  of  draught  from 
the  lake,  or  in  indented  bays  along  the  sides,  from  whence 
their  vegetal  products  are  least  liable  to  reach  the  outflow 
conduit. 

130.  Impounding’. — When  supplying  lakes  have  mod- 
erate drainage  areas  in  proportion  to  the  total  volume  of 
water  required  from  them,  it  is  then  necessary  to  place  the 


PLAX7  GSOWm 


145 


draught  conduit  "below  their  natural  surface  or  to  raise 
their  natural  surface  by  a dam  at  their  outlet,  to  avail  of 
their  storage,  thus  in  a degree  changing  their  condition  of 
nature  into  the  artificial  condition  of  impounding  reser- 
voirs. 

The  theory  of  volume  of  supply  from  given  drainage 
areas  (§  53),  and  the  theory  of  making  available  a large 
proportion  of  the  rainfall  by  impounding  (§  75),  have 
already  been  discussed  in  their  appropriate  sections. 

Important  results,  affecting  the  purity  of  the  water,  may 
follow  from  the  disturbance  of  the  long-maintained  condi- 
tions of  the  shores,  analogous  to  those  of  the  construction 
of  artificial  impounding  reservoirs  in  valleys,  by  embank- 
ments across  the  outflow  streams. 

The  waves,  of  natural  broad  lakes  that  have  but  little 
rise  and  fall,  have  long  since  removed  the  soil  from  large 
portions  of  their  shores,  leaving  them  paved  with  boulders 
and  pebbles,  which  the  ice,  if  in  northern  latitudes,  has 
crowded  into  close  rip-raps,  and  the  removed  soil  has  been 
deposited  in  the  quiet  shallow  bays. 

Upon  the  paved  shores  the  lack  of  vegetable  mold  and 
the  dash  of  the  waters  are  obstacles  to  the  growth  of  vege- 
tation. 

131.  Plant  Growth. — If,  under  the  new  conditions,  the 
waters  are  drawn  down  in  the  summer,  the  wave  power  re- 
duced, the  shallow  bottoms  of  the  bays  uncovered,  and  an 
entire  shore  circuit  of  vegetable  deposit  exposed  to  the  hot 
sun,  a mass  of  luxuriant  vegetation  at  once  springs  into  ex- 
istence upon  this  uncovered  bottom,  and  the  greater  its  thrift 
the  more  rapid  its  decay,  and  the  more  objectionable  its 
gaseous  emanations  that  will  enter  into  solution  in  the  water. 

Such  growths  and  transformations  may  continue  to  re- 
peat themselves  through  several  successive  years,  and  to 


146 


WELL,  SPRING,  LAKE,  AND  RIVER  SUPPLIES. 


some  extent  continuously.  Under  the  former  conditions  of 
deeper  water  the  plant  life  was  of  less  abundance,  of  less 
thrifty  growth,  and  of  less  rapid  decay,  and  the  natural 
processes  of  purification  were  adequate  to  maintain  the 
natural  purity  of  the  water. 

Stimulated  vegetable  growths  result  in  quick  decay  and 
the  production  of  vegetable  muck,  the  foulest  solid  product 
of  vegetable  decompositions  in  water.  Slow  decompositions 
of  vegetable  matter  in  water  rarely  affect  the  water  to  a 
noxious  degree,  and  result  in  the  production  of  a peat  de- 
posit almost  entirely  free  from  deleterious  qualities  in  the 
water. 

The  presence  of  the  fishy  or  cucumber  odor  is  evidence 
that  the  water,  or  a considerable  portion  of  it,  has  been  too 
warm  for  stored  potable  water ; and  that  there  is  too  much 
of  shallow  margin,  or  that  the  storage  lake  has  received  too 
much  of  meadow  drainage.  It  is  not,  as  many  have  sup- 
posed, an  evidence  of  dead  fish  in  the  reservoir,  but  an  effect 
tending  to  drive  the  higher  orders  of  the  fish  more  closely 
about  the  springs  or  inflowing  streams. 

132.  Strata  Conditions. — The  winds  assist  the  ready 
escape  of  the  odorous  gases  when  they  have  risen  near  to 
the  surface,  and  the  stratum  of  water  of  greatest  purity,  in 
summer,  is  usually  a little  below  the  surface,  and  would  be 
at  the  surface  were  it  not  for  the  microscopic  organisms  that 
exist  there,  and  the  floating  matters. 

The  change  of  density  of  water  with  change  of  tempera- 
ture produces  a remarkable  effect  in  autumn.  Water  is  at 
its  greatest  density  at  the  temperature  just  above  freezing 
(39°2  Fall.),  and  when  the  frosts  of  autumn  chill  the  surface 
water  it  is  then  heavier  than  the  water  below,  and  sinks,  dis- 
placing the  bottom  water  ; and  the  vertical  circulation,  stir- 
ring up  the  whole  body,  continues  until  the  surface  is  sealed 


PLANT  AND  INSECT  AGENCIES. 


14? 


by  ice,  when  quiet  again  reigns  at  the  bottom.  This  action 
stirs  up  the  bottom  impurities,  and  often  makes  them  par- 
ticularly offensive  in  autumn,  even  more  than  in  mid- 
summer. 

In  the  case  of  new  flowage  of  artificial  reservoirs  over  a 
meadow  bottom,  the  live  vegetable  growth  has  all  to  go 
through  a certain  chemical  transformation,  the  influence  of 
which  upon  the  water  is  often  detectable,  for  a time,  by  the 
sense  of  smell.  This  action  in  the  water  may  be  consider- 
ably reduced  by  first  burning  thoroughly  the  whole  surface, 
and  destroying  the  organic  life  and  properties,  leaving  only 
the  mineral  ash. 

The  breaking  up  of  the  vegetable  fibres,  if  undestroyed 
by  fire,  and  their  deposition  in  the  quiet,  shallow  bays, 
encourages  the  growth  of  aquatic  plants,  and,  indirectly, 
animal  life  there. 

The  protection  of  the  shores  by  high  water  in  winter,  and 
their  exposure  by  drawing  down  the  water  in  summer,  is 
favorable  to  aquatic  growths  upon  them,  as  in  the  above- 
mentioned  lake  examples. 

133.  Plant  and  Insect  Agencies. — In  cases  of  ex- 
cessive growths  of  either  or  both  vegetal  and  animal  life, 
their  products  are  liable  to  be  drawn  into  the  outflow  con- 
duit and  the  distribution  pipes,  where  their  presence  becomes 
disagreeably  evident  by  the  gaseous  “fishy”  or  “cucum- 
ber” odors  liberated  when  the  water  is  drawn  from 
faucets. 

When  conditions  are  favorable  for  the  production  of 
either  vegetal  or  animal  life  alone,  in  excessive  abundance, 
disagreeable  effects,  especially  if  the  excess  be  animal,  are 
almost  certain  to  follow,  since  both  are  among  the  active 
agents  employed  by  nature  in  the  purification  of  water,  and 
natural  laws  tend  to  preserve  the  due  balance  in  their 


148 


WELL,  SPRING,  LAKE,  AND  RIVER  SUPPLIES. 


growth,  the  one  being  producers  of  oxygen  and  the  other 
of  carbon. 

Newly  flowed  collecting  or  storage  reservoirs  should  be 
promptly  stocked  with  a fine  grade  of  fish,  that  will  feed 
upon  and  prevent  the  overabundance  of  the  Crustacea, 
which  in  turn  will  consume  the  organic  decompositions,  and 
prevent  their  diffusion  through  the  waters. 

134.  Preservation  of  Purity. — General  observation 
teaches  that  neither  vegetation  or  any  species  of  the  infu- 
soria flourish  to  an  objectionable  extent  in  fresh  waters  in 
the  temperate  zone  where  the  depth  exceeds  about  ten  feet, 
though  it  is  true  that  insects  are  liable  to  swarm  upon  the 
surface  of  all  waters  that  arrive  at  a high  temperature. 
Stored  waters,  for  domestic  purposes,  ought  to  have  in  our 
American  climate,  depths  of  not  less  than  twelve  feet. 

To  insure  purity  of  water,  so  far  as  protection  from  its 
own  products  is  concerned,  it  is  necessary  that  the  shallow 
waters  be  cut  off  by  embankments,  or  that  they  be  deep- 
ened, or  that  their  place  be  supplied  by  clean  sand  or 
gravel  filling,  raised  to  a level  above  high  water.  It  is  fre- 
quently advisable,  also,  that  the  shores  of  artificial  impound- 
ing reservoirs  of  moderate  extent  be  provided  with  an 
equivalent  for  the  natural  rip-rap  provided  by  nature 
around  natural  lakes. 

Each  of  the  above  expedients  has  been  successfully 
adopted  by  the  writer  in  his  own  practice.  ' 

Fig.  7 is  an  illustration  of  the  revetment  of  stone  sur- 
rounding the  reservoir  of  the  Norwich,  Conn.,  water- works. 
The  reservoir  in  this  case  is  two  and  one-half  miles  out 
from  the  city,  and  fills  the  office  of  both  a gathering  and 
distributing  reservoir,  for  a gravitation  supply.  Its  circum- 
ference is  two  and  one-quarter  miles,  and  this  revetment 
protects  the  shore  of  the  entire  circuit.  Its  height  above 


NATURAL  CLARIFICATION7. 


149 


Fig.  7. 


high  water,  in  the  vicinity  of  the  dam,  is  four  feet,  and  in 
the  upper  part  of  the  valley  three  feet. 

If  the  supplying  streams  of  a small  lake  bring  with  them 
much  vegetable  matter  in  suspension,  and  the  flow  reaches 
the  conduit  before  complete  clarification  by  natural  pro- 
cesses is  effected,  some  method  of  artificial  filtration  of  the 
water  will  be  necessary,  the  details  of  which  will  be  dis- 
cussed hereafter. 

135.  Natural  Clarification. — The  various  sources  of 
chemical  impregnation  to  which  waters  reaching  lakes,  usu- 
ally are  subject,  whether  flowing  over  or  through  the  earth, 
have  been  already  herein  discussed  (§  101,  et  seq.),  so  that 
persons  of  ordinary  intelligence  and  information  may  detect 
them,  and  form  a tolerably  accurate  estimate  of  their  harm- 
fulness, and  if  they  ought  to  be  considered  objectionable 
when  they  are  to  be  gathered  in  a lake  and  there  subjected 
to  the  processes  in  Nature’s  favorite  laboratory  of  purifi- 
cation. 

Waters  flowing  in  the  brooks  from  the  wooded  hills  and 
the  swamps  almost  always  come  down  to  the  lakes  highly 
charged  with  the  coloring  matter  and  substances  of  forest 
leaves  and  grasses,  and  not  unfrequently  have  a very  per- 


150 


WELL,  SPRING,  LAKE  AND  RIVER  SUPPLIES. 


ceptiblo  reddish  or  chocolate  hue.  The  waters  are  soon 
relieved  of  these  vegetable  impurities  by  natural  processes 
in  the  lake,  and  their  natural  transparency  and  sparkle  is 
restored  to  them.  Sunlight  has  been  credited  with  a strong 
influence  in  the  removal  of  color  from  water.  The  chemical 
transformation  already  begun  upon  the  hills  is  continued  in 
the  lake,  and  the  atmospheric  oxygen  aids  in  releasing  the 
gases  of  the  minutely  subdivided  vegetable  products  pro- 
ducing the  color,  when  the  mineral  residues  have  sufficient 
specific  gravity  to  take  them  speedily  to  the  bottom.  The 
winds  are  the  good  physicians  that  bring  the  restoring 
remedies. 

Ponds  and  lakes  often  receive  a considerable  part  of 
their  supply  from  springs  along  their  borders,  whose  waters 
have  received  the  most  perfect  natural  clarification.  Such 
springs,  from  quartzose  earths,  yield  waters  of  the  most 
desirable  qualities. 

13G.  Great  Lakes. — When  lakes,  on  a scale  of  great 
inland  seas,  like  those  lining  our  northern  boundary,  upon 
which  great  marts  of  trade  are  developing,  are  at  hand, 
many  of  the  above  supposed  conditions  belonging  to 
smaller  lakes  and  ponds,  are  entirely  modified. 

In  such  cases  the  cities  become  themselves  the  worst 
polluters  of  the  pure  waters  lying  at  their  borders,  and 
they  are  obliged  to  push  their  draught  tunnels  or  pipes 
beneath  the  waters  far  out  under  the  lakes  to  where  the 
water  is  undefiled. 

This  system  was  inaugurated  on  a great  scale  by  Mr. 
E.  S.  Clieesboro,  C.E.,  for  Chicago,  and  followed  by  the 
cities  of  Cleveland,  Buffalo,  and  with  submerged  pipe  by 
Milwaukee. 

137.  Dead  Lakes. — The  waters  of  the  Sinks,  or  Dead 
Lakes  of  the  Utah,  Nevada,  and  southern  California,  Great 


METROPOLITAN  SUPPLIES. 


151 


Desert,  from  whicli  there  are  no  visible  outlets,  are  notable 
exceptions  to  general  conditions  of  lake  waters.  Here  the 
salts  gathered  by  the  inflowing  waters,  for  centimes,  which 
evaporating  vapors  can  not  carry  away,  have  been  accu- 
mulating, till  the  waters  are  nauseating  and  repugnant. 

The  skill  of  the  well-borer  must  aid  civilization  when 
these  desert  regions  are  to  become  generally  inhabitable. 

RIVER  WATERS. 

138.  Metropolitan  Supplies. — Rivers  are  of  necessity 
the  final  resort  of  a majority  of  the  principal  cities  of  the 
world  for  their  public  water  supply.  The  volume  of  water 
daily  required  in  a great  metropolis  often  exceeds  the  com- 
bined capacity  of  all  the  springs,  brooks,  and  ponds  within 
accessible  limits,  and  supplies  from  wells  become  impos- 
sible because  of  lack  of  capacity,  excessive  aggregate  cost, 
and  the  sickening  character  of  their  waters. 

Since  rivers  occupy  the  lowest  threads  of  the  valleys  in 
which  they  flow,  their  surfaces  are  lower  than  the  founda- 
tions of  the  habitations  and  warehouses  along  their  banks. 

Their  waters  have  therefore  usually  to  be  elevated  by 
power  for  delivery  in  the  buildings,  the  expense  of  conduct- 
ing their  waters  from  then  sufficiently  elevated  sources  being 
greater  far  than  the  capitalized  cost  of  the  artificial  lift 
nearer  at  hand. 

The  theories  by  which  the  minimum  flow  of  the  stream 
(§  53),  and  the  maximum  demand  for  supply  (§  19),  are 
determined  and  compared  have  been  already  herein  dis- 
cussed ; so  we  now  assume  that  the  supplies  have,  after 
proper  investigation,  been  determined  ample,  and  also  that 
the  geological  structure  (§  198)  of  the  drainage  area  is  found 
ro  present  no  impregnating  strata  precluding  the  use  of  its 


152 


WELL,  SPRING,  LAKE,  AND  RIVER  SUPPLIES. 


waters  for  domestic  and  commercial  purposes,  or  in  tire 
chemical  arts. 

139.  Harmless  and  Beneficial  Impregnations. — 

The  natural  organic  impurities  of  rivers  are  seldom  other 
than  dissolving  vegetable  fibres  "washed  down  from  forests 
'and  swamps,  and  these  are  rarely  in  objectionable  amount ; 
and  the  natural  mineral  impurities  in  solution  are  usually 
magnesia,  common  salt,  lime,  and  iron,  and,  in  suspension, 
’Sand  and  clay.  The  lime,  sand,  and  clay  are  easily  detect- 
ible  if  in  objectionable  amount,  and  the  remaining  natural 
mineral  impregnation  are  quite  likely  to  be  beneficial 
rather  than  otherwise,  since  they  are  required  in  drinking 
water  to  a limited  extent  to  render  them  palatable,  and  for 
promotion  of  the  healthy  activity  of  the  digestive  organs, 
and  the  building  up  of  the  bones  and  muscles  of  our  bodies. 

140.  Pollutions. — We  reiterate  that  it  is  the  artificial 
impurities  that  are  the  bane  of  our  river  waters.  Manufac- 
tories, villages,  towns,  and  cities  spring  up  upon  the  river- 
banks,  and  their  refuse,  dead  animals,  and  sewage  are 
dumped  into  the  running  streams,  making  them  foul  potions 
of  putrefaction  and  destruction,  when  they  should  flow  clear 
and  wholesome  according  to  the  natural  laws  of  their  crea- 
tion and  preservation. 

141.  Sanitary  Discussions. — The  prolific  discussion 
upon  the  sanitary  condition  of  the  water  of  the  river 
Thames,  England,  since  the  report  of  the  Eoyal  Commis- 
sion of  1850,  has  brought  out  a variety  of  conflicting  opin- 
ions in  regard  to  the  efficiency  of  natural  causes  to  destroy 
jsewage  impurities  in  water. 

About  one-half  the  population  of  London,  or  one-half 
million  persons,  received  their  domestic  water  supply  from 
the  Thames  in  1875.  The  drainage  area  above  the  pump- 
ing stations  is  about  3675  square  miles,  and  the  minimum 


SANITARY  DISCUSSIONS. 


158 


summer  flow  is  estimated  to  be  about  350,000,000  imperial 
gallons  daily,  and  of  this  flow  about  15,000,000  gallons  is 
pumped  daily  by  the  water  companies.  Upon  the  Thames 
watershed  above  the  pumping  stations  there  resides  a popu- 
lation of  about  1,000,000  persons,  including  three  cities  of 
over  25,000  persons  each,  three  cities  of  from  7000  to  10,000 
persons  each,  and  many  smaller  towns  and  villages.  The 
whole  of  the  river  and  its  principal  tributaries  are  under 
the.  strictest  sanitary  regulation  which  the  government  is 
able  to  enforce,  notwithstanding  which  a great  mass  of 
sewage  is  poured  into  the  stream. 

Yet  it  is  claimed  by  eminent  authority  that  the  Thames 
water  a short  distance  above  London  is  wholesome,  pala- 
table, and  agreeable,  and  safe  for  domestic  use. 

A remark  by  Dr.  H.  Letheby,  medical  officer  of  health 
for  the  city  of  London  until  his  decease  in  the  spring  of 
1876,  gives  a comprehensive  summary  of  the  argument  in 
favor  of  the  Thames  water,  viz. : “I  have  arrived  at  a very 
decided  conclusion  that  sewage,  when  it  is  mixed  with 
twenty  times  its  volume  of  running  water  and  has  flowed  a 
distance  of  ten  or  twelve  miles,  is  absolutely  destroyed : 
the  agents  of  destruction  being  infusorial  animals,  aquatic 
plants  and  fish,  and  chemical  oxydation.” 

Several  emineut  chemists  testify  that  analyses  detect  no 
trace  of  the  sewage  in  the  Thames  near  London.  Sir  Benja- 
min Broodie,  Professor  of  Chemistry  in  the  University  of 
Oxford,  remarked  in  his  testimony  upon  the  London  water 
supply : “ I should  rely  upon  the  dilution  quite  as  much, 
and  more,  than  upon  the  destruction  of  the  injurious 
matter. 

Dr.  C.  F.  Chandler,  President  of  the  New  York  Board 
of  Health,  and  Professor  of  Chemistry  in  the  School  of 
Hines,  Columbia  College,  has  in  his  own  writings  quoted 


154 


WELL,  SPRING,  LAKE,  AND  RIVER  SUPPLIES. 


many  eminent  authorities,*  with  apparent  indorsement  of 
their  conclusions,  supporting  the  theory  of  the  wholesome- 
ness and  safety  of  the  Thames  water  as  a domestic  supply 
for  the  city  of  London. 

143.  Inadmissible  Polluting  Liquids. — The  Par- 
liamentary Rivers  Pollution  Committee,  when  investigating 
the  subject  of  the  discharge  of  manufacturing  refuse  and 
sewage  into  the  English  rivers,  Mersey  and  Ribble,  and  the 
possibility  of  the  deodorization  and  cleansing  of  the  refuse 
by  methods  then  available,  suggested  f that  liquids  con- 
taining impurities  equal  to  or  iu  excess  of  the  limiting  quan- 
tity defined  by  Prof.  Frankland  ( vide  § 133,  p.  137),  be 
deemed  polluting  and  inadmissible  into  any  stream. 

143.  Precautionary  Views.  — On  the  other  hand, 
many  physicians,  chemists,  and  engineers,  whose  scientific 
attainments  give  to  their  opinions  great  weight,  emphatically 
protest  against  the  adoption  or  use  of  a source  of  domestic 
water  supply  that  is  at  all  subject  to  contamination  by 
sewage  or  putrefying  organic  matters  of  any  kind. 

There  are  certain  laws  of  nature  that  have  for  then 
object  the  preservation  of  human  life  to  its  appointed  ma- 
turity, which  we  term  instinct,  as,  for  instance,  involuntary 
grasping  at  a support  to  save  from  a threatened  fall ; invol- 
untary raising  the  arm  to  protect  the  eye  or  head  from  a 
blow ; involuntary  sudden  withdrawal  of  the  body  from 
contact  with  a hot  substance  that  would  burn.  There  is  also 
an  instinctive  repugnance  to  receiving  any  excrementitious 
or  putrefying  animal  substance,  or  anything  that  the  eye  or 
sense  of  smell  decides  to  be  noxious,  upon  the  tongue  or 
into  the  system.  It  is  not  safe  to  overlook  or  subdue  the 
natural  instincts  created  within  us  for  our  preservation. 

* Public  Health  Papers  of  American  Public  Health  Association,  vol.  i. 

f First  Report.  R.  P.  C.,  1868,  vol.  i,  p.  130. 


PRECAUTION ARY  VIEWS. 


155 


Following  are  a few  opinions  supporting  the  cautionary 
side  of  the  question  : 

“Except*  in  rare  cases,  water  which  holds  in  solution  a 
perceptible  proportion  of  organic  matter  becomes  soon 
putrid,  and  acquires  qualities  which  are  deleterious.  It  is 
evident  that  diarrhoea,  dysentery,  and  other  acute  or  chronic 
affections  have  been  induced  endemically  by  the  continued 
use  of  water  holding  organic  matter  in  large  proportions, 
either  in  solution  or  in  suspension.  It  is  admitted,  as  the 
result  of  universal  observation,  that  the  less  the  quantity  of 
organic  matter  held  by  the  water  we  drink,  the  more  whole- 
some it  is.” 

“Nof  one  has  conclusively  shown  that  it  is  safe  to  trust 
to  dilution,  storage,  agitation,  filtration,  or  periods  of  time, 
for  the  complete  removal  from  water  of  disease-producing 
elements,  whatever  these  may  be.  Chemistry  and  micro- 
scopy cannot  and  do  not  claim  to  prove  the  absence  of  these 
elements  in  any  specimen  of  drinking  water.” 

“It;}:  is  a well- received  fact,  that  decomposing  animal 
matter  in  drinking  water  is  a fertile  producer  of  intestinal 
diseases.” 

Dr.  W olf  (in  Der  Untergrund  und  das  Trinkwasser  der 
Stadte,  Erfurt,  1873)  gives  a large  number  of  cases,  which 
prove  conclusively  that  “bad  water  produces  diarrhoea, 
and  can  propagate  dysentery,  typhoid  fever,  and  cholera, 
and  that  such  water  is  frequently  clear,  fresh,  and  very 
agreeable  to  the  taste.” 

Dr.  Lyon  Playfair,  of  London,  remarks  : “The  effect  of 

* Boutron  and  Boudet.  Annual  of  French  Waters,  1851. 

f Testimony  of  Dr.  R.  A.  Smith  before  the  Royal  Commission  of  Water 
Supply  of  London. 

% Report  of  Medical  Commission  on  Additional  Water  Supply  for  Boston, 
1874. 


156 


WELL,  SPRING,  LAKE,  AND  RIVER  SUPPLIES. 


organic  matter  in  the  water  depends  very  much  upon  the 
character  of  that  organic  matter.  If  it  he  a mere  vegetable 
matter,  such  as  comes  from  a peaty  district,  even  if  the 
water  originally  is  of  a pale  sherry  color,  on  being  exposed 
to  the  air  in  reservoirs,  or  in  canals  leading  from  one  reser- 
voir to  another,  the  vegetable  matter  gets  acted  upon  by  the 
air  and  becomes  insoluble,  and  is  chiefly  deposited,  and 
what  remains  lias  no  influence  on  health.  But  where  the 
organic  matter  comes  from  drainage,  it  is  a most  formid- 
able ingredient  in  water,  and  is  the  one  of  all  others  that 
ought  to  be  looked  upon  with  apprehension  when  it  is  from 
the  refuse  of  animal  matter,  the  drainage  of  large  towns, 
the  drainage  of  any  animals,  and  especially  of  human 
beings.” 

The  Massachusetts  State  Board  of  Health,  in  their  fifth 
annual  report,  remarking  upon  the  joint  use  of  watercourses 
for  sewers  and  as  sources  of  water  supply  for  domestic  use, 
remarks:  “We  believe  that  all  such  joint  use  is  to  be 
deprecated The  importance  of  this  matter  is  under- 

rated for  two  reasons : first,  because  of  the  oft-repeated 
assertion,  made  on  the  authority  of  Dr.  Letheby,  ‘that  if 
sewage- matter  be  mixed  with  twenty  times  its  bulk  of  ordi 
nary  river  water,  and  flow  a dozen  miles,  there  is  not  a 
particle  of  that  sewage  to  be  discovered  by  chemica* 
means  secondly,  because  of  the  feeling  that  to  be  in  any 
way  prejudicial  to  health,  a water  must  contain  enough 
animal  matter  to  be  recognized  readily  by  chemical  tests — 
enough,  in  fact,  to  be  expressed  in  figures.” 

144.  Speculative  Condition  of  the  Pollution 
Question. — Sanitary  writings  have  abounded  with  dis- 
cussions of  this  subject  during  the  last  decade  : still,  look- 
ing broadly  over  the  field  of  discussion,  it  is  evident  that 
the  leading  medical  and  chemical  authorities  have  not 


SPONTANEOUS  PURIFICATION. 


157 


agreed  upon  the  limit  for  any  case,  or  class  of  cases,  when 
water  "becomes  noxious  or  harmful. 

Some  of  the  consumers  of  the  waters  of  the  Thames  in 
England  and  of  the  Mystic  and  Charles  rivers  in  New  Eng- 
land, have  evinced  a remarkable  faith  in  the  toughness  of 
human  constitutions. 

The  whole  subject  of  water  contamination  remains  as 
yet  rather  physiologically  speculative  than  chemically  ex- 
act. It  is  earnestly  to  be  desired  that  the  present  experi- 
mental practice  upon  human  constitutions,  so  costly  in 
infantile  life,  may  soon  yield  a sufficiency  of  conclusive 
statistics,  or  that  science  shall  soon  unveil  the  subtle  and 
mysterious  chemical  properties  of  organic  matters,  at  least 
so  far  as  they  are  now  concealed  behind  recombinations, 
reactions,  and  test  solutions. 

145.  Spontaneous  Purification. — The  river  courses 
are  the  natural  drainage  channels  of  the  lands,  and  it  can- 
not but  be  expected  that  a considerable  bulk  of  refuse,  from 
populous  districts,  will  find  its  way  to  the  sea  by  these 
channels,  however  strict  the  sanitary  regulations  for  the 
preservation  of  the  purity  of  the  streams.  Therefore  it  is  a 
matter  of  high  scientific  interest,  and  in  most  cases  of  great 
hygienic  and  national  importance,  to  determine  wliat  pro- 
portion of  the  organic  refuse  is  destroyed  beyond  the  possi- 
bility of  harm  to  animals  that  drink  the  water,  by  spon- 
taneous decomposition,  and  what  proportion  remains  in 
solution  and  suspension. 

In  ordinary  culinary  and  chemical  processes  we  find 
that  temperature  has  an  important  influence  upon  the  dis- 
solving property  of  water.  Water  of  temperature  below 
60°  Fah.  dissolves  meats,  vegetables,  herbs,  sugar,  or  gum, 
slowly,  comparatively,  and  a cold  atmosphere  does  not  pro- 
mote decomposition  of  organic  matter.  W e therefore  infer 


158 


WELL,  SPRING,  LAKE,  AND  RIVER  SUPPLIES. 


that  a temperature  of  both  atmosphere  and  water  as  high, 
or  nearly  as  high,  as  60°  Fah.  are  required  to  promote 
rapid  oxydation  of  the  organic  impurities  in  water.  In 
winter  the  process  must  proceed  slowly,  and  if  the  stream 
is  covered  by  ice,  be  almost  suspended.  Agitation  of  the 
water  is  absolutely  essential  to  the  long-maintained  pro- 
cess of  oxydation,  in  order  that  the  water  may  continue 
charged  with  the  necessary  bulk  of  oxygen  in  solution ; 
therefore  weirs  across  the  stream,  roughness  of  the  bed  and 
banks  of  the  stream,  and  rapidity-  of  flow  are  essential  ele- 
ments in  rapid  oxydation. 

Dr.  Sheridan  Muspratt  remarks,*  in  respect  to  this  spon- 
taneous purification  of  river  waters  containing  organic  mat- 
ters : “As  a general  rule,  the  carbon  unites  with  oxygen  to 
form  carbonic  acid  ; and  with  hydrogen  to  form  marsh  gas 
or  carbide  of  hydrogen  ; hydrogen  and  oxygen  unite  to 
form  water ; nitrogen  and  oxygen  with  hydrogen  to  form 
ammonia  ; sulphur  with  hydrogen  to  form  sulphide  of  hy- 
drogen ; phosphorus  with  hydrogen  to  form  phosphide  of 
hydrogen. 

‘ ' The  latter  two  are  exceedingly  offensive  to  the  sense  of 
smell,  and  are,  moreover,  highly  poisonous.  Thus  in  the 
spontaneous  decomposition  of  the  organic  matter  contained 
in  water,  there  are  produced  carbonic  acid,  carbide  of  hy- 
drogen, ammonia,  sulphide  of  hydrogen,  and  phosphide  of 
hydrogen.  These  are  the  recognized  compounds  ; but  when 
it  is  borne  in  mind  that  the  gaseous  emanations  of  decom- 
posing animal  matters  are  infinitely  more  offensive  to  the 
sense  of  smell  and  injurious  to  health  than  any  of  the  gases 
above  mentioned,  or  of  any  combination  of  them,  it  can 
only  be  concluded  that  the  effluvia  of  decaying  organic 


Chemistry,  Theoretical,  Practical,  and  Analytical  : Glasgow. 


A SUGAR  TEST  OF  WATER. 


359 


matter  contains  other  constituents,  of  which  the  true  char- 
acter has  not  yet  been  determined.”  This  chemical  puri- 
fication is  assisted  by  vegetal  absorption  and  animalculine 
consumption. 

146.  Artificial  Clarification. — While  water  subjected 
at  all  to  organic,  especially  drainage  or  animal  impurities, 
should  be  avoided,  if  possible,  for  domestic  consumption, 
it  should,  on  the  other  hand,  when  necessarily  submitted 
to,  be  clarified  before  use,  of  its  solids  in  suspension,  by 
precipitation,  deposition  in  storage  or  settling  basins,  or  by 
one  of  the  most  thorough  processes  of  filtration. 

147.  A Sugar  Test  of  the  Quality  of  Water.— The 
Pharmaceutical  Journal  quotes  Heisch’s  simple  sugar  test 
for  water,  as  follows : 

“Good  water  should  be  free  from  color,  unpleasant 
odor  and  taste,  and  should  quickly  afford  a good  lather 
with  a small  proportion  of  soap. 

“ If  half  a pint  of  the  water  be  placed  in  a clean,  color- 
less glass-stoppered  bottle,  a few  grains  of  the  best  white 
lump-sugar  added,  and  the  bottle  freely  exposed  to  the  day- 
light in  the  window  of  a warm  room,  the  liquid  should  not 
become  turbid,  even  after  exposure  for  a week  or  ten  days. 
If  the  water  becomes  turbid,  it  is  open  to  grave  suspicion 
of  sewage  contamination  ; but  if  it  remain  clear,  it  is 
almost  certainly  safe. 


SECTION  II. 


Flow  of  Water  through  Sluices,  Pipes  and  Channels. 


CHAPTER  X. 

WEIGHT,  PRESSURE,  AND  MOTION  OF  WATER. 

148.  Special  Characteristics  of  Water. — If  we  con- 
sider those  qualities  of  water  that  have  reference  to  its 
weight , its  pressure,  and  its  motion , we  shall  observe,  espe- 
cially : That  the  volume  of  the  liquid  is  composed  of  an 
immense  number  of  minute  particles ; that  each  particle 
has  weight  individually ; that  each  particle  can  receive 
and  transmit  the  effect  of  weight , in  the  form  of  pressure, 
in  all  directions ; and  that  the  particles  move  past  and 
upon  each  other  with  very  slight  resistance. 

We  are  convinced  by  the  sense  of  touch  that  the  parti- 
cles of  a body  of  water  are  minute,  and  have  very  little 
cohesion  among  themselves  or  friction  upon  each  other, 
when  we  put  our  hand  into  a clear  pool  and  find  that  the 
particles  separate  without  appreciable  resistance  ; and  also 
by  the  sense  of  sight,  when  we  see  fishes  and  insects,  and, 
with  the  aid  of  the  microscope,  the  tiny  infusorise,  moving 
rapidly  through  the  water,  without  apparent  effort  greater 
than  would  be  required  to  move  in  air. 

11 


162  WEIGHT,  PRESSURE,  AND  MOTION  OF  WATER. 

149.  Atomic  Theory. — Ancient  records  of  scientific 
research  inform  us  that  the  study  of  the  divisibility  and 
nature  of  the  particles  of  matter  occupied,  long  ago,  the 
most  vigorous  minds.  It  is  twenty-two  centuries  since 
Democritus  explained  the  atomic  theory  to  his  fellow- 
citizens,  and  taught  them  that  particles  of  matter  are  capa- 
ble of  subdivision  again  and  again,  many  times  beyond  the 
limit  perceptible  to  human  senses,  but  that  finally  the  atom 
will  be  reached,  which  is  indivisible,  the  unit  of  matter. 
Anaxagoras,  the  teacher  of  Socrates,  maintained,  on  the 
contrary,  that  matter  is  divisible  to  infinity,  and  that  all 
parts  of  an  inorganic  body,  to  infinite  subdivision,  are  simi- 
lar to  the  whole.  This  latter  theory  has  not  been  generally 
accepted.  The  whole  subject  of  the  nature  of  matter,  in  its 
various  conditions,  forms,  and  stages  of  progress,  has  main- 
tained its  interest  through  the  succeeding  centuries,  and  is 
to-day  a favorite  study  of  philosophers  and  theme  of  dis- 
cussion in  lecture  halls. 

150.  Molecular  Theory. — Modern  research  has  dem- 
onstrated that  the  unit  of  water  is  composed  of  at  least  two 
different  substances,  and  therefore  is  not  an  atom.  The 
unit  is  termed  a molecule,  and,  according  to  the  received 
doctrine,  the  foundation  of  each  molecule  of  water  is  two 
molecules  of  hydrogen  and  one  molecule  of  oxygen.  These 
latter  molecules  may  possibly  be  ultimate  atoms. 

The  theory  is  advanced  that  each  molecule  of  water  is 
surrounded  by  an  elastic  atmosphere,  and  by  a few  that  it 
is  itself  slightly  elastic. 

Sir  William  Thompson  estimated  that  between  five  hun- 
dred millions  and  five  thousand  millions  of  the  molecules 
of  water  may  be  placed  side  by  side  in  the  space  of  one 
lineal  inch.  To  enable  us  to  detect  the  outline  of  one  of 
these  molecules,  our  most  powerful  microscope  must  have 


INFLUENCE  OF  CALORIC. 


168 


its  magnifying  power  multiplied  as  many  times  again,  or 
squared. 

A film  of  water  flowing  through  an  orifice  one-hundredth 
of  an  inch  deep,  or  about  the  thickness  of  this  leaf,  would 
be,  according  to  the  above  estimate,  from  five  to  fifty  mil- 
lion molecule  diameters  in  depth.  It  is  impossible  to  com- 
prehend so  infinitesimal  a magnitude  as  the  diameter  of  one 
of  these  molecules,  so  we  shall  be  obliged  to  imagine  them 
so  many  times  magnified  as  to  resemble  a mass  of  transpa- 
rent balls,  like  billiard  balls,  for  instance,  or  similar  spheres, 
and  to  consider  them  while  so  magnified. 

151.  Influence  of  Caloric. — There  is  also  a theory, 
very  generally  accepted,  that  the  molecules  of  water,  more 
especially  their  gaseous  constituents,  are  constantly  subject 
to  the  influence  of  caloric,  the  cause  of  heat,  and  are  in 
consequence  in  incessant  compound  motion,  both  vibratory 
and  progressive,  and  that  they  are  constantly  moving  past 
each  other,  progressing  with  wavy  motion,  or  are  rebound- 
ing against  each  other,  and  against  their  retaining  vessel. 

This  motion  may  be  partially  illustrated  by  the  motion 
of  a great  number  of  smooth,  transparent,  elastic  balls,  in  a 
a vessel  when  the  vessel  is  being  shaken.  It  may  be  dem- 
onstrated by  placing  a drop  of  any  brilliant  colored  liquid, 
for  which  water  has  an  affinity,  into  a vessel  of  quiet  water, 
when  the  drop  will  be  gradually  diffused  throughout  the 
whole  mass,  showing  not  only  that  among  the  molecules  of 
colored  liquid  there  is  activity,  but  that  certain  of  the  mole- 
cules before  in  the  vessel  plunge  into  and  through  the  drop 
from  all  sides,  dividing  it  into  parts,  and  its  parts  again 
into  other  parts,  until  the  particles  are  distributed  through- 
out the  mass. 

While  the  molecules  are  arranged  in  crystalline  form, 
they  require  considerably  more  space  than  when  in  liquid 


164  WEIGHT,  PRESSURE,  AND  MOTION  OF  WATER. 

form,  and  there  are  a less  number  of  them  in  a cubic  inch  ; 
therefore  a cubic  inch  of  ice  weighs  less  than  a cubic  inch 
of  water. 

152.  Relative  Densities  and  Volumes. — The  rela- 
tive changes  in  weight  and  volume  of  water  at  different 
temperatures  are  shown  graphically  in  Fig.  8.  When 


Fig.  8. 


'weight  is  maintained  constant  and  the  temperature  of  the 
water  is  increased  or  decreased,  the  rolume  will  change  as 
indicated  by  the  solid  lines.  "When  rolume  is  maintained 
constant  and  the  temperature  increased  or  decreased,  the 
weight  will  change  as  indicated  by  the  dotted  lines. 

WEIGHT  OF  WATER. 

153.  Weight  of  Constituents  of  Water. — Water  is 
substantially  the  result  of  the  union  (§  150)  of  two  volumes 
of  hydrogen,  having  a specific  gravity  equal  to  0.0689,  and 
one  volume  of  oxygen,  having  a specific  gravity  equal  to 
1.102  ; but  various  other  gases  that  come  in  contact  with 
this  combination  are  readily  absorbed. 

Bulk  for  bulk,  the  oxygen  is  sixteen  times  heavier  than 
the  hydrogen.  Water  at  its  greatest  density  is  about  eight 
hundred  and  fifteen  times  as  heavy  as  atmospheric  air. 

The  density  of  the  vapor  or  gases  enveloping  the  liquid 
molecules  is  greatest  at  a temperature  of  about  39°. 2 Fall. 
At  this  temperature  the  greatest  number  of  molecules  is 


FORMULA  FOR  VOLUMES. 


165 


contained  in  one  cubic  inch,  and  the  greatest  weight  for  a 
given  volume  obtains. 

As  the  temperature  of  water  rises  from  39.2°,  its  gaseous 
elements  expand  and  are  supposed  to  increase  their  activity  ; 
and  a less  number  of  molecules  can  be  contained  in  a cubic 
inch,  or  other  given  volume  ; therefore  the  weight  of  water  de- 
creases as  the  temperature  rises  from  39.2°  Fah.  (tide  Fig.  8.) 

154.  Crystalline  Forms  of  Water. — As  the  temper- 
ature falls  below  39.2°  Fah.,  the  molecules,  under  one  at- 
mosphere of  pressure,  incline  to  arrange  themselves  in 
crystalline  form,  their  action  is  supposed  to  be  more  vibra- 
tory and  less  progressive,  and  they  become  ice  at  a temper- 
ature of  about  32°  Fah. 

The  relative  weights  and  volumes  of  distilled  water  at 
different  temperatures  on  the  Fahrenheit  scale  are  shown 
numerically  in  the  table  on  the  following  page. 

Although  there  is  a slight  difference  in  the  results  of 
experiments  of  the  best  investigators  in  their  attempts  to 
obtain  the  temperature  of  water  at  its  maximum  density,  it 
is  commonly  taken  at  39.2°  Fah.,  and  the  weight  of  a cubic 
foot  of  water  at  this  temperature  as  62.425  pounds,  and  the 
weight  of  a United  States  gallon  of  water  at  the  same  tem- 
perature as  8.379927  pounds. 

155.  Formula  for  Volumes  at  Different  Temper- 
atures.— The  tables  of  weights  and  volumes  of  water  is 
extended,  with  intervals  of  ten  degrees,  to  the  extreme  limits 
within  which  hydraulic  engineers  have  usually  to  experi- 
ment. The  intermediate  weights  and  volumes  for  inter- 
mediate temperatures,  may  be  readily  interpolated,  or 
reference  may  be  had  to  the  following  formulas  taken  from 
Watt’s  “Dictionary  of  Chemistry,”  combining  the  law  of 
expansion  as  determined  by  experiments  of  Matthiessen, 
Sorby,  Kopp,  and  Rossetti. 


166 


WEIGHT,  PRESSURE,  AND  MOTION  OF  WATER. 


TABLE  No.  38. 

Weight  and  Volume  of  Distilled  Water  ai  Different 
Temperatures. 


Temperature 

Fah. 

Weight  of  a cu. 
ft.  in  pounds. 

Difference. 

Ratio  of  volume  to 
volume  of  equal  wt 
at  max.  density  of 
temperature, 

39. 20  Fah. 

Difference. 

Ice. 

57.200 

. 916300 

32° 

62.417 

5-217 

1 .000129 

.083829 

39-2° 

62.425 

.008 

I . ocoooo 

.OOOI29 

40  0 

62.423 

.002 

I . 000004 

. OOOOO4 

5°° 

62 . 409 

.014 

I . 000253 

.000249 

60 

62 . 367 

.042 

I .000929 

.000676 

7°° 

62 . 302 

.065 

I .001981 

.001052 

8o° 

62.218 

. 084 

1.00332 

-OOI339 

9°° 

62.119 

.099 

I . 00492 

.00160 

100 

62 . 000 

.119 

I . 00686 

.00194 

IIO° 

61  867 

•i33 

I . 00902 

.00216 

120° 

61.720 

.147 

I-OH43 

.00241 

130° 

61.556 

. 164 

1 . 0141 1 

.00268 

140° 

61 . 388 

.168 

1 .01690 

.00279 

I5°o 

61 . 204 

. 184 

1. 01995 

.00305 

l6o 

61 . 007 

.197 

1 .02324 

■00329 

170° 

60 . 801 

. 206 

1 . 0267 1 

•00347 

1800 

60.587 

.214 

1 -03033 

00362 

190° 

60 . 366 

.221 

1-03411 

•00378 

O 

200 

60 . 136 

.230 

1 .03807 

. 00396 

2IO° 

59-894 

. 242 

1 .04226 

. 00419 

212° 

59-7°7 

.187 

1 

1 • °43 12 

.OO0S6 

Let  V = ratio  of  a given  volume  of  distilled  water,  at  the 
temperature,  T,  on  Fahrenheit’s  scale,  to  the  volume  of  an 
equal  weight,  at  the  temperature  of  maximum  density. 

W = weight  of  a cubic  foot  of  distilled  water,  in  pounds, 
at  any  temperature,  Fahrenheit. 

For  temperatures  32°  to  70°  Fah. 

Y=  1.00012  - 0.000033914  x (T  - 32)  + 0.000023822  x 
(T  - 32)®  - 0.000000006403  (T  - 32)3. 


COMPRESSIBILITY  AND  ELASTICITY  OP  WATER.  167 


For  temperatures  above  70°. 

Y = 0.99781  + 0.00006117  x (T  - 32)  + 0.000001059  x 
(T  - 32) 8 . 

TTT  62.425 

y 

156.  Weight  of  Pond  Water.  — Fresh  pond  and 
brook  waters  are  slightly  heavier  than  distilled  water,  and 
when  not  loaded  with  sediment  have,  for  a given  volume, 
an  increased  weight  equal  to  from  0.00005  to  0.0001  of  an 
equal  volume  of  distilled  water. 

157.  Compressibility  and  Elasticity  of  Water.— 
The  compression  of  rain-water,  according  to  experimental 
results  of  Canton,  is  0.000046  and  of  sea-water  0.000040  of 
its  volume  under  the  pressure  of  one  atmosphere. 

According  to  experiments  of  Regnault,  water  suffers  a 
diminution  of  volume  amounting  to  48  parts  in  one  million, 
when  submitted  to  the  pressure  of  one  atmosphere,  equal  to 
14.75  pounds  per  square  inch,  and  to  96  parts  wdien  sub- 
mitted to  twice  that  pressure. 

Grassi  found  the  compressibility  of  water  to  be  50  parts 
at  37°  Fah.,  and  44  parts  at  127°  Fah.  in  each  million 
parts,  with  one  atmosphere  pressure. 

A column  of  water  100  feet  high  would,  according  to 
these  estimates,  be  compressed  nearly  one- sixteenth  of  an 
inch. 

The  degree  of  elasticity  of  fluids  was  discovered  by  Can- 
ton in  1762.  He  proved  that  the  volume  of  liquids  dimin- 
ished slightly  in  bulk  under  pressure  and  proportionally 
to  the  pressure,  and  recovered  their  original  volume  when 
the  pressure  ceased. 

This  has  been  confirmed  by  experiments  of  Sturm. 
CErsted,  Regnault,  and  others. 


168 


WEIGHT,  PRESSURE,  AND  MOTION  OF  WATER. 


PRESSURE  OF  WATER. 

158.  Weights  of  Individual  Molecules. — If  again 

we  consider  the  molecules  of  water  magnified,  as  before  ex- 
plained, we  can  conceive  that  each  molecule  has  its  indi- 
vidual weight , and  is  subject , independently , to  the  force 
of  gravity.  Consider  again  the  film  of  water  of  one-hun- 
dredth of  an  inch  in  depth,  flowing  through  the  orifice  of 
same  depth,  and  imagine  the  orifice  to  he  magnified  also  in 
the  same  proportion  as  the  molecules  have  been  imagined 
to  be  magnified,  that  is,  to  five  million  molecule  diameters ; 
then  the  immense  leverage  that  gravity  has,  proportionally, 
uiion  each  molecule  to  set  it  in  motion  and  to  press  it  out 
of  the  orifice  can  be  conceived,  and  the  reason  why  there  is 
apparently  so  little  frictional  resistance  to  the  passage  of 
the  molecules  over  each  other  will  be  apparent. 

159.  Individual  Molecular  Actions. — The  magnified 
molecule  can  also  be  conceived  to  be  acting  independently 
upon  any  side  of  its  retaining  vessel,  or  upon  any  other 
molecule,  with  which  it  is  in  contact,  with  the  combined 
weight  or  pressure  of  all  the  molecules  acting  upon  it. 

In  a volume  of  fluid,  each  molecule  presses  in  any 
direction  from  which  a sufficient  resistance  is  opposed , 
with  a pressure  due  to  the  combined  natural  pressures  of 
all  molecules  acting  upon  it  in  that  direction , and  also 
with  the  pressure  transmitted  through  them  from  any 
exterior  force. 

In  treatises  on  hydrostatics,  propositions  relating  to 
pressures  of  fluids  are  commonly  stated  in  some  form  sim- 
ilar to  the  following  :*  “ When  a fluid  is  pressed  by  its  own 
weight,  or  by  any  other  force,  at  any  point  it  presses 
equally  in  all  directions.” 


* Vide  Hutton’s  Mathematics,  Hydrostatics,  §310. 


INDIVIDUAL  MOLECULAR  REACTIONS. 


169 


160.  Pressure  Proportional  to  Depth. — The  pres- 
sure of  a fluid  at  any  point  on  an  immersed  surface,  is  in 
'proportion  to  the  vertical  depth  of  that  point  Ibelow  the  sur- 
face of  the  fluid  ; but  uot  in  proportion  to  variable  breadths 
of  the  fluid. 

In  vessels  of  shapes  similar  to  Fig.  9 and  Fig.  10,  con- 
taining equal  vertical  depths  of  water,  the  pressures  on 
equal  areas  of  the  horizontal  bottoms  are  equal ; also  the 
pressures  on  equal  and  similar  areas  of  their  vertical  sides, 
having  their  centres  of  gravity  at  equal  depths,  are  equal. 


161.  Individual  Molecular  Reactions. — Any  parti- 
cle of  fluid  that  j dves  a pressure  reacts  with  a force  equal 
to  the  pressure , if  its  m jtion  is  resisted  upon  the  opposite  side. 

Any  point  of  a fixed  surface  pressed  by  a particle  of 
water  reacts  upon  the  particle  with  a force  equal  to  the 
pressure  of  the  particle. 

The  large  body  of  water  in  the  section  A of  the  tank, 
Fig.  9,  is  perfectly  counterbalanced  by  the  slender  body 
in  the  section  a".  A pressure  equal  to  that  due  to  the 
weight  of  all  the  particles  above  the  horizontal  bottom  sur- 
face, f acts  upon  that  surface,  and  the  surface  reacts  with  an 
equal  pressure  and  sustains  all  those  particles.  The  effect 
would  be  similar  if  the  surface,  or  a portion  of  it,  was  in- 
clined or  curved  ; therefore,  only  a pressure  equal  to  the 


170  WEIGHT,  PRESSURE,  AND  MOTION  OF  WATER. 

weight  of  those  particles  vertically  over  the  opening  in  the 
partition,  f,  acts  upon  the  column  "below  the  partition  f. 
The  right  and  left  horizontal  pressures  of  the  individual 
particles  of  A are  transmitted  to  the  particles  on  the  right 
and  left,  which,  in  turn,  react  with  equal  pressures,  aud  sus- 
tain them  from  motion  sideways.  The  particles  in  contact 
with  the  partitions  a and  b transmit  their  pressures  horizon- 
tally to  the  partition,  which  in  turn  react  and  sustain  them, 
and  all  the  particles  remain  in  equilibrium. 

162.  Equilibrium  Destroyed  by  an  Orifice. — If  an 
orifice  is  made  at  the  bottom  of  the  side  b , then  the  particles 
at  that  point  will  be  relieved  of  the  reaction  of  the  point,  or 
of  its  support,  equilibrium  will  be  destroyed,  and  motion 
will  ensue,  and  all  the  particles  throughout  A will  begin  to 
move  toward  the  orifice,  though  not  with  equal  velocities. 

163.  Pressures  from  Vertical,  Inclined  and  Bent 
Columns  of  Water. — In  Fig  10  the  particles  in  the  body 
of  water,  B,  are  pressed  with  a pressure  due  to  the  weight 
of  any  one  vertical  column  of  particles  or  molecules  in  the 
body  of  water  above  the  opening  in  the  partition  g.  conse- 
quently the  reaction  horizontally  from  any  point  in  the 
partition  c',  or  downward  from  any  point  in  the  covering 
partition  g,  or  upward  from  any  point  in  the  bottom  d,  is 
equal  to  the  weight  of  a column  of  molecules  pressing  upon 
that  point,  of  height  equal  to  the  depth  of  the  given  point 
below  the  surface  of  the  water  ah'.  The  pressure  due  to 
this  vertical  column  of  molecules  would  still  remain  the 
same  if  the  column  a g was  inclined  or  bent,  so  long  as  the 
water  surface  remained  in  the  level  a b\  as  is  evident  by 
inspection  of  the  column  b.  '' 

Since  the  downward  reaction  from  any  point  in  the  sur- 
face g is  equal  to  the  pressure  of  a column  of  molecules 
equal  in  height  to  a g,  this  reaction  is  added  to  the  action 


PRESSURE  UPON  A UNIT  OF  SURFACE. 


171 


of  gravity  on  all  the  molecules  beneath  the  given  point  in  g, 
therefore  the  pressure  on  any  point  in  d,  beneath  the  given 
point  in  g,  is  equal  to  the  pressure  of  a column  of  molecules 
of  height  a' d. 

1(54.  Artificial  Pressure. — If  in  the  vessel  illustrated 
by  Fig.  10,  we  close  the  openings  b'  and  b"  at  the  level  of 
the  water  surface,  and  fit  a piston  carrying  a weight  into 
the  opening  a',  then  we  will  increase  the  pressure  at  points 
d , g,  c',  b\  b",  etc.,  respectively,  an  amount  equal  to  the 
pressure  received  by  a point  in  contact  with  the  piston  at  a'. 
This  artificial  pressure  is  equal  in  effect  to  a column  of  fluid 
placed  upon  a'  of  weight  equal  to  the  weight  of  the  loaded 
piston. 

165.  Pressure  upon  a Unit  of  Surface. — Since  one 
cubic  foot  of  water,  measuring  144  square  inches  on  its 
base  and  12  inches  in  height  weighs  62.425  pounds,  there 
must  be  a pressure  exerted  by  its  full  bottom  area  of  62.425 
pounds,  and  by  each  square  inch  of  its  bottom  area  of 


62.425  lbs. 


= I 0.433472  pounds  for  each  foot  of  vertical 


144  sq.  in. 
depth  of  the  water. 

In  ordinary  engineering  calculations  62.5  pounds  is 
taken  as  the  weight  of  one  cubic  foot  of  water,  and  0.434 
pounds  as  the  resulting  pressure  per  square  inch  for  each 
vertical  foot  of  depth  below  the  surface  of  the  water.  These 
weights  used  in  the  computation  of  the  following  table,  give 
closely  approximate  results,  slightly  in  excess  of  the  true 
weights. 


In  nice  calculations,  as  for  instance,  relating  to  tests  of 
turbines  to  determine  their  useful  effect,  or  of  pnmj  ing 
engines  to  determine  their  duty,  the  weights  due  to  che 
measured  temperatures  of  the  water  are  to  be  taken. 


172  WEIGHT,  PRESSURE,  AND  MOTION  OF  WATER. 


TABLE  No.  39. 


Pressures  of  Water  at  Stated  Vertical  Depths  below  thr 
Surface  of  the  Water,  at  Temp.  39. 2°  Fah. 


Depth. 

Pressure  per 
.Sq.  Inch. 

Pressure  per 
Sq.  Foot. 

Feet . 

Pounds . 

Pounds. 

1 

•4335 

62.425 

2 

.8670 

124.85 

3 

I-3°° 

187.27 

4 

1-734 

248.70 

5 

2.167 

312.12 

6 

2.601 

374-55 

7 

3-°35 

436-97 

8 

3.468 

499.40 

9 

3.902 

561.82 

xo 

4-335 

624.25 

11 

4.768 

686.67 

12 

5.202 

749.10 

13 

5-636 

811.52 

14 

6.069 

873-95 

15 

6-5°3 

936.37 

16 

6.936 

998.80 

17 

7-37° 

1061.23 

18 

7.803 

1123.65 

19 

8.237 

1 186.07 

20 

8.670 

1248.50 

21 

9.104 

I3IO-92 

22 

9-537 

1373-35 

23 

9.971 

1435-77 

24 

10.40 

1498.20 

25 

10.84 

1560.62 

26 

1 1.27 

1623.05 

27 

11.70 

1685.47 

28 

12.14 

1747.90 

29 

I2-57 

1810.32 

3° 

13.00 

1872.75 

31 

13-44 

1 935 • 1 7 

32 

i3-87 

1997.60 

33 

I4-3I 

2060.02 

34 

14-74 

2122.45 

35 

I5-I7 

2184.87 

Depth. 

Pressure  per 
Sq.  Inch. 

Pressure  per 
Sq.  Foot. 

Feet. 

Pounds. 

Pounds. 

36 

15.60 

2247  30 

37 

16.04 

2309.72 

38 

16.47 

2372.15 

39 

16.91 

2434-57 

40 

17-34 

2497.00 

41 

17-77 

2559-42 

42 

18.21 

2621.85 

43 

18.64 

2684.27 

44 

19.07 

2746.70 

45 

I9-5I 

2809.12 

46 

19.94 

2871-55 

47 

20.37 

2933-97 

48 

20.81 

2996.40 

49 

21.24 

3058.82 

5° 

21.67 

3121.25 

60 

26.01 

3745-5 

70 

3°-35 

4370 

80 

34.68 

4994 

90 

39.0X 

5618 

IOO 

43-35 

6242.5 

1 10 

47.68 

6867 

1 20 

52.02 

7491 

130 

56-36 

8115 

140 

60.69 

8739 

J5° 

65-03 

9364 

160 

69.36 

9988 

170 

73-70 

10612 

180 

78.03 

11237 

190 

82.36 

1 1861 

200 

86.70 

12485 

210 

91.04 

13109 

220 

95-37 

13733 

23° 

99.71 

14358 

240 

104.04 

14982 

250 

108.37 

15606 

166.  .Equivalent  Forces. — In  many  computations  in 
elementary  statics  we  are  accustomed  to  consider  the  force 


A LINE  A MEASURE  OF  WEIGHT. 


173 


acting  from  a weight  as  equivalent  to  the  force  of  a pressure 
and  to  place  weights  to  represent  statical  forces. 

On  one  square  foot  of  the  bottom  of  a vessel  containing 
one  foot  depth  of  water,  a pressure  is  exerted  by  the  water 
that  would  tend  to  prevent  any  other  force  from  lifting  up 
that  bottom.  We  might  remove  that  water  and  substitute 
the  pressure  of  a quantity  of  oil,  or  of  stone,  or  of  iron,  as 
an  equivalent  for  the  pressure  of  the  water,  but  to  be  an 
exact  equivalent  its  weight  must  be  exactly  the  same  as  the 
weight  of  the  water.  In  this  case  we  should  take  for  the 
62.5  pounds  pressure  in  the  water,  62.5  pounds  weight  of 
oil,  or  of  stone,  or  of  iron. 

167.  Weight  a Measure  of  Pressure. — Weight  is, 
then,  a standard  whose  unit  is  one  pound,  by  which  pres- 
sures may  be  compared  and  measured. 


Fig.  11. 


168.  A Line  a treasure  of  Weight. — In  graphical 

statics  we  are  also  accustomed  to  represent  weights  by  lines 
which  are  drawn  to  some  scale. 

If  two  forces  act  upon  the  centre  of  gravity  of  a body, 
Fig.  11,  one  of  which,  a , is  equal  to  30  pounds,  and  the 
other  b,  to  40  pounds,  we  can,  after  adopting  some  scale, 


174  WEIGHT,  PRESSURE,  AND  MOTION  OF  WATER. 

say  one  inch,  to  equal  one  pound,  represent  the  force  a "by 
a line  30  inches  long,  drawn  from  some  given  point,  g,  in  its 
direction  of  action,  ga',  and  the  force  b by  a line  40  inches 
long,  drawn  from  the  same  point,  in  its  direction,  gb'.  ISTow, 
if  we  draw  lines  from  the  end  of  each  line  thus  produced 
parallel  to  the  other  line  to  r,  completing  the  parallelogram, 
and  then  draw  the  diagonal,  gr,  then  the  resultant  of  the 
two  forces  will  pass  through  the  line  gr , and  the  length  of 
gr  will  represent  the  combined  effect  of  the  two  forces  in 
this  direction.  Its  length  will  be  50  inches  = V\gbvf  + (b'r)2, 
and  the  combined  effect  of  the  two  forces  in  this  direction 
will  be  50  pounds. 

169.  A Line  a Measure  of  Pressure  upon  a Sur- 
face.— Let  the  dimensions  of  the  top  surface  of  the  body  A, 
be  10  feet  long  and  3 feet  wide,  and  its  area  be  30  square 
feet ; let  the  side  dimensions,  B , be  10  feet  loug  and  4 feet 
high,  and  its  area  be  40  square  feet ; let  the  pressure  upon 
each  surface  be  one  pound  per  square  foot,  and  the  direc- 
tion of  the  pressure  be  shown  by  the  arrows  a and  b.  The 
body  being  solid,  the  forces  are  to  be  considered  as  acting 
through  its  centre  of  gravity.  W e can  now  plot  the  pres- 
sure upon  A of  30  pounds  in  its  direction,  and  upon  B of 
40  pounds  in  its  direction,  and  the  diagonal  of  the  parallel- 
ogram gr  will  give  the  direction  and  ratio  of  the  resultant, 
as  before.  The  forces  being  equal  to  those  before  considered 
as  acting  upon  a point,  will  again  give  a diagonal  50  inches 
long  and  indicating  an  effect  of  50  pounds. 

It  is  plain,  then,  that  we  can  take  the  line  ga',  or  the 
line  b'r , which  is  equal  to  it,  to  represent  the  force  or  pres- 
sure a acting  upon  the  point  g or  upon  the  surface  A ; and 
we  can  take  the  line  gb',  or  the  line  a'r,  to  represent  the 
force  or  pressure  b acting  upon  the  point  g or  the  surface  B , 
and  the  line  gr  to  represent  the  combined  effect  of  the  twc 


ANGULAR  RESULTANT  OF  A FORCE 


175 


forces.  In  various  calculations  it  is  convenient  to  Tbe  able 
to  do  this. 

170.  Diagonal  Force  of  Combined  Pressures 
Graphically  Represented. — Again,  if  we  know  the  mag- 
nitude of  the  force  r acting  through  the  centre  of  the  body, 
and  we  desire  to  know  the  magnitude  of  the  effects  upon 
the  sides  A and  B,  in  directions  at  right  angles  to  them, 
that  produced  the  force  r,  we  draw  the  line  r to  a scale  in 
the  direction  the  force  acts,  and  from  both  of  its  ends  draw 
lines  to  the  same  scale  in  directions  at  right  angles  to  the 
sides  A and  B , and  proportional  to  their  areas,  as  ga  and  gb', 
and  complete  the  parallelogram  ; then  will  ga  measured  to 
scale  indicate  the  effect  of  the  force  a upon  A,  and  gb' 
measured  to  scale  indicate  the  force  b upon  B.  If  gr 
measures  50  pounds,  then  will  ga'  measure  30  pounds  and 
gb'  measure  40  pounds. 

171.  Angular  Resultant  of  a Force  Graphically 
Represented. — If  a force  represented  by  the  line  ag, 
Fig.  12,  acts  upon  and  at  right 
angles  to  an  inclined  surface  fe 
at  g,  then  its  horizontal  resultant 
will  be  represented  by  the  line 
bg,  and  the  end  b will  be  perpen- 
dicularly beneath  a.  The  ratios 
of  the  lengths  of  the  lines  ag  and 
ab  and  bg  are  the  ratios  of  the 
effects  of  the  force  in  their  three 
directions  respectively. 

If  a perpendicular  line  be  let  fall  from  f upon  the  hori- 
zontal line  ed,  intersecting  it  in  d,  then  the  ratio  of  fe  to  fd 
will  be  equal  to  the  ratio  of  ag  to  bg ; consequently,  the 
horizontal  pressure  or  effect  of  the  force  ag  upon  fe  would 
be  to  its  direct  effect  as  fd  is  to  fe.  Therefore,  the  ratio  of 


Fig.  12. 


176  WEIGHT,  PRESSURE,  AND  MOTION  OF  WATER. 

the  line  fd  to  fe  equals  tlie  ratio  of  the  horizontal  elfect  of 
the  direct  force  upon  fe. 

Tlie  ratio  of  the  vertical  downward  effect  of  the  force  a 
upon  fe  is  to  its  direct  effect  as  tlie  length  ab  to  the  length 
ag , and  also  as  the  length  ed  to  the  length  ef.  Therefore, 
the  ratio  of  the  line  or  surface  ed  to  the  line  fe  represents 
the  ratio  of  the  vertical  downward  effect  of  the  direct  force 
upon  fe. 

172.  Angular  Effects  of  a Force  Represented  by 
the  Sine  and  Cosine  of  the  Angle. — Also,  ab  is  the 
sine,  and  bg  the  cosine  of  the  angle  agn,  and  we  have  seen 
that  their  ratios  are  to  radius  ag  as  ed  and  fd  are  to  fe; 
therefore  the  vertical  and  horizontal  effects  of  the  force  a 
upon  the  inclined  surface  fe  are  to  its  direct  force  as  the  sine 
and  cosine  of  the  angle  efd  is  to  radius, /e. 

173.  Total  Pressure. — To  find  the  total  pressure  of 
quiet  water  on  any  given  surface:  Multiply  together , its 
area,  in  square  feet ; the  vertical  depth  of  its  centre  of 
gravity,  below  the  water  surface,  in  feet;  and  the  weight 

of  one  cubic  foot  of  water 
in  pounds  (=  62.5  lbs  ). 
In  the  tank,  Fig.  13, 
filled  with  water,  let  the 
depth  ab  he  9 feet ; then 
the  centre  of  gravity  of 
the  surface  ab  will  he  at 
a depth  from  a equal  to 
one-lialf  ab  = 4.V  feet.  If 
the  length  of  the  side  ab 
is  1 foot,  then  the  total  pressure  on  ab  will  equal 

9 ft.  x 1 ft.  x 4t}  ft.  x 62.5  lhs.  — 2531.25  lhs. 

174.  Direction  of  Maximum  Effect. — The  direction 
of  the  maximum  effect  of  a pressure  on  a plane  surface  is 


Fig.  13. 


CENTRES  OF  PRESSURE  AND  OF  GRAVITY. 


177 


always  at  right  angles  to  the  surface.  The  maximum  hori- 
zontal effect  of  the  pressure  on  the  unit  of  length  of  ab 
equals  the  product  of  ab,  into  the  depth  of  its  centre  of 
gravity,  into  the  unit  of  pressure.  The  horizontal  effect  of 
pressure  on  the  unit  of  length  of  ccl  equals  the  product  of 
its  vertical  projection  ce,  into  the  depth  of  its  centre  of 
gravity,  into  the  unit  of  pressure  ; and  the  vertical  effect  of 
pressure  on  ,cd  equals  the  product  of  its  horizontal  projec- 
tion de,  into  the  depth  of  its  centre  of  gravity,  into  the  unit 
of  pressure. 

175.  Horizontal  and  Vertical  Effects. — Assuming 
the  length  of  the  side  cd  to  be  radius  of  the  angle  dee , then 
the  total  pressure  on  cd  is  to  its  horizontal  effect  as  radius 
cd  is  to  the  cosine  ce  of  the  angle  dee , or  as  the  surface  cd, 
is  to  its  vertical  projection  ce  ; and  the  total  pressure  is  to 
its  vertical  effect  as  radius  cd  is  to  the  sine  de  of  the  same 
angle,  or  as  cd  to  de. 

The  total  pressure  on  dg  is  to  its  horizontal  effect  as  dg 
is  to  fg,  or  to  the  cosine  of  the  angle  dgf;  and  to  its  vertical 
effect  as  dg  to  df,  or  to  the  sine  of  the  angle  dgf. 

176.  Centers  of  Pressure  and  of  Gravity. — The 
centre  of  hydrostatic  pressure,  which  tends  to  overturn  or 
push  horizontally  the  surface  of  equal  width,  ab,  is  not  in 
the  center  of  gravity  of  that  surface,  but  in  a point  at  two- 
thirds  the  depth  from  a at  p — 6 feet. 

The  center  of  gravity  of  the  surface  cd  is  at  one-lialf  the 
vertical  depth  ce,  at  h',  or  at  one-half  the  length  of  the  slope 
cd,  at  h.  The  points  h and  h'  are  both  in  the  same  hori- 
zontal plane.  When  the  water  surface  is  at  ac,  the  center 
of  pressure  of  the  surface  cd  is  at  two-thirds  of  the  vertical 
depth  ce,  at  p' , or  at  two-thirds  the  slope  cd,  at  p.  The 
points  p’  and  p are  in  the  same  horizontal  plane.  If  ce 
equals  six  feet,  then  the  center  of  gravity  of  cd  or  ce  will  be 
12 


178 


WEIGHT,  PRESSURE,  AND  MOTION  OF  WATER. 


at  the  vertical  depth  of  three  feet  = ch',  and  the  center  of 
pressure  at  the  vertical  depth  of  four  feet  = cp'. 

The  center  of  gravity  of  the  surface  dg  is  at  a depth 
from  the  water  surface  c,  equal  to  the  sum  of  one-lialf  the 

vertical  depth  fg  added  to  the  depth  ce  = ce  and  the 


center  of  pressure  of  dg  is  at  a vertical  depth  equal  to 

2 (cgf  - (cef  = 7 0 

3 (cfff  - (cef 

177.  Pressure  upon  a Curved  Surface  and  Effect 
upon  its  Projected  Plane. — In  a vessel,  Fig.  14,  filled 
with  water,  one  of  whose  ends,  ab , is  a segment  of  a cylin- 
der, and  opposite  end  in 


Fig.  14. 


aj"  part  of  the  vertical  plane 
a"b",  and  in  part  of  a 
hemisphere  cd,  the  total 
pressure  on  ab  will  he 
as  the  total  surface  ab  ; 
-!  y"  hut  its  horizontal  effect 
will  he  as  the  area  of  its 
vertical  projection  a'b'.  The  total  pressure  on  the  end  a'b', 
will  he  as  the  remaining  surface  of  the  vertical  plane  a'  b,' 
increased  hy  the  concave  surface  of  the  hemisphere  chd,  but 
its  horizontal  effect  will  he  equal  to  its  vertical  projection 
a"'b"'  or  a'b'.  The  vertical  effect  on 
the  plane  a"b"  is  equal  to  zero,  hut 
the  vertical  effect  of  the  pressure  in 
the  hemisphere  is  represented  hy 
the  plan  of  one-lialf  a sphere  of 
diameter  equal  to  cd. 

In  a hollow  sphere,  Fig.  15,  filled 
with  water,  the  total  pressure  will 
he  as  the  total  concave  surface  a'hb'h",  hut  the  horizontal 


Fig.  15. 


FLOATING  AND  SUBMERGED  BODIES. 


179 


effect  will  be  as  its  vertical  projection  ab,  which  represents 
a circular  vertical  plane  of  diameter  equal  to  ab,  and  the 
vertical  effect  will  be  as  its  horizontal  projection  bb",  which 
represents  a horizontal  circular  area  of  diameter  equal 
to  bb". 

In  a pipe,  or  cylinder,  represented  also  in  section  by 
Fig.  15,  the  total  pressure  within  is  as  the  inner  circumfer- 
ential area  a'hbli",  and  when  the  cylinder  lies  horizontally 
the  horizontal  and  vertical  effects  of  its  pressure  in  a unit 
of  length  will  be  represented  by  its  vertical  and  horizontal 
projections  ab  and  bb". 

If  the  cylinder  is  inclined,  the  pressure  at  any  point 
upon  its  circumference  is  as  the  depth  of  that  point  below 
the  surface  of  the  water,  and  the  total  pressure  in  pounds 
upon  any  section  of  the  cylinder  will  be  found  by  multi- 
plying its  area  in  square  feet  into  the  depth  of  its  center  of 
gravity,  in  feet,  below  the  surface  of  the  water  and  their 
product  into  the  weight,  in  pounds  (62.5  lbs.),  of  a cubic 
foot  of  water. 

178.  Center  of  Pressure  upon  a Circular  Area. — 

The  center  of  pressure  of  a vertical  circular  area,  repre- 
sented also  by  Fig.  15,  when  its  top  a is  in  the  water  surface, 
is  at  a depth  below  a equal  to  five -fourths  the  radius  of  the 
circle. 

179.  Combined  Pressures. — The  sum  of  pressures  in 
pounds,  upon  a number  of  adjacent  surfaces,  may  be  found 
by  multiplying  the  sum  of  their  surfaces  in  square  feet  into 
the  depth  of  their  common  center  of  gravity,  in  feet,  below 
the  surface  of  the  water,  and  this  product  into  the  weight  of 
one  cubic  foot  of  water,  in  pounds  (62.5  lbs.). 

180.  Sustaining  Pressure  upon  Floating  and 
Submerged  Bodies. — The  pressure  tending  to  sustain  a 
cylinder  floating  vertically  in  water  c (Fig.  16)  is  equal  to 


180  WEIGHT,  PRESSURE,  AND  MOTION  OF  WATER. 

Fig.  16.  Fig.  17. 


the  vertical  effect  of  the  pressure  on  its  bottom  area.  The 
sustaining  pressure  may  be  computed,  in  pounds,  by  mul- 
tiplying the  bottom  area  of  the  cylinder,  in  square  feet,  into 
its  depth,  in  feet  (which  gives  the  cubical  contents  of  the 
immersed  portion  of  the  cylinder),  and  this  product  into 
the  weight  of  a cubic  foot  of  water. 

The  weight  of  water  displaced  may  be  computed  also  by 
multiplying  the  cubic  contents  of  the  immersed  portion  of 
the  cylinder,  in  cubic  feet,  into  the  weight  of  a cubic  foot 
of  water.  The  two  results  will  be  equal  to  each  other ; 
therefore  the  vertical  effect  tending  to  sustain  the  cylinder 
is  equal  to  the  weight  of  water  displaced. 

To  compute  the  pressure  tending  to  sustain  the  trun- 
cated cone,  or  pyramid,  d,  multiply  the  vertical  projection 
of  the  inclined  surfaces  (=  top  area  — bottom  area),  in  feet, 
into  the  depth  of  their-  common  center  of  gravity,  in  feet, 
and  to  this  product  add  the  product  of  its  bottom  area,  in 
feet,  into  its  depth,  in  feet,  and  then  multiply  the  sum  of 
the  products  into  the  weight  of  a cubic  foot  of  water,  in 
pounds. 

This  sustaining  pressure  will  also  equal  the  weight  of 
the  water  displaced. 

To  compute  the  pressure  tending  to  sustain  the  im- 
mersed cube  e,  multiply,  in  terms  as  before,  the  bottom 


UPWARD  PRESSURE  UPON  A SUBMERGED  LINTEL.  181 


area  into  the  depth  and  into  the  weight  of  water,  and  from 
the  final  product  subtract  the  product  of  the  top  area  into 
its  depth  and  into  the  weight  of  water.  This  sustaining 
pressure  also  equals  the  weight  of  water  displaced. 

The  downward  pressure  on  the  top  of  e tends  to  sink  it, 
and  the  upward  pressure  on  its  bottom  to  sustain  it.  The 
difference  of  the  two  effects  is  the  resultant.  The  resultant 
will  act  vertically  through  the  center  of  gravity  of  the  body. 
If  e is  of  the  same  specific  gravity  as  the  water,  then  its 
weight  will  just  balance  the  resultant,  and  it  will  neither 
rise  or  fall ; if  of  less  specific  gravity  it  will  rise ; if  of 
greater,  it  will  sink.  The  cylinder  c is  evidently  of  less 
specific  gravity  than  the  water,  and  cl  of  the  same  specific 
gravity. 

Let  c be  a hollow  cylinder  with  a water-tight  bottom, 
then  although  it  may  be  made  of  iron,  and  weights  be 
placed  within  it,  it  will  still  float  if  its  total  weight,  includ- 
ing its  load,  is  less  than  the  weight  of  the  water  it  displaces. 
On  the  same  principle  iron  ships  float  and  sustain  heavy 
cargoes. 

181.  Upward  Pressure  upon  a Submerged  Lin- 
tel.—If  L,  Fig.  17,  be  a horizontal  lintel  covering  a sluice 
between  two  reservoirs,  the  upward  pressure  of  the  water 
upon  ij,  tending  to  lift  it,  will  be  equal  to  the  product  of 
the  rectangular  area  ij  into  its  depth  and  into  the  weight 
of  a cubic  foot  of  water ; that  is,  the  upward  pressure  in 
pounds  will  be  equal  to  the  weight  in  pounds  of  a prism 
of  water  haring  the  rectangular  area  ij  for  its  base  and  the 
depth  of  ij  below  the  surface  of  the  water  for  its  height. 

If  the  lintel  is  constructed  of  timber,  at  a considerable 
depth,  and  is  not  equally  as  strong  as  the  enclosing  walls 
of  the  reservoir  at  the  same  depth,  it  may  be  broken  in  or 
thrust  upward. 


182  WEIGHT,  PRESSURE,  AND  MOTION  OF  WATER. 


182.  Atmospheric  Pressure — Upon  the  particles  of 
all  bodies  of  water  resting  in 

Fig.  18. 


open  vessels  or  reservoirs, 
there  is  a force  constantly 
acting,  in  addition  to  the 
direct  force  of  gravity,  upon 
the  independent  particles. 
This  force  conies  from  the 
effect  of  gravity  upon  the 
atmosphere.  The  weight 
of  the  atmosphere  produces 
a pressure  upon  the  sur- 
face of  the  water  of  about 
14.75  pounds  per  square 


inch,  or  about  2124  pounds  per  square  foot.  This  is  equiv- 

/ 14  *75  lbs  \ 

alent  to  a column  of  water  U 433472  ft  = ) ^4.028  feet  high. 


In  the  open  vessel,  Fig.  18.  filled  with  water  to  the  level 
a , the  effect  of  the  pressure  of  the  atmosphere  is  transmitted 
through  the  particles,  and  acts  on  all  the  interior  surface 
below  the  water  surface  abba , with  a force  of  14.75  pounds 
on  every  square  inch,  in  addition  to  the  pressure  from  the 
weight  of  the  water.  There  is  also  an  equal  atmospheric 
pressure  on  the  exterior  of  the  vessel  of  14.75  pounds  per 
square  inch  ; therefore  the  resultant  is  zero,  and  the  weight 
of  the  atmosphere  does  not  tend  to  move  either  side  of  the 
vessel  or  to  tear  the  vessel  asunder. 

183.  Rise  of  Water  into  a Vacuum. — If  the  tube  cd 
be  extended  to  a height  of  thirty-five  or  more  feet  above  the 
surface  of  the  water,  and  a piston,  containing  a proper  valve, 
be  closely  fitted  in  its  upper  end,  then  by  means  of  the  piston 
the  air  may  be  pumped  out  of  the  tube,  and  the  surface  of 
water  in  the  tube  relieved  of  atmospheric  pressure.  The 
equilibrium  of  the  particles  within  the  tube  will  then  be  de- 


TRANSMISSION  OF  PRESSURE  TO  A DISTANCE. 


183 


stroyed,  and  the  pressure  of  the  atmosphere  acting  through 
the  particles  in  the  lower  end  of  the  tube  will  press  the 
water  up  the  tube  to  a height,  according  to  the  perfection 
of  the  vacuum,  of  34.028  feet  approximately.  It  is  atmos- 
pheric pressure  that  causes  pump  cylinders  to  fill  when  they 
are  above  the  free  surface  of  the  water. 

If  the  bottom  of  the  immersed  tube,  cd , be  closed  by  a 
valve,  and  the  tube  filled  with  water,  and  the  top  then 
sealed  at  a height  of  thirty-five  or  more  feet  above  the  sur- 
face of  the  water  ad,  the  valve  at  d may  afterwards  be 
opened,  and  the  pressure  of  the  atmosphere  acting  through 
the  particles  in  the  lower  end  of  the  tube  will  sustain  the 
column  to  a height  of  34.028  feet  approximately. 

184.  Siphon. — If  the  bent  tube  or  siphon,  ef  g,  Fig.  18, 
having  its  1 eg/ <7  longer,  vertically,  than  its  leg  ef,  be  filled 
with  water  and  its  end  e inserted  in  the  water  A,  then  the 
action  of  gravity  upon  the  water  in  the  leg  f g,  will  be 
greater  than  upon  the  water  in  the  leg  ef,  and  the  equi- 
librium in  the  particles  at  f will  be  destroyed.  The  pres- 
sure of  the  atmosphere  on  the  surface  ad,  will  constantly 
press  the  water  A up  the  leg  e f,  tending  to  restore  the  equi- 
librium, and  gravity  acting  in  the  leg  f g will  as  constantly 
tend  to  destroy  the  equilibrium,  consequently  there  will  be 
a constant  flow  of  the  water  A out  of  the  end  g,  until  the 
water  surface  falls  nearly  to  the  level  e,  or  until  the  air  can 
enter  at  e. 

185.  Transmission  of  Pressure  to  a Distance. — 

The  effect  of  pressure  on  a fluid  is  transmitted  through  its 
'particles  to  any  distance,  however  indefinitely  great , to  the 
limit  of  its  volume. 

If  water  is  poured  into  the  open  top  b",  Fig.  10,  the  divi- 
sion b'c ",  will  fill  as  fast  as  the  division  b",  and  the  water 
will  flow  over  b'g,  and  will  reach  the  level  d,  at  approxi- 


184  WEIGHT,  PRESSURE,  AND  MOTION  OF  WATER, 

mately  the  same  time  as  it  reaches  b" ; so  in  any  inverted 
siphon,  or  in  a system  of  water  pipes  of  a town,  water  will 
in  consequence  of  transmitted  pressure,  flow  from  an  ele- 
vated source  down  through  a valley  and  up  on  an  opposite 
hill  to  the  level  of  the  source.  If  the  syphon,  or  pipe,  has 
an  indefinite  number  of  branches  with  open  tops  as  high  as 
the  source,  then  the  surface  of  the  water  at  the  source  and 
in  each  of  the  branches  will  rest  in  the  same  relative  eleva- 
tion of  the  earth’ s curvature. 

186.  Inverted  Siphon. — By  transmission  of  pressure 
through  the  particles,  water  in  a pool  or  lake  near  the  sum- 
mit of  one  hill  or  mountain  is  sometimes,  when  the  rock 
strata  have  been  bent  into  a favoring  shape,  forced  through 
a natural  subterranean  inverted  siphon,  and  caused  to  flow 
out  as  a spring  on  an  opposite  hill  or  mountain  summit. 

187.  Pressure  Convertible  Into  Motion. — Thus  we 
see  that  the  force  of  gravity  in  the  form  of  weight  is  con- 
vertible into  pressure,  and  pressure  into  motion  ; and  that 
motion  may  be  converted  into  pressure,  aud  pressure  be 
equivalent  to  weight. 

Motion  we  are  accustomed  to  measure  by  its  rate,  which 
we  term  its  velocity  ; that  is,  the  number  of  units  of  space 
passed  over  by  the  moving  body  in  a unit  of  time,  as,  feet 
per  second. 

MOTION  OF  WATER. 

188.  Flow  of  Water. — All  forces  tending  to  destroy 
equilibrium  among  the  particles  of  a body  of  water  tend 
to  produce  motion  in  that  body. 

We  have  above  referred  to  the  accepted  theory  of  motion 
due  to  the  influence  of  caloric  ; there  is  a motion  of  water 
due  to  the  winds,  a motion  due  to  the  attraction  of  the 
heavenly  bodies,  and  an  artificial  motion,  as,  for  instance, 


ACCELERATION  OF  MOTION. 


185 


that  due  to  the  pressure  of  a pump-piston.  The  motion 
herein  to  be  considered  is  that  originated  by  the  influence 
of  gravity  and  termed  the  flow  of  water. 

189.  Action  of  Gravity  upon  Individual  Mole- 
cules.— All  natural  flow  of  water  is  due  to  the  force  of 
gravity , acting  upon  and  generating  motion  in  its  indi- 
vidual molecules. 

If  in  the  side  of  a vessel  filled  with  water  there  be  made 
an  orifice ; if  one  end  of  a level  pipe  filled  with  water  be 
lowered  ; or  if  a channel  filled  with  water  have  its  water 
released  at  one  end,  then  equilibrium  among  the  particles 
of  the  water  will  be  destroyed,  and  motion  of  the  water  will 
ensue.  Gravity  is  the  force  producing  motion  in  either  case, 
and  it  acts  upon  each  individual  molecule  as  it  acts  upon  a 
solid  body,  free  to  move,  or  devoid  of  friction. 

190.  Frictionless  Movement  of  Molecules. — The 
molecules  of  water  move  over  and  past  each  other  with  such 
remarkable  ease  that  they  have  usually  been  considered  as 
devoid  of  friction. 

The  formulas  in  common  use  for  computing  the  velocity 
with  which  water  flows  from  an  orifice  in  the  bottom  or  side 
of  a tank  filled  with  water,  assume  that  the  individual 
molecules,  at  the  axis  of  the  jet,  will  issue  with  a velocity 
equal  to  that  the  same  molecules  would  have  acquired  if 
they  had  fallen  freely,  in  vacuo,  in  obedience  to  gravity,  from 
a height  above  the  orifice  equal  to  the  height  of  the  surface 
of  the  water. 

191.  Acceleration  of  Motion. — The  force  of  gravity 
perpetually  gives  new  impulse  to  a falling  body  and  accel- 
erates its  motion , if  unresisted,  in  regular  mathematical 
proportion. 

Experiment  has  shown  that  a solid  body  falling  freely 
in  vacuo , at  the  level  of  the  sea,  passes  through  a space  or 


186 


WEIUHT,  PRESSURE,  AND  MOTION  OF  WATER. 


height  of  16.1  feet  nearly,  during  the  first  second  of  time ; 
has  a velocity  at  the  end  of  the  first  second  of  32.2  feet 
nearly,  and  is  accelerated  in  each  succeeding  second  32.2 
feet  nearly.  The  usual  symbol  of  this  rate  of  acceleration 
is  g,  the  initial  of  the  word  gravity , and  we  shall  have  fre- 
quent occasion  for  its  use. 

The  latitude  and  altitude,  or  distance  from  the  centre  of 
the  earth,  affects  the  rate  of  motion  slightly,  but  does  not 
affect  materially  the  results  of  ordinary  hydrodynamic  cal- 
culations. 

The  resistance  of  the  air  affects  slightly  the  motion  of 
dense  bodies,  and  retards  them  more  if  they  are  just  sepa- 
rating, as  water  separates  into  spray. 

192.  Equations  of  Motion. — The  velocity,  v,  acquired 
by  a solid  body  at  the  end  of  any  time,  t,  equals  the  prod- 
uct of  time  into  its  acceleration  by  gravity,  g,  and  is  directly 
proportional  to  the  time : 


The  height,  7i,  through  which  the  body  falls  in  one 
second  of  time  equals  \g,  and  the  heights  in  any  given 
times,  t , are  as  the  squares  of  those  times  : 


From  these  equations  we  deduce  the  following  general 
equations  of  time,  t ; height , h;  velocity , v;  and  accelera- 
tion, g : 


v : g ::  t : 1,  or  v = gt. 


h : \g  : : : (1)\  or  h = \gtl 

and,  by  transposition,  we  have 


This  value  of  t in  the  equation  of  v gives 


PARABOLIC  PATH  OF  THE  JET. 


187 


t = A 

g 

II 

CM  1 ^ 

II 

= .031063© 

(1) 

2 

II 

1 ^ 
II 

~ = .015536©2 

£ 

(2) 

<s 

1! 

OK 

II 

II 

V2 ~gh  = 8. 0227 

(3) 

V 

* = T 

H 

II 

©2 

— = 32.1908 

2h 

(4) 

The  time , space,  and  velocity  are  at  the  ends  of  the  first 
ten  seconds  as  follows : 


Time  (/) 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

Space \h)  

Velocity  (w) 

16.1 

64.4 

144.9 

257.6 

402.5 

579  6 

788.9 

IO3O.4 

1304. 1 

1610 

32.2 

64.4 

96.6 

128.8 

l6l.O 

193-2 

225.4 

257.6 

289.8 

322 

Acceleration  Cs) 

32.2 

32.2 

32.2 

32.2 

32.2 

32.2 

32.2 

32.2 

32.2 

32.2 

193.  Parabolic  Path  of  the  Jet. — If  we  plot  the 


spaces  of  the  column  of 
spaces  or  heights  to  a 
scale  on  a vertical  line, 
beginning  with  zero  at 
the  top,  and  then  from 
the  space  points  plot 
horizontally  to  scale  the 
velocities,  as  in  Fig.  19, 
and  then  from  zero  draw 
a curved  line  ac , cutting 
the  extremities  of  the 
horizontal  lines,  the 
curve  ac  will  be  a pa- 
rabola, the  vertical  line 
ab  its  abscissa,  and  the 
horizontal  lines  its  ordi- 
nates. 


C « 

O G 

IS 
hS  25 .S 


.Sr  O 


Fig.  19. 

Velocity  in  feet  per  second. 

a 


188  WEIGHT,  PRESSURE,  AND  MOTION  OF  WATER. 

194.  Velocity  of  Efflux  Proportional  to  the  Head. 

— If  in  the  several  sides  of  a reservoir  A,  Fig.  19a,  kept 
filled  with  water,  orifices  with  thin  edges  are  made  at 
depths  of  20  feet,  25  feet,  50  feet,  75  feet,  and  100  feet  from 
the  surface  of  the  water,  then  water  will  issue  from  each 

Fig.  19a. 


orifice  in  a direction  perpendicular  to  the  side,  with  a veloc- 
ity proportional  to  the  square  root  of  the  head  of  water 
above  the  centre  of  gravity  of  the  orifice,  and  equal  approx- 
imately to  the  velocity  one  of  its  particles  would  have 
acquired  if  it  had  fallen  freely  from  the  height  of  the  head. 

195.  Conversion  of  the  Force  of  Gravity  from 
Pressure  into  Motion. — The  accumulated  vertical  force 
of  gravity  due  to  the  head  or  “charge”  will  act  upon  the 


EQUAL  PRESSURES  GIVE  EQUAL  VELOCITIES. 


189 


particles  as  pressure  before  tlie  orifice  is  opened,  but  in- 
stantly npon  an  orifice  being  opened  pressure  will  impel 
the  particles  of  water  in  the  direction  of  the  axis  of  the 
orifice,  and  gravity  will  begin  anew  to  act  upon  the  parti- 
cles in  a vertical  direction.  If  the  axis  of  the  orifice  is  not 
vertical,  gravity  will  deflect  the  particles  through  a curved 
path. 

196.  Resultant  Effects  of  Pressure  and  Gravity 
upon  the  Motion  of  a Jet. — If  on  a line  at,  drawn 
through  the  center  of  an  orifice,  perpendicular  to  the  plane 
of  the  orifice,  we  plot  to  scale  the  products  of  any  given 
times  into  a given  velocity,  and  from  each  of  the  points 
thus  indicated  we  plot  vertically  downward  the  distance,  a 
body  will  fall  freely  in  those  times,  op,  and  then  from  the 
orifice  draw  a line  through  the  extremities  of  the  vertical 
lines,  the  curved  line  thus  sketched  will  indicate  the  path 
of  the  jet  flowing  from  the  orifice.  The  curved  line  is  a 
parabola,  to  which  the  axis  of  the  orifice  is  tangent ; and 
the  distances  ao  upon  the  tangent  are  equal  and  parallel  to 
ordinates,  and  represent  the  force  per  unit  of  time  given  to 
the  particles  of  the  jet  by  pressure,  and  the  verticals  from 
the  tangent  are  equal  and  parallel  to  abscisses,  and  repre- 
sent by  their  increase  the  accelerating  effect  of  gravity  upon 
the  falling  particles.  The  distances  ao  and  op,  ordinates  ap, 
and  abscisses  ad , form  a series  of  parallelograms,  one  angle 
of  which  lies  in  the  orifice  and  the  opposite  angles  of  which 
lie  in  the  curved  path  of  the  jet,  and  the  diagonals  of  which 
are  equal  to  resultants  of  the  effects  of  pressure  and  gravity. 

197.  Equal  Pressures  give  Equal  Velocities  in  all 
Directions. — The  velocities  of  issues,  downward  from  the 
orifice  c and  upward  from  the  orifice  c,  and  horizontally 
from  the  lower  orifice  b',  will  be  equal,  since  they  all  are  at 
the  same  depth. 


190  WEIGHT,  PRESSURE,  AND  MOTION  OF  WATER. 

198.  Resistance  of  the  Air. — Since  the  velocity  of 
upward  issue  from  c is  due  to  the  gravity  force  of  the  head 
dc , acting  as  pressure,  the  jet  should  theoretically  reach  the 
level  of  the  water  surface  d.  The  spreading  of  the  particles 
and  consequent  enhanced  resistance  of  the  air  prevents  such 
result,  and  the  resistance  increases  as  the  ratio  of  area  of 
orifice  to  height  of  head  decreases. 

199.  Theoretical  Velocities. — The  following  table  of 
theoretical  velocities  and  times  due  to  given  heights  or  heads 
has  been  prepared  to  facilitate  calculation : 

TABLE  No.  40. 


Correspondent  Heights,  Velocities,  and  Times  of  Falling 

Bodies. 


X 

II 

n\\ 

v = ^ 2gH 

Vf 

H = — 
zg 

v — \f 2 g H 

'Vf 

Velocity  in  feet 

Time 

Velocity  in  feet 

Time 

per  second. 

in  seconds. 

per  second. 

in  seconds. 

.OIO 

.80 

.0248 

• 145 

3-05 

.0949 

.015  •• 

.98 

.0304 

.150 

3-H 

.0964 

.020 

i-i3 

•0350 

• 155 

3-16 

.0980 

.025 

1.27 

.0394 

. 160 

3.21 

•0995 

.030 

i-39 

•0431 

.165 

3.26 

.IOII 

.035 

1.50 

.0465 

.170 

3-3i 

,I0l6 

.040 

1.60 

.0496 

• 175 

3-36 

. 1042 

.045 

1.70 

.0527 

.180 

3-40 

.1054 

.050 

1.79 

•0555 

.185 

3-45 

. 1069 

•055 

1.88 

.0583 

. 190 

3-50 

.1085 

.060 

1.97 

.0611 

.195 

3-55 

.1100 

.065 

2.04 

.0632 

.20 

3-59 

.1113 

.070 

2. 12 

.0657 

.21 

3-68 

■1141  , 

•075 

2.20 

.0682 

.22 

3.76 

.1166 

.080 

2.27 

.0704 

•23 

3.85 

■1193 

.085 

2.34 

.0725 

.24 

3-93 

. 1221 

.090 

2.41 

.0747 

• 25 

4.01 

.1243 

•095 

2.47 

.0766 

.26 

4.09 

.1268 

.IOO 

2.54 

.0787 

• 27 

4.17 

.1293 

.105 

2.60 

.0806 

.28 

4.25 

• 1317 

.IIO 

2.66 

.0825 

.29 

4-32 

• 1339 

.115 

2.72 

.0843 

.30 

4-39 

.1361 

. 120 

2.78 

.0862 

•31 

4-47 

.1386 

.125 

2.84 

.0880 

•32 

4-54 

.1407 

.130 

2.89 

.0896 

•33 

4.61 

.1429 

• 135 

2.95 

.0914 

• 34 

4.68 

.1451 

.140 

3.00 

.0930 

• 35 

4-75 

.1472 

THEORETICAL  VELOCITIES. 


191 


Correspondent  Heights,  Velocities,  and  Times  of  Falling 
Bodies — ( Continued. ) 


X 

II 

7/  = |/  2^H 

RSI1* 

II 

•** 

11 

X 

v = VzgH 

** 

11 

si 

Head  in  feet. 

Velocity  in  feet 
per  second. 

Time 

in  seconds. 

Head  in  feet. 

Velocity  in  feet 
per  second. 

Time 

in  seconds. 

•36 

4.81 

.1491 

.83 

7-31 

. 2266 

•37 

4.87 

. 1510 

.84 

7-35 

.2278 

.38 

4.94 

• 1531 

•85 

7.40 

.2294 

•39 

5-OI 

• 1553 

.86 

7-44 

.2306 

.40 

5.07 

.1572 

•87 

7.48 

.2319 

.41 

5.14 

•1593 

.88 

7-53 

•2334 

.42 

5-20 

.1612 

.89 

7-57 

•2347 

•43 

5.26 

.1634 

.90 

7.61 

•2359 

•44 

5-32 

.1649 

.91 

7-65 

•2377 

•45 

5-38 

.1668 

.92 

7.70 

.2387 

.46 

5-44 

.1686 

•93 

7-74 

•2399 

•47 

5-50 

.1705 

• 94 

7.78 

.2412 

.48 

5-56 

.1724 

•95 

7.82 

.2424 

•49 

5.62 

.1742 

.96 

7.86 

•2437 

• 50 

5-67 

.1758 

•97 

7.90 

•2449 

•5i 

5-73 

• 1779 

.98 

7-94 

.2461 

•52 

5-79 

• 1795 

•99 

7.98 

.2474 

•53 

5-85 

.1813 

I . 

8.03 

.2491 

•54 

5 90 

. 1829 

1.02 

8.10 

.2518 

•55 

5-95 

.1844 

I.04 

8.18 

•2543 

•56 

6.00 

. i860 

1.06 

8.26 

.2567 

•57 

6.06 

.1879 

1.08 

8-34 

.2589 

•58 

6.  ii 

.1894 

I.  IO 

8.41 

.2616 

•59 

6.17 

• 1913 

1 . 12 

8-49 

.2638 

.60 

6.22 

. 1928 

1. 14 

8-57 

.2660 

.6l 

6.28 

• 1947 

1. 16 

8.64 

.2685 

.62 

6.32 

•1959 

1. 18 

8.72 

.2706 

.63 

6-37 

• 1975 

1.20 

8-79 

.2730 

.64 

6.42 

.1990 

1.22 

8.87 

.2751 

.65 

6.47 

.1999 

I.24 

8-94 

•2774 

.66 

6.52 

.2021 

1.26 

g.oi 

•2797 

.67 

6-57 

.2037 

1.28 

9.08 

. 2819 

.68 

6.61 

• 2049 

1.30 

9.15 

.2842 

.69 

6.66 

. 2065 

1.32 

9.21 

. 2866 

.70 

6.71 

.2080 

*■34 

9.29 

.2885 

•71 

6.76 

.2096 

1.36 

9.36 

. 2906 

.72 

6.81 

.2111 

1.38 

9-43 

.2927 

•73 

6.86 

.2127 

1.40 

9-49 

.2950 

•74 

6.91 

.2142 

1.42 

9-57 

.2968 

•75 

6.95 

.2154 

1.44 

9.63 

.2991 

.76 

6.99 

.2167 

1.46 

9.70 

.3010 

•77 

7.04 

.2182 

1.48 

9-77 

•3030 

•78 

7.09 

.2198 

1.50 

9.83 

.3052 

•79 

7-13 

.2210 

i-55 

9.98 

.3106 

.80 

7.18 

.2226 

1.60 

10.2 

•3137 

.81 

7.22 

.2238 

1.65 

IO.3 

.3204 

.82 

7.26 

.2251  1 

1.70 

10.5 

•3238 

192  WEIGHT,  PRESSURE,  AND  MOTION  OF  WATERS. 


Correspondent  Heights,  Velocities,  and  Times  of  Falling 
Bodi  es — ( Contin  tied) 


H = — 
2 g 

S'  = 4/2£H 

'Vt 

*1* 

II 

32 

v = \ 7.gW. 

t = 4 / — 

V * 

Head  in  feet. 

Velocity  in  feet 

Time 

Head  in  feet. 

Velocity  in  feet 

Time 

per  second. 

in  seconds. 

per  second. 

in  seconds. 

1-75 

10.6 

• 3302 

8.4 

23-3 

.7210 

i .8o 

10.8 

•3333 

8 . 6 

23-5 

•7319 

1.85 

I0.g 

•3394 

8.8 

23.8 

•7395 

I .go 

II.  I 

•3423 

9- 

24.1 

• 7469 

1-95 

II  . 2 

• 3482 

9.2 

24-3 

•7572 

2. 

11. 4 

•3509 

9.4 

24.6 

.7642 

2.1 

11  • 7 

•3590 

9.6 

24.8 

•7742 

2.2 

11. 9 

•3697 

9.8 

25-1 

.7809 

2-3 

12.2 

•3770 

IO. 

25-4 

.7866 

2.4 

12-4 

•3871 

10  5 

26. 

• 8077 

2-5 

12.6 

.3968 

II. 

26.6 

.8277 

2.6 

I2.g 

.4031 

11  • 5 

27.2 

.8456 

2.7 

13.2 

.4091 

12. 

27.8 

• 8633 

2.8 

13-4 

.4179 

12.5 

28.4 

.8803 

2-9 

13.7 

•4234 

13- 

28.9 

•8997 

3- 

13-9 

•4317 

13-5 

29-5 

•9153 

3-i 

14. 1 

•4397 

14. 

30. 

•9333 

3-2 

14-3 

.4476 

14  5 

30.5 

.9508 

3-3 

14.5 

•4552 

15- 

3i -I 

.9646 

3-4 

14.8 

•4595 

15-5 

31.6 

.9810 

3-5 

15- 

.4667 

l6. 

32.1 

.9969 

3-6 

15.2 

•4737 

16.5 

32.6 

I .0123 

3-7 

15.4 

.4805 

17- 

33-1 

1.0272 

3-8 

15.6 

•4872 

17-5 

33-6 

1-0417 

3-9 

15-8 

■4937 

18. 

34- 

1.0588 

4- 

l6. 

.5000 

18.5 

34-5 

1.0725 

4.2 

16.4 

.5122 

19. 

35- 

1.0857 

4-4 

16.8 

• 5238 

19-5 

35-4 

I . 1017 

4.6 

17.2 

•5343 

20. 

35-9 

I .1142 

4-8 

17.6 

•5454 

20.5 

36-3 

1. 1295 

5- 

17.9 

•5587 

21. 

36.8 

I-I4I3 

5-2 

18.3 

.5683 

21.5 

37-2 

1 • I5  59 

5-4 

18.7 

•5775 

22. 

37-6 

I. 1702 

5-6 

19. 

•5895 

22.5 

38.1 

1 . 1S11 

5-8 

19-3 

.6010 

23- 

3S.5 

1 . 1948 

6. 

19.7 

.6091 

23-5 

38.9 

1 . 2082 

6.2 

20. 

.6200 

24. 

39-3 

I . 2214 

6.4 

20.3 

.6305 

24-5 

39-7 

1-2343 

6.6 

20.6 

.6408 

25 

40.1 

1 . 2469 

6.8 

20.9 

.6507 

26 

40.9 

1-2714 

7- 

21.2 

.6604 

27 

4i-7 

1.2950 

7.2 

21.5 

.6698 

28 

42.5 

1.3176 

7-4 

21.8 

.6789 

29 

43. 2 

1 . 3426 

7.6 

22.1 

.6878 

30 

43-9 

1.3667 

7.8 

22.4 

.6964 

3i 

44-7 

1.3870 

8. 

22.7 

.7048 

32 

45-4 

1.4097 

8.2 

23- 

.7130 

33 

46.1 

1-4317 

THEORETICAL  VELOCITIES. 


193 


Correspondent  Heights,  Velocities,  and  Times  of  Falling 
Bodies — ( Continued .) 


H = — 

2/  = 

' = 1/? 

H = — 

V—  V2gR 

* = T / — 

v * 

Head  in  feet. 

Velocity  in  feet 

Time 

Head  in  feet. 

Velocity  in  feet 

Time 

per  second. 

in  seconds. 

per  second. 

in  seconds. 

34 

46.7 

1.4561 

77 

70.4 

2.1874 

35 

47-4 

1.4768 

78 

70.9 

2 . 2003 

36 

48.1 

I .4968 

79 

71-3 

2.2160 

37 

48.8 

1.5164 

80 

71.8 

2.2284 

38 

49-5 

1-5354 

81 

72.2 

2.2438 

39 

50.1 

1-5569 

82 

72.6 

2.259O 

40 

50.7 

1-5779 

83 

73-i 

2.2709 

4i 

5i-3 

1 . 5984 

84 

73-5 

2.2857 

42 

52. 

1.6154 

85 

74.0 

2.2973 

43 

52.6 

1.6350 

86 

74-4 

2.3118 

44 

53-2 

1.6541 

87 

74.8 

2.3262 

45 

53-8 

1.6729 

88 

75-3 

2.3373 

46 

54-4 

1.6912 

89 

75-7 

2-3514 

47 

55- 

I . 7O9O 

90 

76.1 

2.3653 

48 

55-6 

1 . 7266 

9i 

76.5 

2.3791 

49 

56.2 

1 ■ 7438 

92 

76.9 

2.3927 

50 

56.7 

1-7637 

93 

77-4 

2.4031 

5i 

57-3 

1.7801 

94 

77-8 

2.4165 

52 

57-8 

1 ■ 7993 

95 

78.2 

2.4297 

53 

58. 4 

1.8151 

96 

78.6 

2.4427 

54 

59- 

1.8305 

97 

79-0 

2.4557 

55 

59-5 

1.8487 

98 

79-4 

2.4685 

56 

60. 

1.8667 

99 

79.8 

2.4812 

57 

60.6 

1.8812 

IOO 

80.3 

2.4907 

58 

6l  . I 

1.8985 

125 

89.7 

2.7871 

59 

61.6 

1 • 91 56 

150 

98.3 

3.0519 

60 

62.1 

1.9324 

175 

106 

3.3019 

6l 

62.7 

1-9458 

200 

1 14 

3.5088 

62 

63.2 

1 . 9620 

225 

120 

3.7500 

63 

63-7 

1.9780 

250 

126 

3.9683 

64 

64.2 

1.9938 

275 

133 

41353 

65 

64.7 

2 . OO93 

300 

139 

4.3165 

66 

65.2 

2.0245 

350 

150 

4.6667 

67 

65.7 

2.0396 

400 

160 

5.0000 

68 

66.2 

2.0544 

450 

170 

5-2941 

69 

66.7 

2 . 0690 

500 

179 

5.5866 

70 

67.1 

2.0864 

550 

188 

5.8511 

71 

67.6 

2 . 1006 

600 

197 

6.0914 

72 

68.1 

2.1145 

700 

212 

6 6038 

73 

68.5 

2. 1313 

800 

227 

7-0485 

74 

69. 

2.1449 

900 

24I 

7.4689 

75 

76 

69-5 

69.9 

2.1583 

2.1745 

IOOO 

254 

7.8740 

CHAPTER  XL 


FLOW  OF  WATER  THROUGH  ORIFICES. 

200.  Motion  of  the  Individual  Particles. — If  an 

aperture  is  made  in  tlie  bottom  or  side  of  a tank,  filled  with 
water,  the  particles  of  water  will  move  from  all  portions  of 
the  body  toward  the  opening,  and  each  particle  flowing  out 
will  arrive  at  the  aperture  with  a velocity,  V,  dependent 
upon  the  pressure  or  head  of  water  upon  it,  and,  as  we  shall 
see  hereafter,  upon  its  initial  position. 

201.  Theoretical  Volume  of  Efflux.— If  we  assume 
the  fluid  veins  to  pass  out  through  the  orifice  parallel  with 
each  other,  and  with  a velocity  due  to  the  head  upon  each, 
and  the  section  of  the  jet  to  be  equal  to  the  area,  S,  of  the 
orifice,  then  the  theoretical  volume,  or  quantity,  Q,  of  dis- 
charge will  equal  S x V=  S V2gH ; A being  the  head  upon 
the  centre  of  the  orifice,  and  g the  acceleration  of  gravity 
per  second  = 32.2  feet.  We  have  then  for  the  theoretical 
volume 

Q = 8 \/WL 

202.  Converging  Path  of  Particles.— The  particles 
are  observed  to  approach  the  orifice,  not  in  parallel  veins, 
but  by  curved  converging  paths,  and  if  the  partition  is 
“ thin the  convergence  is  continued  slightly  beyond  the 
partition,  a distance  dependent  upon  the  velocity  of  the 
particles. 

203.  Classes  of  Orifices. — If  the  top  of  the  orifice  is 
beneath  the  surface  of  the  water,  the  orifice  is  termed  a sub- 
merged orifice,  and  if  the  surface  of  the  water  is  below  the 


RATIO  OF  MINIMUM  SECTION  OF  JET. 


195 


top  of  the  orifice,  the  notch  is  termed  a “ weir We  are 
now  to  consider  submerged  orifices. 

204.  Form  of  Submerged  Orifice-jet. — In  Fig.  20 
is  shown  a submerged  circular  orifice  in  thin  partition. 


Fig.  21. 


In  Fig.  21  are  delineated  more  clearly  the  proportions 
of  the  issuing  jet  at  the  contracted  vein,  or  vend  conlractd , 
as  it  was  termed  by  Newton.  The  form  of  the  contracted 
vein  has  been  the  subject  of  numerous  measurements,  and 
as  the  result  of  late  experiments  writers  now  usually  assign 
to  the  three  dimensions  FK,  fTc , and  LI,  the  ratios  1.00, 
0.7854,  0.498,  as  mean  proportions  of  circular  jets  not  ex- 
ceeding one-lialf  foot  diameter. 

205.  Ratio  of  Minimum  Section  of  Jet. — The  par- 
ticles of  the  jet  that  arrive  at  the  centre  of  the  orifice  have  a 
direction  parallel  with  the  axis  of  the  orifice.  The  particles 
that  arrive  near  the  perimeter  have  converging  directions, 
and  since  they  have  individually  both  weight  and  velocity, 
they  have  also  individual  force  or  momentum  in  their  direc- 
tions. This  force  must  be  deflected  into  a new  direction, 
and  as  it  can  be  most  easily  deflected  through  a curved 


196 


FLOW  OF  WATER  THROUGH  ORIFICES. 


path,  the  curve  is  continued  until  the  particles  have  paral- 
lelism. The  point  where  the  direction  of  the  particles  is 
parallel  is  at  a distance  from  the  inside  of  a small  square- 
edged  orifice,  equal  to  about  one-lialf  the  diameter  of  the 
orifice,  and  the  diameter  of  the  jet  at  that  point  is  equal 
to  about  0.7854  of  the  diameter  of  the  orifice.  The  cross- 
section  of  a circular  jet  at  the  same  point  has  therefore  a 
mean  ratio  to  the  area  of  the  orifice  as  (0.7854)2  to  (1.00)2, 
or  as  0.617  to  1.00. 

206.  Volume  of  Efflux. — If  the  velocity  due  to  the 
head  upon  the  center  of  the  orifice  is  the  mean  velocity  of 
all  tlie  particles  of  the  jet,  then  we  have  for  the  volume  of 
discharge, 

Q = 0.617  S x V,  or  Q = 0.617  SV2gH.  (2) 

The  real  volume,  Q,  of  the  jet,  and  its  ratios  of  velocity 
and  of  contraction,  have  been  the  subjects  of  many  obser- 
vations, and  have  engaged  the  attention  of  the  ablest  ex- 
perimentalists and  hydraulicians,  from  time  to  time,  during 
many  years. 

207.  Coefficient  of  Efflux.  — In  every  jet  flowing 
through  a thin  orifice  there  is  a reduction  of  the  diameter 
of  the  jet  immediately  after  it  passes  the  orifice.  Some 
fractional  value  of  the  area  S,  or  the  velocity  V,  or  the 
the  theoretical  volume  Q.  must  therefore  be  taken — that  is, 
they  must  be  multiplied  by  some  fraction  coefficient  to  com- 
pensate for  the  reduction  of  the  theoretical  volume*  of  the 
jet.  This  fractional  coefficient  is  termed  the  coefficient  of 
discharge.  Place  the  symbol  c to  represent  this  coefficient, 
and  the  formula  for  volume  of  discharge  becomes 

Q — cS  V2gH.  (3) 

208.  Maximum  Velocity  of  tlie  Jet. — The  point 
where  the  mean  velocity  of  the  particles  is  greatest  is  in  the 


PRACTICAL  USE  OF  A COEFFICIENT. 


197 


least  section  of  the  jet,  and  here  only  can  it  approximate  to 
V2 gH.  The  mean  velocity  will  he  less  at  the  entrance  to 
the  orifice,  and  also  after  passing  the  contraction,  than  in 
the  contraction.  When  speaking  of  the  velocity  of  the  par- 
ticles or  of  the  jet  hereafter,  in  connection  with  orifices,  the 
maximum  velocity — that  is,  the  velocity  in  the  contraction 
— is  referred  to,  unless  otherwise  specially  stated. 

209.  Factors  of  the  Coefficient  of  Efflux. — If  the 
edges  of  the  orifice  are  square,  the  circumferential  particles 
of  the  jet  receive  some  reaction  from  them  ; therefore  only 
the  axial  particles  can  have  a velocity  equal  to  V2gH \ and 
the  mean  velocity  is  a small  fraction  less. 

In  such  case  the  general  coefficient  of  discharge  (c)  will 
be  the  product  of  two  factors,  one  representing  the  reduc- 
tion of  velocity,  and  the  other  the  reduction  of  the  sectional 
area  of  the  jet. 

We  shall  have  occasion  to  investigate  these  factors  after 
we  have  determined  the  value  of  the  general  coefficient. 

210.  Practical  Use  of  a Coefficient. — The  usefulness 
of  a coefficient , when  it  is  to  be  applied  to  new  computa- 
tions, depends  upon  its  accord  with  practical  results. 

All  new  and  successful  hydraulic  constructions  of  orig- 
inal design  must  have  their  proportions  based  upon  com- 
putations previously  made.  Those  computations  must  be 
founded  upon  hydrodynamic  formula;  in  which  the  co- 
efficient performs  a most  important  office.  In  fact  the 
skillful  application  of  formulse  to  hydraulic  designs  de- 
pends upon  the  skillful  adaptation  of  the  one  or  more  co- 
efficients therein. 

The  coefficient  product  adopted  must  harmonize  with 
results  before  obtained,  practically  or  experimentally,  and 
the  parallelism  of  all  the  conditions  of  the  old  or  experi- 
mental structure  and  the  new  design  cannot  be  too  closely 


198 


FLOW  OF  WATER  THROUGH  ORIFICES. 


scrutinized  when  an  experimental  result  is  to  control  a new 
design  for  practical  execution. 

211.  Experimental  Coefficients.— A few  experimental 
results  are  here  submitted  as  worthy  of  careful  study. 

From  Miclielotti.  — The  following  table  of  experi- 
ments with  square  and  circular  orifices,  by  Miclielotti,  we 
find  quoted  by  Neville.*  They  refer  to  a very  carefully 
made  set  of  experiments,  with  an  extensive  apparatus 
specially  prepared,  near  Turin,  where  the  apparatus  was 
supplied  with  the  waters  of  the  Doire  by  a canal. 

The  table  is  given  by  Neville  in  French  measures,  but 
they  are  given  here  as  we  have  reduced  them  to  English 
measures. 

TABLE  No.  41. 

Coefficients  from  Michelotti’s  Experiments. 


Description,  and  Size  of  Orifice, 
in  Feet. 


Square  orifice,  3.197"  x 3.197" 
= .071  square  foot  section. . .. 


Square  orifice,  2.13156"  x 2.13156’ 
= .0315  square  foot  section  . . j 

Sq.  orifice,  r.06578"  x 1.06578" 
= .0079  square  foot  section.  . 

Circular  orifice,  3.197"  diameter  { 
= .05577  square  foot  section..  ) 

Circular  orifice,  2.13156"  diam.  j 
= 0.2477  square  foot  section.. 

Circular  orifice,  1.06578"  diam. 
= .0062  square  foot  section. . . 

Circular  orifice,  6.378"  diameter. 


Depth  upon 
the  center  of 
the  orifice 
in  feet. 

Quantity 
discharged  in 
cubic  feet. 

~ - 
1 ime  of 
discharge  in 
seconds. 

Resulting 
coefficients 
of  discharge. 

f 7-05 

561.240 

600 

.619 

7-30 

685.762 

720 

.619 

12.43 

625.652 

510 

.610 

12.59 

741.036 

600 

.6ll 

23-13 

502.931 

300 

.612 

23.14 

604. 362 

360 

.613 

7.06 

399.266 

900 

.660 

12.17 

512.650 

900 

.645 

22.86 

466. 500 

600 

■643 

7.20 

191.940 

1800 

.628 

12.59 

198.300 

1440 

.612 

22.90 

681.500 

3600 

.625 

7-13 

657.130 

900 

.6ll 

12.31 

691.200 

720 

.610 

23.03 

631.090 

4S0 

.612 

7-23 

591.610 

1S00 

.616 

11.71 

713.700 

1680 

.605 

23-44 

696. 700 

1200 

.605 

7-33 

299.449 

3600 

.619 

12.51 

392.370 

3600 

.620 

23-45 

538.158 

3600 

.621 

6.92 

.619 

< 

12.01 

.619 

* Hydraulic  Tables,  by  John  Neville,  C.E.  ; M.R.I.A.,  London,  1853. 


EXPERIMENTAL  COEFFICIENTS. 


199 


From  Abbe  Bossut. — From  experiments  made  by  the 
Abbe  Bossut  we  have  the  following  results,  as  reduced  to 
English  measures : 


TABLE  No.  42. 
Coefficients  from  Bossut’s  Experiments. 


Description,  Position,  and  Size  of  Orifice, 

IN  INCHES. 

Depth  of  the 
centre  of 
the  orifice, 
in  feet. 

Discharge, 
in  cubic 
feet  per 
minute. 

Resulting 

coeificient. 

Lateral  and  circular,  .53289"  diameter 

9-59 

1.096 

.613 

“ “ “ 1.06578"  “ 

9 59 

4-344 

.617 

“ “ “ -532S9"  “ 

4-273 

.723 

.616 

“ “ “ 1.06578"  “ 

4.273 

1-952 

.619 

“ “ “ 1.06578"  “ 

.0529 

•341 

.649 

Horizontal  and  circular,  .53289"  diameter 

12.54 

1-255 

.614 

“ “ “ 1.06578"  “ .... 

12.54 

5.040 

.617 

“ “ “ 2.13156"  “ 

12.54 

20  201 

.618 

Horizontal  and  square,  1.06578"  x 1.06578". . . . 

12.54 

6.417 

.617 

“ “ “ 2.13156"  x 2.13x56" 

12.54 

25.717 

.618 

Horizontal  and  rectangular,  1.06578"  x .26644". 

12.54 

T -593 

.613 

From  Rennie. — We  have  also,  from  experiments  of 
Rennie  with  circular  and  square  orifices,  under  low  heads, 
the  following : 


TABLE  No.  43. 
Coefficients  for  Circular  Orifices. 


Heads  at  the  centre 
of  the  orifice, 
in  feet. 

t inch 
diameter. 

1 inch 
diameter. 

£ inch 
diameter. 

1 inch 
diameter. 

Mean  Values. 

T 

.671 

•634 

.644 

•633 

645 

2 

■653 

.621 

.652 

.619 

.636 

3 

.660 

•636 

.632 

.628 

•639 

4 

.662 

.626 

.614 

.584 

.621 

Means 

.661 

.629 

•635 

.616 

-635 

200 


FLOW  OF  WATER  THROUGH  ORIFICES. 


Coefficients  for  Rectangular  Orifices. 




Heads  at  the 
centre  of  gravity, 
in  feet. 

1 inch  x 1 inch. 

2 inches  wide 
x £ inch  high. 

ii  inches  wide 
x § inch  high. 

Equilateral 
triangle  of 
1 square  inch, 
base  down. 

Same  triangle, 
with  base  up. 

I 

.617 

.617 

.663 



•596 

2 

•635 

■635 

.668 

— 

•577 

3 

.606 

.606 

.606 

— 

•572 

4 

■593 

•593 

•593 

•593 

•593 

Means 

.613 

.613 

.632 

.593 

.585 

From  Castel. — In  1836,  M.  Castel,  the  accomplished 
hydraulic  engineer  of  the  city  of  Toulouse,  made  with  care 
certain  experiments  by  request  of  D’Aubuisson,  to  determine 
the  volume  of  water  discharged  through  apertures  in  thin 
partitions. 

He  placed  a dam  of  thin  copper  plate  in  a sluice  which 
was  2.428  feet  broad,  and  in  the  plate  opened  three  rectan- 
gular apertures,  each  3.94  inches  wide  and  2.36  inches  high. 
The  distance  between  the  orifices  was  3.15  inches.  The 
flow  took  place  under  constant  heads  of  4.213  inches  above 
the  centres  of  gravity  of  the  orifices,  with  contractions  as 


follows : 

t Coefficient  for  the  middle 6198 

One  orifice  open.  1 “ “ right 6192 

l “ “ left 6194 

1 Coefficient  for  the  two  outsides 6205 

Two  orifices  open.  •<  “ “ middle  and  right 6205 

( “ “ “ “ left 6207 

Three  orifices  open,  coefficient  for  all 6230 


Subsequently,  he  experimented  with  two  orifices,  1.97 
inches  wide  and  1.18  inches  high,  with  results  as  follows  : 


Head. 


3-379 

6.693 


No.  of  orifices  open. 


Coefficient 


( I .621 

I 2 .622 


j: 


.619 

.621 


EXPERIMENTAL  COEFFICIENTS. 


201 


When  more  than  one  aperture  was  open  in  these  exper- 
iments of  Castel,  the  volume  of  water  discharged  induced 
considerable  velocity  in  each  of  the  supplying  sluices. 
This  actually  increased  the  effective  head.  Its  effect  is  here 
recorded  in  the  coefficient  instead  of  in  the  head,  conse- 
quently an  increased  coefficient  is  given. 

In  such  cases  the  real  head  is  the  observed  head  in- 
creased by  the  head  due  to  the  velocity  of  approach  = 


H + 


V2 

64.4' 


From  Lespinasse. — From  among  experiments  on  a 
larger  scale,  the  following  by  Lespinasse,  with  a sluice  of 
the  canal  of  Languedoc,  are  of  interest : 


TAB  LE  No.  44. 
Coefficients  Obtained  by  Lespinasse. 


Openings. 

Head  on  the 
Centre. 

Discharge  in 
One  Second. 

Coefficient. 

Breadth. 

Height. 

Area. 

Feet . 

Feet . 

Sq.  feet. 

Feet. 

Cubic  feet. 

4.265 

1.805 

7-745 

14-554 

145.292 

.613 

<< 

1.640 

6.992 

6.63X 

92.635 

.641 

u 

1.640 

6.992 

6.247 

88.221 

.629 

<i 

1.509 

6.466 

12.878 

138.937 

.641 

u 

r-575 

6.723 

I3-536 

128.764 

.647 

u 

1-575 

6.723 

6 394 

83.948 

.616 

it 

1-575 

6.723 

6.217 

79-857 

• 594 

« 

1-575 

6.717 

6.480 

85.219 

.621 

From  Gen.  Ellis. — Gen.  Theo.  G.  Ellis  has  reported 
in  a paper*  presented  to  the  American  Society  of  Civil 
Engineers,  the  results  of  some  experiments  very  carefully 
conducted  by  him  at  the  Holyoke  testing  flume  in  the  sum- 
mer of  1874. 


* Hydraulic  Experiments  with  Large  Apertures. 
1876,  Vol.  V,  p.  19. 


Jour.  Am.  Soc.  Civ.  Eng 


202 


FLOW  OF  WATER  THROUGH  ORIFICES. 


The  coefficients  for  the  minimum,  mean,  and  maximum 
velocities  are  given  to  indicate  generally  the  range,  and  the 
results  obtained  by  Gen.  Ellis. 

The  volume  of  water  discharged  was  determined  by 
weir  measurement,  and  computed  by  Mr.  James  B.  Fran- 
cis’ formula. 

The  edges  of  the  orifices  were  plated  with  iron  about 
one-half  inch  thick,  jointed  square. 


Vertical  Aperture,  2 ft.  x 2 ft. 

Minimum  head,  2.061  feet.  Coefficient,  .60871  1 Centre  of  aperture,  1.90  feet 
Mean  “ 3.037  “ “ -59676  f above  top  of  weir. 

Maximum  “ 3-538  “ “ .60325  ) Temp,  of  water,  73°  Fah. 

Vertical  Aperture,  2 ft.  horizontal  x 1 ft.  vertical. 

Minimum  head,  1.7962  feet.  Coefficient,  .59748  I Centre  of  aperture,  2.40  feet 
Mean  “ 5.7000  “ “ -59672  V above  top  of  weir. 

Maximum  “ 11.3150  “ “ .60572  ) Temp,  of  water,  76°  Fah. 

Vertical  Aperture,  2 feet  horizontal  x .5  feet  vertical. 

Minimum  head,  1.4220  feet.  Coefficient,  .61165  I Centre  of  aperture,  2.15  feet 
Mean  “ 8.5395  “ “ .60686  y above  top  of  weir. 

Maximum  “ 16.9657  “ “ .60003  ) Temp,  of  water,  76"  Fah. 


Vertical  Aperture,  i ft.  x i ft. 

Minimum  head,  1.4796  feet.  Coefficient,  .58230 
Mean  “ 9.8038  “ “ .59612 

Maximum  “ 17.5647  “ “ .59687 


Horizontal  Aperture,  i ft.  x i ft.  and  Slightly  Submerged 

Issue. 


Minimum  head,  2.3234  feet.  Coefficient,  .59871 
Mean  “ 8.0926  “ “ .60601 

Maximum  “ 18.4746  “ “ .60517 


Top  surface  of  orifice  .441 
feet  above  crest  of  weir. 


Horizontal  Aperture  (in  plank)  with  Curved  Entrance  and 
Slightly  Submerged  Issue. 


Minimum  head,  3.0416  feet. 
Mean  “ 10.5398  “ 

Maximum  “ 18.2180  “ 


Coefficient,  .95118 
“ .94246 

“ 94364 


Issue  about  level  with  crest 
of  weir. 


COEFFICIENTS  DIAGRAMMED. 


203 


The  range,  and  results  generally,  of  Gen.  Ellis’  experi- 
ments with  circular  vertical  orifices,  are  indicated  by  the 
following  extracts  from  his  extended  tables : 


TABLE  No.  4 5. 

Coefficients  for  Circular  Orifices,  obtained  by  Gen.  Ellis. 


Diameters. 

Head. 

Coefficients. 

2 feet. 

1.7677  feet. 

.58829 

u u 

5.8269  “ 

.60915 

u u 

9.6381  “ 

•6153° 

I foot. 

1. 1 470  feet. 

•57373 

« u 

10.8819  “ 

•5943i 

u a 

17.7400  “ 

•59994 

•5  foot. 

2.1516  feet. 

.60025 

u u 

9.0600  “ 

.60191 

(6  (6 

17.2650  “ 

.59626 

212.  Coefficients  Diagrammed. — The  coefficients,  as 
developed  by  the  several  experimenters,  seem  at  first  glance 
to  be  very  fitful,  and  without  doubt  the  apparatus  used 
varied  in  character  as  much  as  the  results  obtained 

To  arrange  all  the  series  of  coefficients  that  appeared  to 
have  been  obtained  by  a reliable  method,  in  a systematic 
manner,  we  have  plotted  all  to  a scale,  taking  the  heads 
for  abscisses  and  the  coefficients  for  ordinates.  The  curves 
thus  developed  were  brought  into  their  proper  relations, 
side  by  side,  or  interlacing  each  other. 

Then  we  were  able  to  plot  in  the  midst  of  those  curves 
the  general  curves  due  to  each  class  of  orifice  under  the 
several  heads,  and  those  apparently  due  to  the  law  govern- 
ing the  flow  of  water  through  submerged  orifices. 

From  these  curves  we  have  prepared  tables  of  coefficients 
for  various  rectangular  orifices,  with  greatest  dimension, 


204 


FLOW  OF  WATER  THROUGH  ORIFICES. 


both  horizontal  and  vertical,  with  ratios  of  sides  varying 
from  0.125  to  1,  to  4 to  1,  and  for  heads  varying  from 
0.2  feet  to  50  feet. 

The  curves  increase  from  those  for  very  low  heads  rap- 
idly as  the  heads  increase,  until  their  maxima  are  reached, 
then  decrease  gradually  until  their  minima  are  reached, 
and  then  again  increase  very  gradually,  the  head  in- 
creasing all  the  time.  This  increase,  and  decrease,  and 
increase  again  of  the  coefficients,  arranges  them,  when  thus 
plotted,  into  two  curves  of  opposite  flexure,  and  with  ah 
the  curves  tending  to  jiass  through  one  intermediate  point. 

213.  Effect  of  Varying’  the  Head,  or  the  Propor- 
tions of  the  Orifice.-— The  effect  of  increasing  or  decreas- 
ing the  head  upon  a given  orifice  is  clearly  shown  by  the 
several  columns  of  coefficients  in  Tables  46  and  47. 

The  effect  of  increasing  or  decreasing  the  ratio  of  the 
base  to  the  altitude  of  an  orifice  will  be  manifest  by  tracing 
the  lines  of  coefficients  horizontally  through  the  two  tables, 
for  any  given  head. 

These  effects  should  be  duly  considered  when  a coef- 
ficient is  to  be  selected  from  the  table  for  a special  appli- 
cation. 

The  coefficients  apply  strictly  to  orifices  with  sharp, 
square  edges,  and  with  full  contraction  upon  all  sides.  The 
heads  refer  to  the  full  head  of  the  water  surface,  and  not  to 
the  depressed  surface  over  or  just  in  front  of  an  orifice  when 
the  head  is  small. 

A very  slight  rounding  of  the  edge  would  increase  the 
coefficient  materially,  as  would  the  suppression  of  the  con- 
traction upon  a portion  of  its  border  by  interference  with 
the  curve  of  approach  of  the  particles. 


COEFFICIENTS  DIAGRAMMED, 


205 


TABLE  No.  46. 

Coefficients  for  Rectangular  Orifices. 

In  thin  vertical  partition,  with  greatest  dimension  vertical. 


Breadth  and  Height  of  Orifice. 


Head  upon 
centre  of  orifice. 

4 feet  high, 
1 foot  wide. 

2 feet  high, 
1 foot  wide. 

feet  high, 
1 foot  wide. 

i foot  high, 
1 foot  wide. 

Feet . 

.6 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

•7 

.... 

.8 

.... 

.... 

•9 

.... 

.6051 

i 

.6076 

.6050 

1-25 

.6072 

.6046 

i-5° 

.6093 

.6068 

.6043 

i 75 

.6090 

.6065 

.6041 

2 

.6086 

.6062 

.6039 

2. 25 

.6083 

.6060 

.6037 

2-5 

.61c  0 

.6080 

.6057 

•6o35 

2-75 

.6095 

.6077 

•6o55 

.6034 

3 

.6091 

.6073 

.6052 

.6032 

3-5 

.6083 

.6067 

.6048 

.6028 

4 

.6077 

.6062 

.6044 

.6025 

4-5 

.607  t 

.6056 

.6040 

.6021 

5 

.6065 

.6051 

•6035 

.6017 

6 

.6054 

.6042 

.6028 

.6014 

7 

.6046 

.6034 

.6022 

.601 1 

8 

.6037 

.6027 

.6017 

.6010 

9 

.6032 

.6020 

.6013 

.6c  10 

10 

.6030 

•6015 

.6010 

.6010 

15 

.6030 

.6018 

.6010 

.601 1 

20 

•6033 

.6024 

.6012 

.6012 

25 

.6048 

.6028 

.6014 

.6012 

3° 

.6054 

.6034 

.6017 

.6013 

35 

.6060 

.6039 

.6021 

.6014 

40 

.6066 

.6045 

.6025 

.6015 

45 

.6054 

.6052 

.6029 

.6016 

5° 

,6086 

.6060 

.6034 

.6018 

206 


FLOW  OF  WATER  THROUGH  ORIFICES. 


TABLE  No.  47. 

Coefficients  for  Rectangular  Orifices. 

In  thin  vertical  partition,  with  greatest  dimension  horizontal. 


Breadth  and  Height  of  Orifice. 


Head  upon 
centre  of  orifice. 

0.75  feet  high, 
1 foot  wide. 

0.50  feet  high, 
1 foot  wide. 

0.25  feet  high, 
1 foot  wide. 

0.125  feet  high, 
1 foot  wide. 

Feet . 

Coefficient. 

Coefficient. 

Coejfficient. 

Coefficient. 

0.2 

.... 

.... 

•3 

.... 

.... 

.6260 

• 4 

.... 

.6194 

.6248 

•5 

.6146 

•6184 

.6243 

.6 

.6136 

.6 r 76 

•6233 

•7 

.6095 

.6127 

.61  70 

.62  28 

.8 

.6090 

.6121 

•6i6S 

X223 

•9 

.6086 

.6116 

.6160 

.62  20 

i 

.6082 

.6112 

•6i57 

.62 17 

1.25 

.6077 

.6106 

.615° 

.6208 

i-5° 

.6072 

.6102 

.6145 

.6200 

i-75 

.6067 

.6097 

.6140 

•6x94 

2 

.6063 

.6094 

•6i3S 

.61  <-  7 

2.25 

.6059 

.6090 

.6131 

.61 80 

2.50 

.6056 

.6086 

.61 26 

.6174 

2-75 

•6o5  3 

.6081 

.6122 

.6168 

3 

.6050 

.6078 

.61 18 

.61 62 

3-5° 

.6043 

.6071 

.61 10 

.610 

4 

.6037 

.6065 

.6103 

•6x39 

4-5° 

.6032 

.6059 

.6096 

.61 29 

5 

.6028 

••6053 

.6090 

.61 20 

6 

.6022 

.6043 

.6077 

.6103 

7 

.6018 

.6036 

.6067 

.6089 

8 

.6013 

.6030 

.6058 

.bo  7 7 

9 

.601 1 

.6024 

.6050 

.6066 

10 

.6010 

.6020 

.6043 

.6060 

15 

.6012 

.6013 

•6o33 

.6066 

20 

.6014 

.6018 

.6036 

.6074 

25 

.6016 

.6022 

.6040 

.6083 

3° 

.6018 

.6027 

6044 

.6092 

35 

.6022 

.6032 

.6049 

.6103 

40 

.6026 

.6037 

•6o55 

.61 14 

45 

.6030 

.6043 

.6062 

.6125 

5° 

•6o35 

.6050 

.6070 

.6140 

PECULIARITIES  OF  EFFLUX. 


207 


2514.  Peculiarities  of  Efflux  from  an  Orifice.— 

In  Fig.  22,  containing  a horizontal  orifice,  the  horizontal 
line  cutting  a has  an  altitude  above  the  orifice  equal  to  3.5 
diameters,  and  the  horizontal  line  cutting  e equal  to  10 
diameters  of  the  orifice.  As  the  altitude  of  the  water  sur- 


Fig.  22. 


face  above  a square  orifice  increases  from  very  low  heads  to 
the  level  a , the  particles  continually  find  new  advantage  or 
less  hindrance  in  their  tendency  to  flow  out  of  the  orifice, 
possibly  by  decrease  of  the  vortex  effect  accompanying 
very  low  heads  over  orifices  nearly  square  ; afterwards  the 
resistance  increases  up  to  the  altitude  e,  possibly  by  more 
effective  reaction  from  the  inner  edges  of  the  orifice,  is, 
until  gravity  is  enabled  to  gather  the  jet  well  into  a body 
and  establish  firmly  its  path.  For  altitudes  greater  than 
ten  diameters  the  coefficients  for  square  orifices  remain 
nearly  constant. 


208 


FLOW  OF  WATER  THROUGH  ORIFICES. 


Similar  effects  are  observed  when  the  orifices  are  rectan- 
gles, other  than  squares,  though  their  first  change  occurs  at 
different  depths. 

These  phenomena  are  not  fully  accounted  for  by  ex- 
periment. 

215.  Mean  Velocity  of  the  Issuing  Particles.— 

We  have  heretofore  assumed  in  our  theoretic  equations, 
that  all  the  particles  of  water  bcdef  g,  Fig.  22,  will  arrive 
at  the  point  of  greatest  contraction  of  the  issuing  jet,  with  a 
velocity  equal  to  that  which  a solid  body  would  have  ac- 
quired by  falling  freely  from  e to  o,  which,  according  to  the 
the  theorem  of  Toricelli,  and  its  demonstrations  frequently 
repeated  by  other  eminent  philosophers,  would  be  equal  to 
V2 yll.  H being  equal  to  the  height  e o. 

The  experiments  of  Mariotte,  Bossut,  Michelotti,  Ponce- 
let,  Pousseile,  and  others,  covering  a large  range  of  areas  of 
orifice,  and  of  head,  show  that  this  is  very  nearly  correct ; 
and  the  velocity  of  issue  of  the  axial  particles  has  in  some 
of  the  experiments  appeared  to  slightly  exceed  the  value  of 
V2 gH.  An  average  of  experiments  gives  the  mean  velocity 
of  the  particles  as  a whole  through  the  minimum  section  as 
.974  V2yH. 

Them  dynamic  effect,  if  applied  to  work  should  have 
.974  V2 (jH  instead  of  V2yH  as  the  factor  of  velocity. 

216.  Coefficients  of  Velocity  and  Contraction. — 
We  have  then,  .974  for  mean  coefficient  of  velocity , indi- 
cating a loss  of  .026  per  cent,  of  theoretic  volume  or  dis- 
charge by  reduction  of  velocity  ; .637  for  mean  coefficient 
of  contraction , indicating  a loss  of  36.3  percent,  of  theoretic 
volume  by  contraction ; and  .62  nearly  for  mean  coefficient  of 
discharge , including  all  losses,  a total  of  about  38  per  cent. 

The  coefficient  of  velocity  we  will  designate  by  cv , and 
the  coefficient  of  contraction  by  cc. 


VOLUME  OF  EFFLUX  FROM  A SUBMERGED  ORIFICE.  209 


Then  cv  x cc  — c = coefficient  of  discharge  or  volume. 

217.  Velocity  of  Particles  Dependent  upon  tlieir 
Angular  Position. — Bayer  assumed  the  hypothesis  that, 
the  velocities  of  the  particles  approaching  the  orifice  from 
all  sides  are  inversely  as  the  squares  of  their  distances  from 
its  centre,  but  this  should  undoubtedly  be  applied  only  to 
particles  in  some  given  angular  position. 

Gravity  will  not  act  with  equal  force  in  the  direction  of 
the  orifice,  upon  each  of  the  particles  e,/',  g,  and  Ti , Fig.  22, 
though  they  are  all  equally  distant  from  o,  but  more  nearly 
in  the  ratios  of  the  cosines  of  the  angles  eoe , eof,  eog,  etc., 
and  it  is  not  probable  that  the  particle  h will  acquire  a 
velocity  at  its  maximum  through  the  contraction,  quite 
equal  to  that  which  e will  acquire.  If  the  velocity  of  e is 
assumed  equal  to  unity,  and  the  mean  velocity  of  all  the 
particles  equal  to  .974,  then,  according  to  the  hypothesis  of 
the  angular  distance,  the  mean  velocity  will  be  that  due  to 
particles  having  their  cosines  equal  to  .974,  or  an  angular 
distance  of  13°,  as  at  b and  f. 

218.  Equation  of  Volume  of  Efflux  from  a Sub- 
merged Orifice. — Neville  suggests  a formula*  for  the 
discharge  of  water  from  rectangular  orifices,  more  theoreti- 
cally exact  than  the  above  simple  formulas,  as  follows  : 


D 


V%gh 


bb  + \d)- 


dh  i 


(4) 


when  D = volume  of  discharge, 

A — area  of  orifice, 

h — head  upon  the  centre  of  the  orifice, 
d — depth  of  the  orifice,  or  distance  between  its 
bottom  and  top, 

C = coefficient  of  discharge. 


* Third  Edition  of  Hydraulic  Tables,  page  48.  London,  1875.  Also  vide 
equation  3,  page  283,  ante. 


210 


FLOW  OF  WATER  THROUGH  ORIFICES. 


This  formula  can  be  advantageously  applied  when  the 
orifice  is  large  and  but  slightly  submerged,  as  is  frequently 
the  case  with  sluice  gates  controlling  the  flow  of  water  from 
storage  reservoir's  or  canals  into  flumes  leading  to  water- 
wheels, or  with  head-gates  of  races  or  canals. 

Good  judgment  must,  however,  be  exercised  in  each  case 
in  the  selection  of  the  coefficient  of  velocity  ( cv ) and  the  co- 
efficient of  contraction  (cc),  the  factors  of  c,  especially  the 
coefficient  of  contraction  (§  216),  which  is  usually  much  the 
most  influential  of  the  two.  (Vide  §370,  p.  360.) 

219.  Effect  of  Outline  of  Symmetrical  Orifices 
upon  Efflux. — According  to  the  various  series  of  experi- 
ments, the  coefficient  for  a circular  orifice  under  any  given 
head  is  substantially  the  same  as  for  a square  orifice  under 
the  same  head,  and  it  is  probable  that  the  coefficients  for 
elliptical  orifices  is  substantially  the  same  as  that  for  their 
circumscribing  rectangles. 

220.  Variable  Value  of  Coefficients. — The  coeffi- 
cients obtained  by  careful  experiment  and  recorded  above, 
as  also  tables  of  coefficients,  indicate  unmistakably  that  the 
value  of  c in  the  equation 

Q = cS  V2gH 

is  a variable  quantity,  and  that  a general  mean  coefficient 
cannot  be  used  universally  when  close  approximate  results 
are  desired,  but  that,  for  a particular  case,  reference  should 
always  be  made  to  a coefficient  obtained  under  conditions 
similar  to  that  of  the  case  in  question. 

221.  Assumed  Mean  Volume  of  Efflux. — In  ordi- 
nary approximate  calculations,  and  in  general  discussions 
of  formulas  for  square  and  circular  orifices,  whether  the  jet 
issues  horizontally  or  vertically,  it  is  customary  to  assume 
0.62  as  the  ratio  of  the  actual  to  the  theoretical  volume  of 


CIRCULAR,  AM)  OTHER  FORMS  OF  JETS. 


231 


discharge.  This  makes  the  equation  for  ordinary  calcu- 
lations : 

Q = .Q2SV2gH,  or  Q = .62 SV.  (5) 

The  expression  for  effect  of  acceleration  of  gravity  (2 g) 
being  a constant  quantity,  may  be  combined  with  the  co- 
efficient, when  (.62  V2g  — 4.9725)  we  have  the  equation 


Q 4 9725$  I7//,  or  approximately,  Q = 5.S  V H.  (6) 


Q being  the  discharge  in  cubic  feet  in  one  second,  it  will  be 
multiplied  by  60  to  determine  the  discharge  in  one  minute, 
and  by  3600  to  determine  the  discharge  in  one  hour. 

222.  Circular,  and  other  Forms  of  Jets. — A cir- 
cular aperture,  with  full  contraction,  gives  a jet  always 
circular  in  section,  until  it  is  broken  up  into  globules  by 
the  effects  of  the  varying  velocities  of  its  molecules  and  the 
resistance  of  the  air.  Through  the  vend  contracta  its  form 
is  that  of  a truncated  conoid. 

Polygonal  and  rectangular  orifices  give  jets  that  continu- 
ally change  their  sectional  forms  as  they  advance. 

Fig.  22a,  from  D’Aubuisson’s  Treatise  on  Hydraulics, 
illustrates  the  transformations  of 
forms  of  a jet  from  a square  orifice, 

ACEG.  The  jet  is  square  at  the 
entrance  to  the  aperture,  assumes 
the  form  'bcdefgha  a short  distance 
in  front  of  it,  and  the  form  ac'e’g'  a 
short  distance  further  on,  and  con- 
tinues to  assume  new  forms  until 
its  solidity  is  destroyed.  Symmetrical  orifices,  without  re- 
entrant angles,  give  symmetrical  jets  that  assume  symmet- 
rical, varying  sections. 

Star-shaped  and  irregular  orifices,  upon  close  observa* 


Fig.  22a. 


212 


PLOW  OF  WATER  THROUGH  ORIFICES. 


tion,  are  found  to  give  very  complex  forms  of  jets.  Theii 
coefficients  of  efflux  have  not  been  fully  developed  by  ex- 
periment. 

223.  Cylindrical  and  Divergent  Orifices.— In  Fig. 
23  and  Fig.  24  showing  cylindrical  and  divergent  orifices, 
if  the  diameters,  is,  of  the  orifices,  are  greater  than  the 


Fig.  23.  Fig.  24.  Fig.  25.  Fig.  26. 


thickness  of  the  partitions,  the  coefficients  of  discharge  will 
remain  the  same  as  in  thin  plate.  In  such  cases  the  jets 
will  pass  through  the  orifices  without  touching  them,  ex- 
cept at  the  edges,  is.  Such  orifices  are  also  termed  thin. 

224.  Converging'  Orifices. — In  Fig.  25  and  Fig.  26. 
showing  converging  orifices  in  thin  partitions,  if  the  diam- 
eters, is,  are  taken,  the  coefficients  will  be  reduced  to  .58,  or 
a little  less;  but  if  the  diameters,  ot,  are  taken,  the  co- 
efficients will  be  increased  nearly  to  .90,  and  will  be  greater, 
for  any  given  velocity,  in  proportion  as  the  forms  of  the 
orifices  approach  to  the  form  of  the  perfect  vend  contracted 
for  that  velocity. 

When  the  converging  sides  of  the  orifice  in  Fig.  25,  pro- 
longed, include  an  angle  of  16°,  the  coefficient  should  be 
about  .93,  and  when  in  Fig.  26  the  sides  of  the  orifice  are  in 
the  form  of  the  vend  contracted , the  coefficient  should  be 
about  .95. 


PUMPING  STATION, 


CHAPTER  XII. 


FLOW  OF  WATER  THROUGH  SHORT  TUBES. 

225.  All  Ajutage. — If  a cylindrical  orifice  is  in  a parti- 
tion whose  'thickness  is  equal  to  two-and-one-half  or  three 
times  the  diameter  of  the  orifice  ; or  if  the  orifice  is  a tube 
of  length  equal  to  from  two  and  one-half  to  three  interior 
diameters,  then  the  orifice  is  termed  a short  tribe , or  ajutage. 
The  sides  of  short  tubes  may  be  parallel , divergent , or  con- 
vergent. 

226.  Increase  of  Coefficient. — There  is  an  influence 
affecting  the  flow  of  water  through  short  cylindrical  tubes. 
Fig.  28,  sufficient  to  increase  the  coefficient  materially,  that 
does  not  appear  when  the  flow  is  through  thin  partition. 
The  contraction  of  the  jet  still  occurs  as  in  the  flow  through 
thin  partition,  but  after  the  direction  of  the  particles  has 
become  parallel  in  the  vend  contractd , a force  acting  from 
the  axis  of  the  jet  outward,  together  with  the  reaction  from 
the  exterior  air,  begins  to  dilate  the  section  of  the  jet  and 
to  fill  the  tube  again.  The  tube  is  in  consequence  again 
filled  at  a distance,  depending  upon  the  ratio  of  the  velocity 
to  the  diameter,  of  about  two  and  one-half  diameters  from 
the  inner  edge  of  the  orifice.  The  axial  particles  of  the  jet, 
not  receiving  so  great  a proportion  of  the  reaction  from  the 
edges  of  the  orifice  as  the  exterior  particles,  obtain  a greater 
velocity.  A portion  of  their  force  is  transmitted  to  their 
surrounding  films  through  divergent  lines,  and  the  velocity 
of  the  exterior  particles  within  the  tube  is  augmented,  and 
the  section  of  the  jet  is  also  augmented,  until  its  circumfer- 


214 


FLOW  OF  WATER  THROUGH  SHORT  TUBES. 


ence  touches  the  tube.  At  the  same  time,  the  transmission 
of  force  from  the  axis  toward  the  circumference  tends  to 
equalize  the  velocity  of  the  particles  throughout  the  section, 
and  to  materially  reduce  their  mean  velocity,  and  conse- 
quently the  coefficient  of  velocity,  cv. 

227.  Ajutage  Vacuum  and  its  Effect.  — Immedi- 
ately upon  the  issue  of  the  jet,  beyond  the  contraction,  the 
velocity  of  the  particles  tends  to  impel  forward  the  impris- 
oned air,  and  as  soon  as  the  tube  fills  to  cause  a vacuum* 
about  the  contraction.  The  full  force  of  gravity  is  here  act- 
ing upon  the  jet  in  the  form  of  velocity  ; the  jet  is  therefore 
without  pressure  in  a transverse  direction. 

As  soon  as  the  exterior  of  the  jet  is  relieved  from  the 
pressure  of  the  atmosphere  about  the  contraction,  its  par- 
ticles are  deflected  to  parallelism  with  less  force  and  in  a 
shorter  distance  from  the  entrance  to  the  aperture,  and  the 
contraction  is  consequently  lessened ; also  the  pressure  of 
the  atmosphere  upon  the  reservoir  surface  tends  to  augment 
the  velocity  of  entry  of  the  particles  into  the  aperture 
toward  the  vacuum,  and  atmospheric  pressure  equally 
resists  the  issue  of  the  jet,  the  combined  effect  resulting  in 
the  expansion  of  the  jet. 

228.  Increased  Volume  of  Efflux.  — If  the  cylin- 
drical tube  terminates  at  the  point  where  the  moving  par- 
ticles reach  the  circumference  and  fill  the  tube,  and 
before  the  reaction  from  the  roughness  of  the  interior  of 
the  tube  has  begun  sensibly  to  counteract  the  accelerating 
force  of  gravity,  the  capacity  of  discharge  is  then  found  to 
be  increased  about  twenty-five  per  cent.,  and  the  mean  co- 
efficient becomes  .815  approximately,  or  if  the  tube  projects 


* If  the  inside  of  a smooth  divergent  tube  is  greased,  so  as  to  repel  the  par 
tides  of  water  and  prevent  contact,  the  vacuum  cannot  take  place. 


DIVERGENT  TUBE. 


215 


into  the  reservoir,  .72,  instead  of  .62,  as  in  the  orifice  in  thin 
plate.  We  have  now  for  the  volume  of  water  discharged, 
in  cubic  feet  per  second, 


Q = . 815  SVZg  H,  or  Q = .815  8 V,  or  Q = 6. 54  S VH.  (1) 

If  the  section  of  the  tube  is  expressed  in  terms  of  the 
diameter,  in  feet  or  fractional  parts  of  feet,  then  since  8 =■ 
.7854 d 2,  the  equation  will  become 

Q = 6.54  (.7854c?2)  VH  = 5.137 d*  VH.  (2) 

229.  Imperfect  Vacuum. — If  the  tube  is  of  less 
length  than  above  indicated,  so  that  the  vacuum  is  not 
perfect,  the  conditions  of  flow  and  the  coefficient  will  be 
similar  to  that  through  thin  plate ; and  if  the  tube  is  length- 
ened, the  flow  will  be  reduced  by  reaction  from  the  interior 
of  the  tube,  in  which  case  the  tube  will  be  termed  a pipe. 


Fig.  28. 


Fig.  29. 


Fig.  80. 


230.  Divergent  Tube. — When  a short  divergent  tribe , 
Fig.  29,  is  attached  by  its  smaller  base  to  the  inside  of  a 
plane  partition,  the  phenomena  of  discharge  will  be  similar 
to  that  through  an  orifice  in  thin  plate,  unless  a vacuum 
shall  be  established  about  its  contraction,  as  in  the  case  of 


216 


FLOW  OF  WATER  THROUGH  SHORT  TUBES. 


short  cylindrical  tubes.  This  can  only  occur  when  the 
divergence  is  slight,  or  the  velocity  great. 

For  ordinary  cases,  the  mean  coefficient  of  discharge 
through  square-edged  divergent  tubes  maybe  taken  as  .62, 
but  it  is  subject  to  considerable  variation  in  tubes  of  small 
divergence,  as  the  divergences,  the  ratio  of  length  to  diam- 
eter, and  the  velocity  of  flow  or  head  varies. 

When  a vacuum  takes  place  in  a divergent  tube,  the 
discharge  exceeds  that  from  a cylindrical  tube  with  diam- 
eter equal  to  the  smaller  diameter  of  the  divergent  tube, 
and  the  coefficient  of  volume  may  then  even  become  greater 
than  unity. 

231,  Convergent  Tube. — When  a short , convergent 
tube , Fig.  30,  is  attached  by  its  larger  base  to  the  inside  of 
a plane  partition,  and  its  coefficient  of  flow  with  a perfect 
vacuum  is  determined  for  its  diameter  of  entrance,  as  above 
in  the  cases  of  thin  plate,  cylindrical  and  divergent  tubes, 
then  the  coefficient  of  volume  will  be  found  to  decrease  as 
the  angle  of  convergence  increases. 

Contraction  will  take  place  as  in  thin  plate,  until  the 
angle  of  convergence,  that  is,  the  included  angle  between 
the  sides  produced,  exceeds  13°,  and  a vacuum  will  also  be 
produced  ; but  the  exterior  of  the  jet  will  reach  the  inner 
circumference  and  fill  the  tube  at  a shorter  distance  from 
the  point  of  least  contraction,  as  the  angle  increases,  and 
the  augmenting  effect  of  the  vacuum  will  be  reduced. 

232.  Additional  Contraction. — There  is  always  an 
additional  contraction  just  after  the  exit  of  the  jet  from 
convergent  tubes. 

The  coefficient  of  discharge  will  remain  in  excess  of  the 
coefficient  for  thin  plate  until  the  second  contraction  equals 
that  in  thin  plate,  after  which  the  coefficient  will  be  less 
than  for  thin  plate. 


COEFFICIENT  OF  SMALLER  DIAMETER. 


217 


233.  Coefficients  of  Convergent  Tubes. — In  the 
following  table  are  given  the  coefficients  of  discharge  for 
the  larger  and  the  smaller  diameters,  also  of  the  velocity , 
for  several  angles  of  convergence.  The  table  is  based  upon 
careful  experiments  by  Castel.  The  length  of  the  tube  was 
2.6  diameters,  and  the  smaller  diameter  and  length  of  tube 
remained  constant. 

TABLE  No.  48. 

Castel’s  Experiments  with  Convergent  Tubes. 


Smallest  diameter  — .05085  feet. 


Angle  of  convergence. 

Larger  diameter. 

Smaller  diameter. 

Velocity. 

Coefficient. 

Coefficient. 

Coefficient . 

o° 

o' 

0.829 

0.829 

0.830 

1° 

36' 

.809 

.866 

.866 

3° 

10 

.786 

•895 

.894 

4° 

10' 

.771 

.912 

.910 

0 

26' 

•747 

.924 

.920 

7° 

52 

.691 

.929 

•93i 

8° 

5s; 

.671 

•934 

.942 

IO° 

20 

.647 

•938 

-95° 

12° 

4 

24' 

,6n 

.942 

•955 

13° 

•597 

.946 

.962 

14° 

28' 

•577 

.941 

.966 

160 

36' 

•545 

•938 

.971 

19° 

28' 

.501 

.924 

.970 

21° 

0' 

.480 

.918 

.971 

23° 

o' 

•457 

•9X3 

•974 

29° 

58' 

•39° 

.896 

•975 

40° 

20' 

•319 

.869 

.980 

48° 

50' 

.276 

•847 

•984 

The  coefficients  for  the  larger  diameter  have  been  com- 
puted from  the  remaining  data  of  the  table  for  insertion 
here. 

234.  Increase  and  Decrease  of  Coefficient  of 
Smaller  Diameter. — When  the  coefficient  of  volume  is 


218 


FLOW  OF  WATER  THROUGH  SHORT  TUBES. 


determined  for  tire  smaller  diameter,  or  issue  of  a short, 
convergent  tube,  the  coefficient  is  found  to  increase  from 
that  for  cylindrical  tubes  at  angle  0°  to  an  angle  of  about 
13°  30',  when,  under  the  conditions  upon  which  Casters 
table  was  based,  it  has  increased  from  .83  to  .95.  After- 
wards, the  coefficient  gradually  reduces,  until  at  180°  it 
becomes  .62,  as  in  thin  plate. 

235.  Coefficient  of  Final  Velocity. — The  coefficient 
of  final  velocity  of  issue  gradually  increases  as  the  angle  of 
convergence  increases,  until  it  rises  from  .83  * at  angle  0C  to 
nearly  unity  at  angle  180° ; but  that,  for  angles  less  than 


comes  greater  than  when  the  orifice  is  in  plane  partition, 
and  the  contraction  becomes  still  more  marked.  Borda, 
when  experimenting  with  such  a tube,  in  which  the  vacuum 
was  not  perfected,  found  the  coefficient  to  be  .515.  This 
coefficient  may  be  considered  as  an  extreme  minimum. 

237.  Compound  Tube.— When  two  or  more  of  the 
short  tubes  above  described  are  joined  together  endwise 
into  one  tube,  as  in  Fig.  32,  the  new  tube  thus  formed  is 
termed  a compound  tube. 

* Its  mean  velocity,  in  a cylindrical  tube,  after  the  jet  has  expanded  beyond 
the  contraction. 


Fig.  31. 


13°,  is  not  the  true  coefficient  of 
velocity,  since  it  refers  to  the  ve- 
locity of  issue  at  the  end  of  the 
tube,  instead  of  in  the  contrac- 
tion. 


236.  Inward  Projecting 
Ajutage. — When  an  orifice,  or 
the  entrance  of  a short  tube,  is 
projected  into  the  interior  of  a 
reservoir,  as  in  Fig.  31,  the  angle 
of  approach  of  the  particles  be- 


COEFFICIENTS  OF  COMPOUND  TUBES. 


219 


Fig.  32. 


Venturi  experimented  with  various  forms  and  propor- 
tions of  compound  tubes,  and  observed  remarkable  results 
produced  by  certain  of  them,  which  apparently  augmented 
the  force  of  gravity. 

With  a tube  similar  to  Fig.  32,  but  with  less  perfect 
contraction,  having  the  included  angle  of  the  divergent  tube 
equal  to  5°  6',  the  smallest  diameter  equal  to  0.1109  feet, 
and  the  length  equal  to  nine  diameters,  the  coefficient,  com- 
puted for  the  smallest  diameter,  when  flowing  under  a con- 
stant head  of  2.89  feet,  was  1.46,  or  about  2.4  times  that  of 
an  equal  orifice  in  thin  plate. 

238.  Coefficients  of  Compound  Tubes. — Other  forms 
of  compound  tubes,  with  conical  diverging  ajutages  of  dif- 
ferent lengths  and  angles,  gave  results  as  follows : 

TABLE  No.  49. 

Experiments  with  Divergent  Ajutages. 


Ajutage. 

Coefficient. 

Ajutage. 

Coefficient. 

Angle. 

Length. 

Angle. 

Length. 

3°  3°' 

Feet. 

0.364 

0-93 

5°  44' 

Feet. 

.193 

.82 

4°  38' 

1.095 

1. 21 

10°  l6' 

.865 

•91 

4°  38' 

1.508 

1. 21 

10°  16' 

.147 

.91 

4°  38' 

1.508 

1-34 

140  14' 

.147 

.6l 

5 3 44' 

0.577 

1.02 

220  FLOW  OF  WATER  THROUGH  SHORT  TUBES. 

7 

239.  Experiments  with  Cylindrical  and  Com- 
pound Tubes. — The  following  table  gives  interesting  re- 
sults of  experiments  by  Eytelwein  with  both  cylindrical 
and  compound  tubes. 

He  first  experimented  with  a series  of  cylindrical  tubes 
of  different  lengths,  but  of  equal  diameters  ; he  then  placed 
between  the  cylindrical  tubes  and  the  reservoir  a conical 
converging  tube  of  the  form  of  the  vend  contracta,  and 
repeated  the  experiments ; and  afterwards  added  also  to 
the  discharge  end  a conical  diverging  tube  with  5°  6'  angle, 
Fig.  33. 

Fig.  33. 


TABLE  No.  SO. 

Experiments  with  Compound  Tubes. 


Length  of  tube  P in 
diameters. 

Length  of  tube  P 
in  feet. 

Coefficient  for 
tube  P. 

Coefficient  for 
tube  CP. 

Coefficient  for 
tube  CPD. 

0.038 

O.OO33 

O.62 

... 

.... 

1. 000 

•0853 

.62 

.967 

.... 

3.000 

•2559 

.82 

•943 

1. 107 

12.077 

I.0302 

•77 

.870 

.978 

24.156 

2.0605 

•73 

.803 

•905 

36-233 

3.0907 

.68 

.741 

.836 

48.272 

4.1176 

•63 

.687 

.762 

6o.n6 

5-H79 

.60 

.648 

.702 

The  diameter  of  the  tube  P was  0.0853  feet,  and  the  flow 
took  place  under  a computed  average  head  of  2.3642  feet 
The  mean  head  was  computed  by  the  formula, 


PERCUSSIVE  FORCE  OF  PARTICLES. 


221 


W 


= r 


h — h n2 


l_2  (V H — Vh)_ 


(3) 


in  which  E=  maximum  head,  7i  — minimum  head,  H 1 = 
mean  head. 

240.  Tendency  to  Vacuum. — The  effect  of  the  per- 
cussion of  the  axial  particles,  tending  to  produce  a vacuum, 
and  of  the  enlargement  of  the  circumference  of  the  jet  in  D, 
is  apparent  until  the  length  reaches  thirty- six  diameters, 
and  is  greatest  at  three  diameters  length,  though  still  less 
than  with  Pig.  28,  because  the  surface  of  contact  of  the  jet 
against  the  tube  is  greater. 

241.  Percussive  Force  of  Particles. — The  percus- 
sive effect  of  particles  of  water  in  rapid  motion  is  illustrated 
by  another  experiment  of  Ventu- 
ri’s, with  apparatus  similar  to 
Fig.  34. 

A is  a high  tank  kept  filled 
with  water,  and  C is  a smaller 
tank  at  its  base,  full  of  water  at 
the  beginning  of  the  experiment. 

P is  an  open-topped  pipe  placed 
in  the  small  tank,  and  has  holes 
pierced  around  its  base,  so  that 
the  water  in  C may  enter  it  freely 
and  rise  to  the  level  c.  From  A a small  tube,  e,  leads  a jet 
into  P. 

Upon  the  tube  e being  opened,  the  whole  body  of  water 
in  P is  set  in  motion  and  begins  to  flow  over  its  top,  and  the 
body  of  water  in  C is  drawn  into  the  pipe  P through  the 
perforations,  and  the  surface  of  C will  be  seen  to  fall  grad- 
ually from  c to  d,  until  air  can  enter  through  the  perfora- 
tions and  destroy  the  partial  vacuum  in  P. 


Fig.  34. 


222 


FLOW  OF  WATER  THROUGH  SHORT  TUBES. 


For  a clear  conception  of  the  effect  of  the  particles  of  the 
jet  upon  the  particles  in  P,  imagine  all  the  particles  and 
the  apparatus  to  be  greatly  magnified,  so  that  there  will 
appear  to  be  a jet,  e,  of  balls,  like  billiard  balls,  for  illus- 
tration, through  a mass,  P,  of  similar  balls. 

242.  Range  of  a Set  of  Eytelwein’s  Experiments. 
— In  the  last  table  (No.  50),  there  appears  the  mean  coef- 
ficients due  to  several  distinct  classes  of  apertures,  viz.  : 
0.62  due  to  a tube  orifice  or  orifice  in  thin  plate,  with  length 
equal  to  0.038  diameters ; 0.82  due  to  a short  cylindrical 
tube , with  length  equal  to  3 diameters  ; 0.943  due  to  lessened 
contraction  by  the  convergent  entrance,  with  length  equal 
to  3 diameters  ; and  1.107  (which  in  more  perfect  form  of 
compound  tube  we  have  found  to  be  1.46)  due  to  convergent 
entrance  and  divergent  exit,  with  length  equal  3 diameters. 

There  also  appears  the  increase  of  coefficient  from  orifice 
to  short  tube , and  then  the  gradual  reduction  of  all  the 
coefficients  by  increase  of  length  of  tube  (into  pipe ) from  3 
to  60  diameters  long. 

These  phenomena  cannot  fail  to  be  of  interest  to  students 
in  that  branch  of  natural  philosophy  wlucli  relates  to  hydro- 
dynamics, and  the  practical  hydraulician  cannot  afford  to 
overlook  their  effects. 

243.  Cylindrical  Tubes  to  be  Preferred. — There  is 
rarely  occasion  for  the  practical  and  honest  use  of  the 
divergent  tube,  when  its  object  cannot  better  be  accom- 
plished by  a slightly  increased  diameter  of  cylindrical  tube. 
The  capability  of  the  divergent  ajutage  to  increase  the  dis- 
charge from  a given  diameter  of  orifice,  was  known  to  the 
ancient  philosophers,  and  to  some  of  the  Roman  citizens  who 
had  grants  of  water  from  the  public  conduits,  and  D'  Au- 
buisson  states  that  a Roman  law  prohibited  their  use  within 
524  feet  of  the  entrance  of  the  tube. 


CHAPTER  XIII. 


FLOW  OF  WATER  THROUGH  PIPES,  UNDER  PRESSURE. 

244.  Pipe  and  Conduit.— A cylindrical  tube  intended 
to  convey  water  under  pressure  is  termed  a pipe  when  its 
length  exceeds  about  three  times  its  interior  diameter  ; or 
immediately  after  its  length  has  become  sufficient  for  the 
completion  of  the  vacuum  about  the  jet  flowing  into  it. 

A long  pipe  constructed  of  masonry  is  termed  a conduit , 
and  when  it  is  a continuous  tube,  or  composed  of  sections 
of  tubes  with  their  axes  joined  in  one  continuous  line  and 
adapted  to  convey  water  under  pressure,  it  is  termed  a main 
pipe,  sub-main , branch , waste , or  service  pipe , according 
to  its  office. 

245.  Short  Pipes  give  Greatest  Discharge. — The 
greatest  possible  discharge  through  a cylindrical  tube,  due 
to  a given  head,  occurs  when  its  length  is  just  sufficient  to 
allow  of  the  completion  of  the  vacuum  about  the  contrac- 
tion of  its  jet  at  the  influence,  if  its  influent  end  is  then 
sufficiently  submerged  to  maintain  the  pipe  full  at  the 
issue. 

In  the  discussion  of  short  tubes  (§  228),  we  have  seen 

that  their  coefficient  of  discharge  is  increased  from  0.62 

(that  for  thin  plate)/to  a mean  of  0.815.  There  is  still  a loss 

of  eighteen  per  cent,  of  the  theoretical  volume,  due-  chiefly 

to  the  contraction  of  the  vein  at  its  entrance  to  the  tube, 

' 

from  which  results  a loss  of  velocity  and  a loss  of  energy  as 
the  jet  expands  to  fill  the  tube. 


224  FLOW  OF  WATER  THROUGH  PIPES,  UNDER  PRESSURE. 

LOSS  OF  FORCE,  OR  EQUIVALENT  HEAD,  AT 
THE  ENTRANCE  TO  A PIPE. 

246.  Theoretical  Volume  from  Pipes.— Let  A,  Fig. 

35,  be  a reservoir  containing  water  one  hundred  feet  deep  = 
Z/,  to  the  level  of  its  horizontal  effluent  pipe,  P.  Let  the 
pipe  P be  one  foot  in  diameter  = d. 

Then  the  theoretical  volume  of  discharge  will  equal 
it 2 gU  x .7854fZ 2 = 63.028  cubic  feet  per  second  ; but  when 
the  pipe  is  three  diameters  long  ( = 3 feet),  the  real  discharge 
according  to  experiment  will  be 


Q = .815  V2gHx  .7854<Z2,  (1) 

= 51.40  cubic  feet  per  second. 

Fig.  35. 


Let  V represent  the  theoretical  velocity;  then  will  the 
total  head  II  = =100  feet. 

Let  v represent  the  measured  velocity  of  discharge,  and 

P 

ft  the  head  necessary  to  generate  v,  then  h = — • 


MECHANICAL  EFFECT  OF  THE  EFFLUX. 


225 


24:7.  Mean  Efflux  from  Fipes. — 1 The  section  of  the  jet, 
having  expanded  beyond  the  contraction  issues  with  a diam- 
eter equal  to  that  of  the  tube,  and  the  coefficient  of  velocity, 
is  consequently  equal  to  the  coefficient  of  discharge,  c, 
which  is,  at  a mean,  .815  and  the  theoretical  velocity  V — 
v v 

= -gjg  = 80.25  feet  per  second. 


24S.  Subdivision  of  the  Head. — The  total  head  H. 
acting  upon  a short  cylindrical  tube,  consists  of  two  por- 
tions, one  of  which,  = 66^  per  cent,  of  II.  generates  v — 
.815  V = 65.4  feet  per  second.  The  remaining  331  per  cent, 
of  II  acts  in  the  form  of  pressure  to  overcome  the  resistance 
of  entry  of  the  jet  into  the  tube.  Let  It  be  the  equivalent 
of  the  neutralized  velocity. 

The  head  due  to  v is  h — = 66.5  feet  in  the  above  as- 

2 9 


sumed  case,  and  the  head  due  to 


,815 


the  head  due  to  v is 


W _ _ t)  - (1  _ 33  5 ^t 

\8152x2^  2 gf  ~ V.2  7 2 a ~ 66'°  leet* 


*9 


The  ratio  of  7i'  to  h is  therefore  — l)  = .5055  for  this 


case,  and  (h  + h')  = (Ji  + .5055  h)  — H. 


249.  Mechanical  Effect  of  the  Efflux. — Since  the 
dynamic  force  of  the  jet  is  as  the  effective  head  acting  upon 
it,  the  loss  of  .505  of  h is  a matter  of  importance,  espe- 
cially in  cases  of  short  pipes. 


The  theoretical  velocity  being  = 


v 

.815’ 


the  theoretical 


energy  of  the  jet,  under  the  same  assumed  conditions,  is 
X 2g  x Q x w = 321250  foot  pounds  per  second  = 584.09 


15 


226  FLOW  OF  WATER  THROUGH  PIPES,  UNDER  PRESSURE. 


H.P. ; id  representing  the  weight  in  pounds  (=  62.34)  per 
cubic  foot  of  the  water,  and  Q the  volume  or  quantity  of 
water  in  cubic  feet  per  second. 

The  energy  E,  due  to  v,  is  expressed  by  the  equation, 

E = % X Q X W (2) 


213631.2  foot  pounds  per  second  = 388.42  H.P. 

The  loss  of  energy  from  the  quantity  of  water  Q during 
the  efflux  in  one  second,  being  proportionate  to  the  loss  of 
head,  is, 


( | h x II  ~S)xQw  = ih  ~ *)! x Qw ■ (3) 


— 107618.75  foot  pounds  per  second  = 195.67  HP. 

250.  Ratio  of  Resistance  at  Entrance  to  a Pipe. 
— The  ratio,  .505,  of  h to  h,  is  very  nearly  a mean  for  tubes 
whose  edges  are  square  and  flush  in  a plane  partition.  If 
the  entrance  of  the  tube  is  well  rounded  in  trumpet-mouth 
form,  corresponding  to  the  form  of  the  rend  contracta,  the 
coefficient  of  velocity  cv  will  be  increased  to  about  .98,  and  the 

ratio  of  resistance  will  become  ^ — ij  = .0412,  equal  in 

this  case  (Fig.  35)  to  about  four  feet  head,  and  the  head 
that  can  be  made  available  for  work  will  equal  ninety-six 
feet. 

The  disadvantage  of  the  square  edges,  as  respects  both 
volume  and  dynamic  force,  is  apparent.  This  resistance  of 
entry  of  the  jet  into  a tube,  whose  ratio  of  head  we  have 
determined,  is  force,  or  its  equivalent  head  irrecoverably 
lost.  Its  maximum  for  a given  head  occurs  when  the  tube 
is  about  three  diameters  long,  the  velocity  being  then  at  its 
maximum,  and  thereafter  its  value  is  reduced  as  the  pipe  is 
lengthened,  and  with  the  square  of  the  velocity. 


COEFFICIENTS  OF  EFFLUX  FROM  PIPES. 


227 


RESISTANCE  TO  FLOW  WITHIN  A PIPE. 

251.  Resistance  of  Pipe- wall. — We  have  heretofore 
considered  the  whole  head  II  as  applied  to  and  entirely 
utilized  in  overcoming  the  resistance  of  entry  of  the  jet  into 
the  pipe,  and  in  generating  the  velocity  among  the  particles 
of  the  jet. 

We  will  now  consider  the  resistances  within  the  pipe  and 
its  appendages,  and  the  portion  of  the  velocity  that  must  he 
converted  into  hydraulic  pressure  to  overcome  them. 

252.  Conversion  of  Velocity  into  Pressure. — If 
the  pipe  P,  Fig.  35,  of  three  diameters  length,  he  extended 
as  at  P',  a new  resistance  arising  within  the  added  length 
acts  upon  the  jet  and  again  reduces  the  volume  of  flow.  A 
portion  of  the  velocity  of  the  jet  is  converted  into  working 
or  hydraulic  force,  and  is  applied  to  overcome  the  resistances 
presented  within  the  pipe,  and  the  proportion  of  the  velocity 
thus  consumed  is  almost  directly  proportional  to  the  length 
added  of  the  pipe,  of  the  given  diameter. 

253.  Coefficients  of  Efflux  from  Pipes. — The  effects 
upon  the  volume  of  discharge  through  a given  pipe  conse- 
quent upon  varying  its  length  will  he  apparent  upon  inspec- 
tion of  a table  of  coefficients  of  efflux,  c,  due  to  its  several 
lengths  respectively. 

We  will  assume  the  pipe  to  he  one  foot  diameter,  of 
clean  cast  iron,  when  the  coefficients  determined  experi- 
mentally have  mean  values  about  as  follows  : 


TABLE  No.  51. 

Coefficients  of  Efflux  ( c ) for  Short  Pipes. 


Lengths,  in  diameters  . . 

i 

5 

10 

25 

50 

75 

100  125 

1 

150 

175 

200 

225 

250 

275 

3°° 

Coefficients  (c).  

.62 

.792 

.770 

.714 

.643 

.588 

.548  .512 

.485 

.462 

.440 

.420 

•405 

.386 

•378 

228 


FLOW  OF  WATER  THROUGH  PIPES. 


Plotted  as  ordinates,  beginning  with  the  theoretical 
coefficient,  unity,  they  range  themselves  as  in  Fig.  36. 


Fig.  86. 


254.  Reactions  from  the  Pipe-wall. — A fair  sam- 
ple of  ordinary  pipe  casting,  a cement-lined,  lead,  or  glazed 
earthenware  pipe  are  each  termed  smooth  pipes,  but  a good 
magnifying  lens  reveals  upon  their  surfaces  innumerable 
cavities  and  projections. 

The  molecules  of  water  are  so  minute  that  many  thou- 
sands of  them  might  be  projected  against  and  react  from  a 
single  one  of  those  innumerable  projections,  even  though  it 
was  inappreciable  to  the  touch,  or  invisible  to  the  naked 
eye. 

A series  of  continual  reactions  and  deflections,  originated 
by  the  roughness  of  the  pipe,  act  upon  the  individual 
molecules  as  they  are  impelled  forward  by  gravity,  and 
materially  retard  * their  flow. 

In  a given  pipe,  having  a uniform  character  of  surface, 
the  sum  of  the  reactions,  for  a given  velocity,  is  directly  as 


* The  resistance  was,  by  tbe  earlier  pliilosopliers,  attributed  chiefly  to  the 
adhesion  of  the  fluid  particles  to  the  sides  of  the  pipe,  and  to  the  cohesion 
among  the  particles.  Vide  Downing,  who  accepts  the  views  of  Du  Buat,  D'Au- 
buisson,  and  other  eminent  authorities.  Practical  Hydraulics,  p.  200.  Lon- 
don,  1875. 


FORMULA-  OF  RESISTANCE  TO  FLOW. 


229 


its  wall  surface,  or  as  the  product  of  the  inner  circumfer- 
ence into  the  length.  Since  in  a pipe  of  uniform  diameter 
the  circumference  is  constant,  the  sum  of  the  reactions  is 
also  directly  as  the  length. 

The  impulse  of  the  flowing  particles,  and  therefore  their 
reactions  and  eddy  influences,  are  theoretically  proportional 
to  the  head  to  which  their  velocity  is  due,  which  is  propor- 
tional to  the  square  of  the  velocity,  or,  in  general  terms,  the 
effective  reactions  are  proportional  nearly  to  the  square  of 
the  velocity. 

The  resistances  arising  from  the  interior  surface  of  the 
pipe  are,  therefore,  not  only  as  the  length , hut  as  the 
square  of  the  velocity , nearly. 

The  effect  of  the  resistances  is  not  equal  upon  all  the 
particles  in  a section  of  the  column  of  water,  hut  is  greatest 
at  the  exterior  and  least  at  the  centre,  or,  in  a given  section, 
approximately  as  its  circumference  divided  by  a function 
of  its  area* 

255.  Origin  of  Formulas  of  Flow. — These  simple 
hypotheses  constitute  the  foundation  of  all  the  expressions 
of  resistance  to  the  flow  of  water  in  pipes,  as  they  appear  in 
the  varied,  ingenious,  and  elegant  formulas  of  those  emi- 
nent philosophers  and  hydranlicians  who  have  investigated, 
the  subject  scientifically. 

256.  Formula  of  Resistance  to  Flow. — Place  R to 
represent  the  sum  of  all  the  resistances  arising  from  the 
circumference  of  the  pipe  (excluding  those  due  to  the  entry); 
C for  the  contour  or  circumference  of  the  pipe,  in  feet ; S for 
the  section  of  the  interior  of  the  pipe,  iu  square  feet ; l for 
the  length  of  the  pipe,  in  feet ; and  v for  the  mean  velocity 

* The  law  of  the  effects  of  the  resistances  is  believed  to  have  been  first  for- 
mulated in  the  simple  algebraic  expressions  now  in  general  use,  by  M.  Chezy, 
about  the  year  1775. 


230 


FLOW  OF  WATER  THROUGH  PIPES. 


of  flow,  in  feet  per  second.  Then  the  resistance  to  flow  is 
expressed  in  equivalent  head  by  the  equation 

= (4) 

257.  Coefficient  of  Flow. — In  the  equation  a new 
coefficient  m appears,  which  also  is  to  be  determined  by 
experiment.  It  is  not  to  be  confounded  with  the  c hereto- 
fore investigated,  but  will  hereafter  be  investigated  inde- 
pendently. 

258.  Opposition  of  Gravity  and  Reaction. — We 

have  seen  that  gravity  (§  189)  is  the  natural  origin  and  the 
accelerating  force  that  produces  motion  of  water  in  pipes. 

Its  effect,  if  no  resistance  was  opposed,  would  be  to  con- 
tinually accelerate  the  flow.  On  the  other  hand,  if  its  effect 
was  removed,  the  resistances  would  bring  the  column  to  a 
state  of  rest. 

The  two  influences  oppose  each  other  continually,  and 
therefore  tend  to  the  production  of  a rate  of  motion  in  which 
they  balance  each  other. 

259.  Conversion  of  Pressure  into  Mechanical 
Effect. — When  the  motion  has  become  sensibly  constant, 
a portion  of  the  effect  of  gravity  that  appeared  as  velocity 
in  the  cases  of  orifices  and  short  tubes,  or  its  equivalent  in 
the  form  of  head  is  consumed  by  impact  upon  the  rough 
projections  of  the  pipe  wall  and  reactions  therefrom,  and  the 
remaining  force  due  to  gravity  or  head  is  producing  the 
velocity  of  flow  then  remaining. 

260.  Measure  of  Resistance  to  Flow. — The  effect 
of  the  resistance  along  a mam  pipe,  when  discharging 
water  from  a reservoir,  as  in  Fig.  37,  may  be  observed  by 
attaching  a series  of  pressure  gauges  at  intervals,  or  by  at 
tacliing  a series  of  open-topped  pipes,  as  at  PP1P2,  etc. 


RESISTANCE  INVERSELY. 


231 


Fig.  37. 


If  the  end  f of  the  pipe  is  closed,  water  will  stand  in  all 
the  vertical  pipes  at  the  same  level,  dk,  as  in  the  reservoir. 

If  the  diameter  of  the  pipe  is  uniform  throughout  its 
length,  and  the  flow,  the  full  capacity  of  the  pipe,  then 
water  will  stand  in  the  several  vertical  pipes  up  to  the  in- 
clined line  a'f ; provided  that  the  top  of  be  closed  so  that 
there  may  be  a tendency  to  vacuum  at  n,  and  provided  also 
that  n is  not  more  than  thirty  feet,  or  the  height  to  which 
the  pressure  of  the  atmosphere  can  maintain  the  pipe  full, 
above  the  line  a'f,  at  n'. 

When  f is  an  open  end  discharging  into  air,  and  the 
vacuum  at  n is  not  maintained,  a'n  will  be  the  total  effec- 
tive head,  and  the  portion  of  the  pipe  nf  will  be  only  parti- 
ally filled. 

261.  Resistance  Decreases  as  the  Square  of  the 
Velocity.— If  the  discharge  of  the  pipe  is  throttled  at  /,  by 
a partial  closing  of  a valve,  by  a contraction  of  the  issue,  or 
by  diversion  of  the  stream  into  other  pipes  of  less  capacity, 
and  a portion  of  the  velocity  is  in  consequence  converted 
into  pressure  equivalent  to  the  head/'/1,  then  the  resistance 
will  be  lessened  as  the  square  of  the  velocity  decreases,  and 
water  will  stand  in  the  vertical  pipes,  or  the  gauges  will  in- 
dicate the  inclined  line  a"f.  This  is  the  usual  condition  of 
mains  in  public  water  supplies. 


232 


FLOW  OF  WATER  THROUGH  PIPES. 


262.  Increase  of  Bursting-  Pressure. — One  effect  of 
throttling  the  discharge  is  seen  to  be  an  increase  of  bursting 
pressure  upon  the  pipes,  which  is  greater  when  the  exit  is 
entirely  closed  than  when  there  is  a constant  flow,  and  which 
decreases  as  the  velocity  increases,  though  a sudden  clos- 
ing of  a valve  against  a rapid  current  will  probably  prove 
disastrous  to  an  ordinary  pipe  that  is  fully  able  to  sustain 
a legitimate  pressure  due  to  the  head. 

263.  Acceleration  and  Resistance. — Let  ab  (Fig.  38) 
be  a vertical  pipe  discharging  water  from  a reservoir  A, 
maintained  always  full.  If,  before  the  water  entered  the 


Fig.  38. 


pipe,  a single  particle  had  been  dropped  into  its  centre  from 
a,  the  velocity  of  movement  of  the  particle  would,  in  couse 
quence  of  the  effect  of  gravity  upon  it,  have  been  constantly 
accelerated  through  its  whole  passage  along  the  axis. 


DESIGNATION  OF  h"  AND  l. 


233 


Its  velocity,  wlien  it  had  reached  b,  would  have  been 
equal  to  V2gH,  when  H represents  the  vertical  height  ab 
in  feet. 

The  greater  the  height  ab  the  greater  the  sum  of  the  ac- 
celerations by  gravity,  and  also,  if  the  pipe  is  flowing  full, 
the  greater  the  length  ab  the  greater  the  sum  of  the  resist- 
ances acting  upon  the  column  of  water  to  retard  it. 

264.  Equation  of  Head  Required  to  Overcome 
the  Resistance. — Let  v be  the  velocity  of  the  jet  issuing 
from  b,  h the  head  to  which  v is  due,  and  7^''  the  head  act- 
ing upon  the  resistance  R,  and  m a coefficient. 

Then  the  ratio  of  the  amount  of  the  force  of  gravity,  or 
equivalent  head,  h",  converted  into  hydraulic  pressure  to 
balance  the  resistances  within  the  given  length  of  pipe,  and 
for  the  given  head,  is  to  the  head,  7i , producing  the  velocity 
CJ  'ift 

as  ^ x to  x r-  to  ; hence  the  equation  of  resistance 
S 2g  2g 


265.  Designations  of  h1’  and  l. — In  long  pipes  the 
total  head,  H—Ti  + h'-sr  Ji". 

The  head,  or  charge  of  water  li'  acting  upon  the  resist- 
ances, is  the  vertical  height  of  the  surface  of  the  reservoir, 
less  the  height  aa"  — h (Fig.  38),  necessary  to  generate  the 
velocity  v,  and  also  less  the  height  a" a'  — h'  necessary  to 
overcome  the  resistance  of  entry,  above  the  centre  of  the 
discharging  jet  at  the  exit ; or  if  the  discharge  is  into 
another  body  of  water,  above  the  surface  of  the  lower 
body. 

The  length  l to  be  taken,  is  the  actual  length  of  the  axis 
of  the  pipe. 

In  topographical  surveys  the  chain  is  held  horizontal 


head  is 


(51 


234 


FLOW  OF  WATER  THROUGH  PIPES. 


and  the  distance  df  is  in  plotting  expressed  by  its  projec- 

A"  Ttf 

tion  a'Jc,  but  for  pipes  the  true  ratio  -j  is  . 

Then  whatever  the  position  or  direction  of  the  pipe  a'b, 
or  aif,  or  if,  or  onf  (abstracting  for  the  present  any  resist- 
ance of  curvature),  the  equation  of  h"  measures  the  resistance 
unless,  in  the  case  of  a pipe  discharging  near  to  its  full  capa- 
city, an  upward  curve,  n,  shall  rise  more  than  thirty  feet 
above  the  line  of  hydraulic  mean  gradient  a'f,  when  li  is 
to  be  taken  in  two  sections,  first  from  a'  to  n vertically,  and 
second  from  n to  f vertically  reduced  by  the  etfect  of  the 
vacuum,  if  any,  or  as  a simple  channel  without  pressure  if 
the  length  nf  does  not  fill. 

266.  Variable  Value  of  m. — In  the  equation  of  h",  (5), 
we  have  the  coefficient  m,  whose  several  values  are  to  be 
deduced  from  actual  measurements  of  the  flow  of  water 
through  pipes,  and  whose  governing  conditions  are  to  be 
closely  observed  and  studied. 

The  physical  conditions  of  various  pipes  are  so  different 
that  special  coefficients  are  required  for  each  class  of  con- 
ditions. 

A slight  increase  in  the  roughness  of  the  interior  surface 
of  the  pipe,  occasional  sudden  enlargements  or  contractions 
oi  the  diameter  of  the  pipe,  and  sudden  bends  in  the  direc- 
tion of  the  pipe,  may  be  instanced  as  sufficient  departures 
from  the  conditions  of  straight  pipes  with  uniform  diameters 
and  surfaces  to  materially  modify  the  value  of  its  coefficient 
of  flow. 

267.  Investigation  of  Values  of  m.— For  the  de- 
termination of  a series  or  table  of  coefficients,  m,  for  full 
pipes,  we  will  select  data  from  published  tables  of  * exper- 

* Reclierches  experimentales  relatives  au  movement  de  l’eau  dans  le 
tuyaux.  Paris,  1857. 


DEFINITION  OF  SYMBOLS. 


235 


I meats  by  Henry  Darcy,  made  while  he  was  director  of  the 
public  water  service  of  the  city  of  Paris  ; from*  experiments 
by  Geo.  S.  Greene,  made  while  chief  engineer  of  the  Croton 
Aqueduct  Department  of  New  York  city  ; from  experiments 
by  Geo.  H.  Bailey,  Esq.,  made  while  chief  engineer  of  the 
Jersey  City  Water- works  ; from  some  of  the  famous  exper- 
iments of  Du  Buat,  Couplet,  and  Bossut,  which  furnished 
the  chief  data  for  the  elegant  formulas  of  those  eminent 
philosophers,  as  well  as  those  of  Pronyf  and  Eytelwein, 
and  from  other  extended  experiments. 

268.  Definition  of  Symbols. — By  transposition  we 
have 


m = 2g  x 


8 


h" 

X -T-  x 


C l 


(7) 


The  member  is  the  ratio  of  the  height  which  the  par- 
ticles fall  through  in  the  given  length,  equal  or  the 

sine  of  the  angle  of  inclination  leaf,  Fig.  38.  The  inclina- 
tion cm  is  termed  the  “ slope ,”  or  the  hydraulic  mean  gra- 
dient| and  is  usually  designated  by  the  letter  i.  The  point 
a 1 is  always  beneath  the  surface  of  the  water  a depth  aa' 
necessary  to  generate  the  velocity  v in  the  pipe,  and  to 
overcome  the  resistance  of  entry,  whether  the  pipe  be  in  the 
position  af,  if,  or  onf. 

The  depth  aa)  varies  as  the  velocity  varies,  and  the 
“slope”  i corresponds  to  an  imaginary  right  line  connect- 
ing the  points  a’  and/'. 

8 

The  member  ~,  as  now  inverted  (§  256)  refers  to  the 
ratio  of  the  section  to  the  contour  of  the  given  pipe,  or  to  the 

* Descriptive  Memoir  of  the  Brooklyn  Water-works,  by  James  P.  Kirk- 
wood. Van  Nostrand,  N.  Y.,  1867. 

f Vide  Recherekes  Pliysico-Matkematiques  sur  la  Tkeorie  du  Mouvement 
des  Eaux  Courantes,  1804. 


236 


FLOW  OF  WATER  THROUGH  PIPES. 


sectional  area 

— tt  • — 7 — . it  is  termed  the  “ mean  radius , or,  in 

wetted  perimeter 

tlie  cases  of  pipes  and  channels  partially  filled,  the  hydrau- 
lic mean  depth,  and  is  usually  designated  by  the  letter  r. 
The  value  of  r for  full  pipes  is  always  equal  to  one-fourth 

of  the  diameter  — j,  according  to  well-known  properties  of 
the  circle. 

269.  Experimental  Values  of  the  Coefficient  of 

Flow. — We  have  then,  as  an  equivalent  for  equation  (7) : 


2 qri 
m — -JL— 


,2  > 


or 


2 gh"S 
m — -Tt7  2 . 
Clvz 


(8) 


TABLE  No.  5 2 a. 


2 g dh 


m = ~ x 7 
4v2  l 


Experimental  Coefficients  (m)  of  Flow  of  Water  in 
CLEAN  Pipes,  under  Pressure. 

Experiments  by  Hamilton  Smith,  Jr.,  (Sheet-iron  Asphaltum-coated  Pipes,} 
at  North  Bloomfield,  California,  where  2 g = 64.29. 


Diameter  = d 
in  feet. 

Head  = h, 
in  feet. 

Length  = /, 
in  feet. 

Velocity  = v , 
in  feet  per  sec. 

Coefficient  = m. 

.911 

22.650 

684.8 

10.048 

.00479 

.911 

17.832 

697.0 

S.6S5 

. 00496 

.911 

12.098 

713-9 

6.952 

.00518 

.911 

9.618 

721.3 

6.115 

.00520 

.911 

6.203 

730.6 

4-755 

.00554 

1.056 

22.711 

684.9 

10-755 

.004S6 

1.056 

I5-5I9 

699.6 

8.679 

.00499 

1 .056 

10.127 

709.2 

6.982 

.00495 

1.056 

4-799 

718.4 

4.612 

.00532 

1.230 

22.036 

684.4 

12.302 

.00419 

1.230 

17.132 

695.6 

10.750 

.00421 

1.230 

11.592 

705.0 

8-517 

.00446 

1-230 

8.713 

710.7 

7-334 

.00450 

1.230 

7-813 

712.4 

6.S61 

.00459 

1.230 

3-614 

719.9 

4.398 

.00511 

1.416 

296.1 

4438.7 

20. 130 

.00373 

EXPERIMENTAL  COEFFICIENTS. 


237 


TABLE  No.  52. 

Experimental  Coefficients  ( m ) of  Flow  of  Water  in  Clean 

2 ghS  2 gri  2 gr  h 

Pipes,  under  Pressure,  m = = — — = — - x — 

Civ-  v 2 l v- 


EXPERIMENTS  BY  H.  DARCY  (Cast-iron  Pipes). 


Diameter  = d, 
in  feet. 

Head  = k'\ 
in  feet. 

Length  = 2, 
in  feet. 

Velocity  = w, 
in  feet  per  sec. 

Coefficient  = m. 

O.2687 

O.066 

328.09 

O.2885 

.OIO4478 

ii 

I.742 

it 

L8399 

.0067800 

tt 

3-347 

it 

2.5946 

.0065508 

a 

13. 260 

ft 

5-I509 

.0065850 

ft 

39.299 

ft 

8.9242 

.0065162 

ft 

56.011 

it 

I°.7II5 

.0064320 

0.4501 

0.079 

328.09 

0.4887 

•OO73054 

ii 

.686 

a 

I.6o2I 

.0059026 

tt 

1-558 

a 

2.5021 

.0054960 

ft 

54-975 

I5-3929 

.0051240 

0.6151 

0.089 

328.09 

0.6544 

.0062884 

a 

1.207 

a 

2.4991 

.0058476 

a 

2.641 

a 

3-7I55 

•0057898 

a 

4-369 

a 

4.9045 

•0055296 

€t 

12.500 

a 

8.2564 

•0055482 

it 

47.872 

ft 

16.2360 

•0054948 

0.9751 

0.092 

328.09 

0.7997 

.0068802 

(6 

.883 

a 

2-7I34 

•0057306 

it 

1.762 

a 

3-7863 

.0058728 

it 

3-625 

a 

5-4039 

•0059314 

it 

7.562 

a 

7-8330 

.0058890 

it 

13-473 

ft 

10-3575 

.0060010 

t.6427 

0. 148 

328.09 

I-3765 

.0062950 

it 

.148 

a 

1.4685 

•O0553IO 

it 

.197 

a 

1-5549 

.0065688 

it 

•394 

ft 

2-5954 

.0047160 

ft 

.853 

a 

3-6637 

.0051216 

tf 

.820 

ft 

3.6900 

.0048536 

238 


FLOW  OF  WATER  THROUGH  PIPES. 


TABLE  No.  53. 


Experimental  Coefficients  (m)  of  Flow  of  Water  in  Clean 


Pipes,  under  Pressure. 


2 gh"S 2 gri 

Civ 2 — 


EXPERIMENTS  BY  THE  WRITER  (Wrought-iron  Cement-lined 

Pipe). 


Diameter  = d, 
in  feet. 

Head  = h", 
in  feet. 

Length  = /, 
in  feet. 

Velocity  = v. 
in  feet  per  sec. 

Coefficient  = m. 

I.6667 

1.86 

8171.O 

O.949 

.006785 

66 

3.60 

66 

I.488 

•005338 

66 

5-93 

66 

J-925 

.005254 

66 

8.48 

66 

2.329 

•005133 

66 

IO-93 

66 

2.598 

•005317 

66 

12.91 

66 

2.867 

•005157 

66 

16.  28 

66 

3-271 

.004996 

66 

18.60 

66 

3-439 

•005163 

66 

22.22 

66 

3-741 

•OO5213 

66 

24-54 

3.920 

.005243 

66 

25-58 

66 

4.00 

•005249 

it 

26. 16 

66 

4.04 

.005262 

TABLE  No.  54. 

EXPERIMENTS  BY  DU  BUAT  (Tin  Pipes). 


O.0889 

•973 

10.401 

5 • 1 79 

.004992 

66 

1.484 

10.401 

6-334 

.005089 

66 

.0481 

12.304 

0.7717 

•009393 

66 

•375 

12.304 

2.606 

.006424 

66 

1. 220 

12.304 

5.220 

.005207 

66 

.013 

65-457 

0.141 1 

.014276 

66 

1.022 

66 

1-775 

.007091 

ii 

1-954 

66 

2.546 

.006585 

TABLE  No.  55. 

EXPERIMENTS  BY  BOSSUT  (Tin  Pipes). 


0.0889 

0.331 

53-284 

1.085 

.001698 

66 

.976 

86.O94 

1.979 

.004142 

.11841 

.864 

3I-956 

2-945 

•005943 

66 

2.066 

I9I.84O 

1.679 

.007282 

66 

I.699 

31- 956 

4.308 

.005461 

.178 

•765 

3i-956 

3-58i 

•005363 

66 

2.019 

191.840 

2.196 

.006270 

66 

I.892 

95-905 

2.250 

.011190 

66 

d=«w 

I. 491 

3I-956 

5-23° 

.004901 

EXPERIMENTAL  COEFFICIENTS. 


239 


TABLE  No.  56. 


Experimental  Coefficients  ( m ) of  Flow  of  Water  in  Clean 

2gh  S 


Pipes,  under  Pressure,  m — 


Civ1 


EXPERIMENTS  BY  COUPLET  (Iron  Pipes). 


liaameter  = d , 
in  feet. 

Head  = h", 
in  feet, 

Length  = 2, 
in  feet. 

V elocity  = v, 
in  feet  per  sec. 

Coefficient  = m. 

0.4439 

O.492 

7481.88 

O.1785 

.OOI475 

66 

I.005 

7481.88 

.2802 

.012230 

•4374 

I.484 

7481.88 

•3665 

.010390 

66 

I.670 

66 

.4258 

.008667 

66 

2.130 

66 

.4640 

.009309 

66 

2.215 

66 

.4728 

.009323 

1.5988 

12.  629 

3836.66 

3-4779 

.007004 

TABLE  No.  57. 


EXPERIMENTS  BY  W.  A.  PROVIS.  (Lead  Pipes.) 


0.125 

2.91666 

20.00 

6.1495 

.006465 

66 

66 

40.00 

4.7588 

.005398 

66 

66 

60.00 

3-9°32 

.005360 

66 

66 

80.00 

3-396I 

.005287 

66 

<6 

100.00 

3.0897 

.005122 

TABLE  No.  58. 

EXPERIMENTS  BY  RENNIE. 

With  glass  pipes  slightly  rounded  at  the  ends. 


5.0020833 

1.0 

1.0 

7.1627 

.000653 

66 

2 

66 

10.4196 

.000408 

66 

3 

66 

12.9409 

.000601 

66 

4 

66 

14.6240 

.000627 

.0041666 

1.0 

1.0 

5-6450 

.001672 

66 

2 

66 

8.3676 

.001916 

66 

3 

66 

10.0497 

.001992 

66 

4 

66 

1 1.6000 

.001994 

.00625 

1.0 

1.0 

5-5487 

.004162 

66 

2 

66 

8.1852 

.0048! 4 

66 

3 

66 

9-8551 

.003956 

66 

4 

66 

10.8320 

.004378 

.00833 

1.0 

1.0 

6.1028 

.004584 

66 

2 

66 

8.5386 

.004684 

6% 

3 

66 

10.8003 

.004392 

4 

66 

13.0400 

.004016 

340 


FLOW  OF  WATER  THROUGH  PIPES. 


TABLE  No.  59. 

Experimental  Coefficients  (m)  of  Flow  of  Water  in  Old 
Pipes,  under  Pressure,  m = 

Civ 


EXPERIMENTS  BY  H.  DARCY.  (Foul  Iron  Pipes.) 


Diameter  = d, 
in  teet. 

Head  = h", 
in  feet, 

Length  = /, 
in  feet. 

Velocity  = v, 
in  feet  per  sec. 

Coefficient  = m. 

O.H94 

O.223 

328.09 

O.2669 

.018342 

44 

.600 

44 

•4273 

.OI92IO 

44 

2.198 

44 

.8291 

•°l8735 

44 

5-°°3 

44 

I.2494 

.018784 

44 

10.630 

44 

I.8079 

.OI9055 

44 

i3-632 

44 

2.0772 

.018511 

©.2628 

0.213 

328.09 

O.404O 

.Ol68lI 

44 

.820 

44 

.8242 

•OI555I 

44 

2-379 

44 

I.4645 

.014288 

44 

5.282 

44 

2.2226 

•013774 

44 

10.17 1 

44 

3-°5I7 

.OI4082 

44 

14.879 

44 

3-7434 

.013679 

©.8028 

0.308 

328.09 

1.0080 

.OII934 

44 

.663 

44 

1.4824 

.011878 

44 

I-552 

44 

2.3218 

•011334 

44 

3-773 

44 

3.6283 

.OII285 

t€ 

7-5I3 

44 

5-°727 

.OII494 

44 

10.499 

44 

6.0169 

.OII417 

€4 

13.468 

44 

6.8037 

.OII454 

44 

45-870 

44 

12.5779 

.OII4I5 

TABLE  No.  60. 

EXPERIMENT  BY  GEN.  GEO.  S.  GREENE,  C.  E„ 
Upon  a New  York  City  cast-iron  Main.  (Tuberculated.) 

$.o  | 20.215  I 11217.00  | 2.99967  | .00966 

EXPERIMENT  BY  GEO.  H.  BAILEY,  C.  E., 

Upon  a Jersey  City  cast-iron  Main.  (Tuberculated.) 

1-6667  | 28.1285  | 29715.00  | I.43795  | .01228 


EXPERIMENTAL  COEFFICIENTS. 


241 


TABLE  60 . — (Continued.) 

Experimental  Coefficients  (m)  of  Flow  of  Water  in  Old 
Pipes,  under  Pressure,  m — 

Llir 

EXPERIMENT  UPON  THE  COLINTON  MAIN.* 

Eight  years  in  use. 


Diameter  = 
in  feet. 

Head  = h". 
in  feet. 

Length  = /, 
in  feet. 

Velocity  = v, 
in  feet  per  sec. 

Coefficient  = m. 

1-3334 

184 

3815 

14.50° 

.OO4923 

66 

230 

2576s 

5-252 

•005556 

66 

420 

29580 

6.816 

.006559 

LAMBETH  WATER  WORKS  MAIN. 


2-5 

25 

54120 

1.772 

.OO5918 

I-583 

41 

22440 

2-734 

.006229 

I 

38 

5200 

4-353  ! 

.006208 

LIVERPOOL  WATER 

WORKS  MAIN. 

I 

i 27 

8140 

2.644  | 

.OO7633 

CARLISLE  WATER 

WORKS  MAIN. 

* 

34-5 

66  00 

3-568  | 

.006610 

EXPERIMENTS  BY  THE  WRITER. 

With  unlined  wrought  iron  pipe  (gas  tubing),  the  jet  entering  through  a stop, 
cock  and  piston  meter,  with  coefficient  c — .58  when  length  =0.25.  The 
pipe  had  been  in  use  one  week,  but  had  rusted  considerably. 


O.08334 

28.73 

0.25 

46.70 

.... 

66 

85-57 

9 

18.964 

•035467 

66 

98-34 

735 

4.850 

.007636 

66 

96.38 

1337 

3-538 

.007722 

66 

87-33 

2040 

2.722 

.007746 

* Vide  Proceedings  of  Inst.  Civ.  Engineers,  p.  4,  Feb.  6th,  1855,  London. 


16 


2P2 


FLOW  OF  WATER  THROUGH  PIPES 


TABLE  No.  6 1. 


Series  or  Coefficients  of  Flow  (ni)  of  Water  in  Clean  Pipes 
under  Pressure,  at  Different  Velocities,  and  in  Pipes 

2 gh"  S 2gri\ 


of  Different  Diameters. 


Civ* 


) 


Velocity. 

Diameters. 

inch. 

H" 

I n 

i Vi" 

1# 

.1458'. 

2" 

.0417  feet 

.0625'. 

.0834'. 

.1250'. 

.1667'. 

Feet  per 
Second. 

Coefficient . 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

. I 

.01200 

.01181 

.OII4O 

.01120 

.01 IOO 

.01080 

0 2 

.01146 

.01125 

.OI IOO 

.01077 

.01056 

.OIO3O 

•3 

.01107 

.01080 

.01070 

.01030 

.OIOIO 

.00980 

•4 

.01070 

.01045 

.01025 

.OIOOO 

.00965 

.OO94O 

•5 

.01045 

.OIOI3 

.00995 

.00960 

.00930 

.OO9IO 

.6 

.01020 

. OO9OO 

■00955 

.00932 

.OO904 

.00890 

•7 

.OIOO4 

. 00967 

. OO93O 

.00906 

.00883 

.00870 

.8 

. 00984 

. 00946 

. OO9IO 

.00887 

.00863 

.00852 

•9 

. 00967 

. OO93O 

.00895 

.00869 

.00850 

.00837 

1.0 

• °°953 

•°°9I5 

. 00883 

.00857 

.00840 

.00826 

1. 1 

.00937 

. 00902 

. 00869 

.00845 

.00828 

. 00815 

I.  2 

. OO923 

. oo'888 

.00857 

.00833 

.00816 

.00804 

i-3 

.00912 

. 00878 

. 00848 

.00824 

.00807 

.00795 

i-4 

. OO9OO 

. 00868 

.00838 

.00816 

.00798 

. 00787 

i-5 

. 00890 

.00859 

.00830 

.00807 

.00793 

.00780 

i.6 

. 00881 

. 00850 

.00823 

.00800 

.00785 

.00774 

i-7 

.00873 

.00843 

.00815 

.00793 

.00779 

.00768 

i.8 

. 00865 

. 00836 

.00809 

.00787 

* °°7  7 3 

.00762 

i-9 

.00857 

. 00829 

. 00803 

.00780 

.00767 

- °°7  5 7 

2.0 

. 00850 

.00822 

.00793 

.00776 

.00762 

.00752 

2.25 

.00835 

. 00806 

.00783 

.00763 

.00749 

.00740 

2-5 

.00818 

.00793 

.00770 

.0075° 

.00737 

. 00729 

2-75 

. 00803 

.00780 

.00759 

.00738 

.00727 

.00719 

3-o 

.00792 

.00769 

.00749 

.00729 

.OO7I9 

.00710 

3-5 

. 00769 

. 00748 

.00729 

.007 I I 

.00701 

.00693 

4 

.00750 

.00730 

.00713 

.00696 

.00697 

. 00680 

5 

.00718 

. 00701 

. 00686 

.00671 

.00674 

.00657 

6 

.00691 

. 00678 

.00666 

.00652 

.00645 

.00638 

7 

. 00669 

. 00658 

.00648 

. 00636 

.00629 

.00623 

8 

. 00652 

.00643 

.00633 

.00623 

.00616 

.00611 

9 

. 00638 

. 00629 

.00622 

.00612 

.00607 

.00601 

10 

.00626 

. 00618 

. 006  r 2 

. 00602 

•oo597 

•°°593 

12 

. 00609 

. 00603 

.00598 

.00589 

•00585 

.00580 

14 

.00597 

• °°5  93 

. 005SB 

.00580 

• °°577 

• °°5  7 3 

l6 

. 00588 

.00584 

. 00580 

•00573 

•00570 

.00566 

18 

. 00582 

.00578 

• °°5  7 5 

. 00568 

.00566 

.00561 

20 

.00577 

•00573 

.00570 

.00564 

.00561 

. 005 5 7 

FLOW  OF  WATER  THROUGH  PIPES. 


24:3 


TABLE  No.  61  — (Continued). 

Coefficients  of  Flow  (m)  of  Water  in  Clean  Iron  Pipes 
under  Pressure. 


Velocity. 

Diameters. 

3 inrh 

4„ 

6" 

8" 

10" 

12" 

.25  feet 

•3333/- 

o'- 

.6667' . 

•8333'- 

i' . 

Feet  per 
Second. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient > 

. I 

•oio55 

.OIOIO 

.00925 

.00840 

.00800 

.00750 

. 2 

.01005 

.00950 

. 00870 

.00800 

.00765 

. 007 18 

•3 

.00950 

. OO9OO 

. 00840 

.00772 

.00740 

. 00697 

•4 

. 00914 

•00875 

. 00817 

.00757 

.00724 

.00685 

•5 

. 00885 

. 00850 

•00794 

. 00740 

.00707 

.00670 

.6 

. 00860 

. 00828 

•00775 

•00725 

.00693 

. 00660 

•7 

. 00838 

. 00808 

•00757 

.00714 

.00680 

.00650 

.8 

. 00820 

. 00790 

•00744 

.00702 

.00670 

.00640 

•9 

. 00803 

.00777 

•00733 

.00693 

' .00662 

.00632 

I.  0 

. 00792 

•00765 

•00723 

.00687 

.00655 

.00626 

1. 1 

. 00780 

•00754 

•00713 

.00.678 

. 00646 

. 00620 

1.2 

.00768 

•00744 

.00705 

.00670 

.00639 

.00612 

i-3 

.00761 

•00737 

. 00698 

.00663 

.00633 

. 00607 

1.4 

■00753 

. 00729 

. 00691 

.00658 

.00628 

. 00603 

i-5 

.00747 

•00723 

. 00685 

.00652 

.00623 

.00598 

i.6 

. 00740 

.00717 

. 00679 

.00648 

.00619 

.°°594 

i-7 

•00735 

. 007 1 2 

•00673 

.00643 

.00615 

.00591 

i.8 

.00730 

. 00707 

. 00669 

.00639 

.00611 

.00587 

1.9 

•00725 

. 00702 

. 00665 

.00635 

.00608 

.00585 

2.0 

.00721 

. 00698 

. 00661 

. 00632 

.00605 

.00582 

2.25 

.00710 

.00687 

. 00652 

.00623 

.00597 

•00575 

2-5 

.00700 

.00678 

. 00644 

.00616 

.00590 

. 00569 

2-75 

. 00692 

. 00669 

. 00636 

.00608 

.00584 

.00564 

3-o 

.00684 

. 00662 

. 00630 

.00604 

.00580 

. 00560 

3-5 

. 00668 

. 00649 

.00618 

.00592 

.00571 

•00552 

4 

•00657 

. 00638 

. 00608 

.00584 

.00563 

.00544 

5 

. 00636 

. 00618 

•00591 

.00568  - 

•00551 

•00533 

6 

. 00620 

. 00603 

.00578 

•00557 

.00540 

.00524 

7 

. 00607 

.00590 

.00567 

•00548 

.00532 

.00517 

8 

•00595 

O 

00 

10 

0 

0 

•00559 

•00540 

.00525 

.005 1 2 

9 

•00587 

.00572 

•00552 

•00535 

.00520 

•00507 

10 

. 00580 

.00566 

•00547 

.00531 

.00516 

.00503 

12 

.00569 

.00558 

.00540 

•00525 

.00510 

.00497 

14 

•00563 

•00551 

■00534 

.00519 

.00505 

•00493 

l6 

•00557 

•00545 

. 00528 

•00514 

.OO5OI 

.00487 

18 

.00552 

•00540 

•00524 

.00509 

.00497 

. 00484 

20 

.00547 

■00536 

.00520 

.00504 

.00493 

.00481 

244 


FLOW  OF  WATER  THROUGH  PIPES. 


TABLE  No.  61  — (Continued). 

Coefficients  of  Flow  (in')  of  Water  in  Clean  Cast-Iron 
Pipes  under  Pressure. 


Velocity. 

Diameters. 

14  inch. 

16" 

18" 

20" 

24" 

27" 

.1667  feet 

I-3333'- 

I-5/* 

1.6667'. 

27. 

2.25'. 

Feet  per 
Second. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient . 

Coefficient. 

. I 

. 00730 

. 00700 

. 00670 

.00650 

.00620 

. 00580 

. 2 

.00695 

. 00665 

. 00640 

.00635 

.00580 

•00550 

-3 

. 00670 

. 00640 

.00618 

.00600 

•00550 

.00528 

-4 

.00655 

. 00624 

. 00602 

.00586 

.00538 

.005 16 

-5 

. 00640 

. 00610 

•00590 

•00572 

•00530 

.00508 

.6 

. 00630 

. 00602 

. 00582 

•00563 

•00523 

.00502 

•7 

. 00621 

•00595 

•00574 

•00554 

•00537 

.00497 

.8 

. 00613 

.00588 

. 00568 

.00548 

.00512 

•00493 

•9 

. 00606 

•00584 

•00563 

•00543 

.00508 

.00489 

I.  o 

. 00602 

•00579 

•00559 

•00539 

•00505 

•00485 

1. 1 

.00596 

■00575 

•00555 

•00535 

.OO50I 

.00482 

I.  2 

.0059° 

•00570 

•00551 

•00531 

.00498 

.00478 

!-3 

. 00586 

. 00566 

•00547 

.00528 

.00496 

•00477 

1.4 

. 00582 

.00562 

•00543 

•00525 

.00493 

.00474 

i-5 

.00578 

•00559 

•00540 

•00523 

.00491 

. OO472 

i.6 

•00574 

•00556 

•00537 

.00520 

.00488 

. OO470 

i-7 

.00571 

•00553 

■00535 

.005 18 

.00486 

. 00468 

3.8 

.00568 

•00550 

•00532 

•005I5 

.00485 

. 00467 

1.9 

.00566 

•00547 

•00530 

•00513 

.00483 

•00465 

2.0 

.00563 

•00545 

. 00528 

.00511 

.00482 

.00464 

2.25 

•00557 

•00539 

•00523 

. 00506 

.00478 

. 00461 

2-5 

•00551 

•00533 

•00517 

.00502 

.00474 

.00458 

2-75 

.00546 

•00530 

•00513 

.00498 

.00471 

•00455 

3-o 

.00542 

.00526 

.00510 

•00495 

.00468 

•00453 

3-5 

•00535 

. 00538 

•00503 

.00490 

.00464 

.00449 

4 

•00527 

.00512 

.00498 

•00485 

.00461 

.00446 

5 

•00517 

•00503 

. 00489 

.00478 

•00455 

.00441 

6 

.00509 

. 00496 

.00483 

.00472 

•00450 

•00437 

7 

■00503 

. OO49I 

. 00478 

.00468 

.00447 

•00434 

s 

.00498 

. 00486 

.00475 

•00465 

.00444 

.00431 

9 

.00494 

.00483 

.00472 

.00462 

.OO44I 

.OO429 

10 

.00491 

. 00480 

. 00470 

.00460 

•00439 

.00427 

32 

.00486 

•00475 

•00465 

•oo455 

•00436 

.00424 

14 

.00483 

. OO47 I 

. 00460 

•00452 

•00433 

.00421 

36 

•00477 

.00467 

•00456 

.00449 

•00430 

.00438 

38 

•00473 

.00464 

■00454 

.00446 

.00428 

.00436 

20 

. OO47 I 

.00461 

•00452 

•00443 

.00426 

.00434 

FLOW  OF  WATER  THROUGH  PIPES, 


245 


TABLE  No.  61  — (Continued). 

Coefficients  of  Flow  (in)  of  Water  in  Clean  Cast-Iron 
Pipes,  or  Smooth  Masonry,  under  Pressure. 


Velocity. 

Diameters. 

30  inch. 

36" 

3'- 

33" 

40" 

44" 

48" 

4'- 

•2.5  feet 

2.75  '• 

3-3333'- 

3.6667'. 

Feet  per 
Second. 

Coefficient. 

Coefficie?it. 

Coeffiicient. 

Coefficient. 

Coefficient. 

Coefficient. 

• 4 

. OO492 

•00475 

•00450 

.00425 

.00404 

•00387 

•5 

.00485 

.00465 

•00443 

.OO42O 

.OO4OO 

•00383 

.6 

.00479 

. 00460 

. 00440 

.00417 

.00398 

.00381 

•7 

.00475 

•00456 

.00436 

.00414 

•00395 

.00380 

.8 

. 0047 1 

.00452 

•00433 

.00412 

•00393 

•00378 

■9 

.00468 

. 00449 

•00430 

.OO4IO 

•00391 

.00376 

1.0 

.00465 

.00447 

.00428 

.00408 

.00390 

•00375 

X.  I 

. 00462 

.00444 

. 00426 

.00406 

.00388 

.00374 

1.2 

.00460 

.00442 

.00424 

.00405 

•00387 

.00373 

i-3 

.00458 

. OO44O 

.00422 

.00404 

.00386 

.00372 

i-4 

.00456 

.00438 

.00421 

.00403 

.00386 

.00371 

i-5 

.00454 

•00437 

. OO42O 

.00402 

•00385 

.00370 

i.6 

•00453 

. 00436 

.00419 

.OO4OI 

.00384 

. 003  7 o- 

i-7 

.00451 

•00435 

.00418 

.OO4OO 

.00383 

. 00369 

i.8 

.00450 

•00434 

.00417 

.00399 

.00383 

. 00369 

i-9 

.00448 

•00433 

. 004x6 

.00398 

.00382 

. 00368 

2.0 

.00447 

.00432 

.00416 

.00398 

.00382 

.00368 

2.25 

.00445 

.00430 

.00414 

.00396 

.00381 

•00367 

2-5 

.00443 

. 00428 

.00413 

•°°395 

.00380 

. 00366 

2-75 

.00440 

.00426 

. OO4I I 

.00394 

•00379 

.00365 

3-° 

.00438 

. OO424 

. OO4IO 

•°°393 

•00378 

.00364 

3-5 

•00435 

. OO42 I 

. 00408 

.00391 

•00376 

■00363 

4 

.00432 

. OO419 

. 00406 

.00389 

•00375 

.00362 

5 

.00427 

•00415 

.00403 

.00386 

.00372 

.00360 

6 

.OO424 

. OO412 

. OO4OO 

•00385 

.00370 

•00358 

7 

.OO42I 

. OO409 

.00397 

.00383 

.00368 

•00357 

8 

.00419 

. 00407 

•00395 

.00381 

.00367 

•00354 

9 

.00417 

.00405 

■00393 

.00379 

•00365 

•00353. 

10 

•00415 

.00403 

.00391 

.00378 

.00364 

.00352 

12 

.0041 1 

.OO4OO 

.00388 

•00375 

.00362 

.00350 

14 

.00408 

.00397 

. 00386 

•00373 

.00360 

.00348 

16 

. 00406 

■00395 

.00384 

•00371 

•00358 

.00347 

18 

.OO404 

•00393 

.00382 

.00369 

•00357 

.00346 

20 

.00403 

. OO392 

. 00381 

.00367 

•00356 

.00345 

946 


FLOW  OF  WATER  THROUGH  PIPES. 


TABLE  No.  61  — (Continued). 

Coefficients  of  Flow  (m)  of  Water  in  Cast-Iron  Pipes,  or 
Smooth  Masonry,  under  Pressure. 


Velocity. 

Diameters. 

54  inch. 

60” 

72" 

84" 

7'- 

96" 

8'. 

4.5  feet. 

s'- 

6'. 

Feet  per 
Second. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

•4 

.00362 

•00344 

.00316 

. OO294 

.00274 

•5 

.00360 

.00342 

•00314 

. OO292 

.00272 

.6 

.00358 

•00341 

•00313 

. OO29O 

.OO271 

•7 

.00357 

•00340 

, .OO312 

.00289 

.00270 

.8 

.00356 

•00339 

.00311 

.00288 

. 00269 

•9 

•00355 

•00338 

.OO3IO 

. 00287 

.00268 

1.0 

•00355 

•00337 

.OO309 

. 00287 

. 00267 

1. 1 

•00354 

■00337 

.00308 

. 00286 

.00267 

I.  2 

•00353 

•00336 

•00307 

.00286 

. 00266 

i-3 

•00352 

.00336 

•00307 

.00285 

.00266 

1.4 

•00352 

•00335 

•00307 

.00285 

.00265 

i-5 

.00351 

•00335 

.00306 

. 00285 

. 00265 

i.6 

•00351 

•00334 

.00306 

.00284 

.00265 

i-7 

.00350 

•00334 

•00305 

. 00284 

. 00265 

i.8 

•00350 

•00333 

•00305 

.00283 

. 00265 

1.9 

.00349 

•00333 

•00305 

. 00283 

. 00265 

2.0 

•00349 

•00333 

•00305 

.00283 

.00264 

2.25 

.00348  • 

■00332 

.00304 

.00282 

.00264 

2-5 

•00347 

.00331 

•00303 

. 00282 

. 00264 

2-75 

.00346 

•00331 

.OO302 

. 00281 

.00264 

3-o 

.00346 

•00330 

.OO3OI 

.00281 

. 00264 

3-5 

•00345 

.00329 

.00300 

.00280 

.00263 

4 

•00343 

.00328 

.OO299 

. OO279 

.00263 

5 

.00342 

•00327 

.OO297 

.00277 

.00262 

6. 

.00340 

•00325 

.00296 

. 00276 

. 00262 

7 

•00338 

.00324 

■00295 

.00275 

.00261 

8 

•00337 

•00323 

.OO294 

.00275 

. 00261 

9 

•00336 

. OO322 

.OO294 

.00274 

. 00260 

10 

•00335 

. OO32I 

.00293 

.00273 

.00260 

12 

.00333 

.00319 

.00293 

.OO272 

.00259 

14 

•00332 

.00317 

.00293 

. OO272 

.00259 

l6 

•00331 

.00316 

.OO292 

.OO27I 

.00259 

18 

•00330 

•00315 

.00292 

. OO27I 

. 00258 

20 

.00329 

•00314 

.OO292 

.00271 

.00258 

COEFFICIENTS  “ m"  AND  " c"  FOR  SMOOTH  PIPES. 


EFFECTS  OF  TUBERCLES. 


24? 


270.  Peculiarities  of  the  Coefficient  (m)  of  Flow. — 

In  the  tables  and  diagram  of  coefficients  (rri)  of  flow  in  pipes, 
as  well  as  in  those  of  coefficients  of  discharge  (c)  through 
orifices,  there  is  variation  in  value  with  each  variation  in 
velocity  of  the  jet.  In  the  case  of  pipes,  there  is  also  a 
variation  with  the  variation  of  diameter  of  jet,  that  equally 
demands  attention. 

It  will  be  observed  in  the  tables  of  experiment  above 
quoted  that  the  coefficient  decreases  as  the  diameter  or 
hydraulic  mean  radius  increases,  and  also  that  with  a 
given  diameter  the  coefficient  decreases  as  the  velocity 
increases;  thus,  with  a given  low  velocity,  we  may  trace 
the  decrease  of  the  coefficient  from  0.0120  for  a half -inch 
pipe  to  0.0027  for  a ninety-six  inch  pipe ; and  with  a given 
diameter  of  one-half  inch  we  may  trace  the  decrease  of  the 
coefficient  from  0.0120  for  .5  foot  velocity  per  second  to 
0.00597  for  14  feet  velocity  per  second,  and  with  a given 
diameter  of  96  inches  we  may  trace  the  decrease  of  the 
coefficient  from  0.0027  for  a velocity  of  .5  foot  per  second 
to  0.00259  for  a velocity  of  14  feet  per  second. 

We  have  then  a large  range  of  coefficients  applicable  to 
clean,  smooth,  and  straight  bores.  When  the  bores  are  of 
coarse  grain,  or  are  slightly  tuberculated,  the  range  is  still 
greater,  and  the  values  of  coefficients  of  the  smaller  diam- 
eters quite  sensibly  affected ; and  if  the  bores  are  very 
rough  or  tuberculated,  the  values  of  coefficient  for  small 
diameters  and  low  velocities  are  very  much  augmented. 

271.  Effects  of  Tubercles. — These  effects,  in  tubercu- 
lated pipes,  as  compared  with  clean  pipes,  are  illustrated  in 
the  following  approximate  table,  which  we  have  endeavored 
to  adjust  to  a common  velocity  of  three  feet  per  second  for 
all  the  diameters.  The  data  for  very  foul  pipes  is  however 
scanty,  though  sufficient  to  show  that  the  coefficients  do  in 


248 


FLOW  OF  WATER  THROUGH  PIPES. 


extreme  cases  exceed  the  limits  given  for  the  small  diam- 
eters ; and  that  conditions  from  clean  to  foul  may  occur, 
with  the  several  diameters,  that  shall  cover  the  entire  range 
from  minimum  to  maximum  coefficients,  and  calling  for  a 
careful  exercise  of  judgment  founded  upon  experience. 


TABLE  No.  62. 


Coefficients  for  Clean,  Slightly  Tuberculated,  and  Foul  Pipes, 

of  Given  Diameters,  and  with  a Common  Velocity  of  3 feet 

c / ( 2 gh  'd  ) i ( 2 gri  i *\ 

per  Second.  ( v — \ - = \ — (-  • 

V ( (4 m)  / / m 1 


Hydraulic 
Mean  Radius, 
S _ d 
C 4 

Diameter. 

__ 

Clean. 

C* 

Slightly 

tuberculated. 

C 

Foul. 

L 

Feet. 

Inches. 

Coe/ vi. 

Coe/ 1,  m. 

Coe/.^  vi. 

.0104 

.0417 

1 

o. 00753 

.0156 

.0625 

3 

4 

•00745 

.0208 

.0834 

1 

•00734 

.0312 

.1250 

.00722 

.0364 

.1458 

.00707 

.0417 

.1667 

2 

.00692 

.0625 

.2300 

3 

.00683 

O.OIO27 

0.04969 

•0833 

•3334 

4 

.00662 

.00962 

.04460 

.1250 

.5000 

6 

.00630 

.00885 

•03650 

.1667 

.666  7 

8 

.00604 

.00830 

•03043 

.2083 

•8334 

10 

.00581 

.00783 

.02650 

.2500 

I. OOOO 

12 

•00559 

.00745 

.02409 

.2917 

1. 1667 

14 

.00542 

.00716 

.02250 

•3333 

I-  3333 

l6 

.00526 

.00690 

.02121 

•3750 

1. 5000 

18 

.00511 

.00665 

.02006 

.4167 

1.6667 

20 

.00496 

.00645 

.01901 

.5000 

2.0000 

24 

.00470 

.00607 

-01755 

• 5 6 2 5 

2.2500 

27 

•00453 

.00582 

.01669 

.6250 

2. 5000 

3° 

.00438 

•00559 

•0x593 

.6875 

2-75°° 

33 

.00424 

•00539 

.01524 

.7500 

3.0000 

36 

.00410 

.00520 

.01466 

•8333 

3-3333 

40 

•00394 

,00496 

•01393 

• 9i67 

3.6667 

44 

•00378 

.00474 

•01330 

I. OOOO 

4.0000 

48 

.00364 

.00456 

.01270 

* Vide  Classification  of  Pipes,  page  *269. 


EQUATION  OF  VELOCITY. 


249 


272.  Classification  of  Pipes  and  their  Mean  Co- 
efficients.— Ii\  ordinary  calculations,  the  mean  coefficient 
for  medium  diameters  and  velocities  may  be  taken,  for  clean 
pipes,  as  .00644  ; for  rough  or  slightly  tuberculated  pipes, 
as  .0082  ; and  for  very  rough  or  very  foul  pipes,  as  .012, 
These  coefficients  apply  approximately  to  pipes  of  about 
five  inches  diameter,  when  the  velocities  are  about  three 
feet  per  second,  reference  being  made  to  the  diameter  of  the 
pipe  itself  when  clean. 

273.  Equation  of  the  Velocity  Neutralized  by  Re- 
sistance to  Flow. — Having  now  developed  the  several 
values  of  rn  as  applicable  to  the  several  conditions  of  pipes, 
we  will  again  transpose  our  equation  and  remove  v,  the 
member  expressing  velocity  of  flow,  to  one  side  by  itself, 
and  we  have  the  equation  of  velocity  of  flow : 


or 


or 


or 


or  v ~ cj  1 ' = c Vri  when  c = V (8) 


In  which  h"=  the  resistance  head,  in  feet. 


I — the  length  of  the  pipe,  in  feet. 
d — the  internal  diameter  of  the  pipe,  in  feet. 

C — the  internal  circumference  of  the  pipe,  in  feet. 
S — the  sectional  area  of  the  pipe,  in  square  feet. 


i — the  sine  of  inclination  = -j. 


r — the  hydraulic  mean  radius  = ^ — -. 


g = 32.2 


250 


FLOW  OF  WATER  THROUGH  PIPES. 


274.  Equation  of  Resistance  Head.— By  transposi- 
tion again  we  have  the  equation  for  that  portion,  7il!,  of  the 
total  head  H included  in  the  slope  i : 


h"  = 


CZmtf 

2g£ 


or 


_ (4m)  M 


-iff  l v 4 Iv 

or  h = m - x h-  = — rr. 

r 2g  c2d 


(9) 


Let  cr  represent  the  maximum  ratio  of  li  to  h,  or  coeffi- 
cient of  resistance  of  entry  of  the  jet  = .5055. 


275.  Equation  of  Total  Head.— Then  for  short  pipes, 

rj  v 2 / l\  v 2 

II  — — + crK-  + m) 

2 a 2a  \ r> 


or7 


and 


also, 


ig  2g 

H={  ! + * + »{)£ 


r/  2<? 
r>  2 g 


v = 


^ ]* 

1.5  + m - 
r 


2gH 


1.5 


(4ra  a)  j 


(10) 

(11) 

(12) 


The  value  of  cr  decreases  with  v and  inversely  with 
increase  of  A". 

276.  Equation  of  Volume. — The  velocity  v having 
been  ascertained,  we  have,  for  volume  of  flow  q per  second, 


v = — and  q = .7854^?) ; 
.7S54a~ 


* Compare  Weisbach’s  Mechanics  of  Engineering,  translated  by  E.  B. 
Coxe,  A.  M.  N.  Y„  1870,  p.  870. 


SUBDIVISIONS  OF  TOTAL  HEAD. 


251 


also,  we  have 


Q - 


.7854 d1 


V2 gHx  j i.5  4-4^- 


d J 
Hdh  )i 


/s-  ( -Hd  H 

or  g = .7854l^x  \^5d  + 4ml\ 

or  approximately 

j )i 


„QK . 72  ( dh" ) i 

q — .78o4c?  X c- j 1 


— .3927 c- 


l 


(13) 


277.  Equation  of  Diameter.  — By  transposition 
again  for  the  value  of  d,  we  have 


db  = 


6.303 


; X j 1.5^  + 


or  approximately,  when  c = V2g  -a  to, 


db  = 


^ and  d — J 

(.3927c)2£  ' .1542ca£' 


(14) 


In  this  last  equation  of  d , the  assistance  of  the  table  of 
velocities  for  given  slopes  and  diameters  (p.  259),  and  the 
table  of  coefficients,  to,  for  given  velocities  and  diameters 
(§  269,  p.  242),  will  be  required,  since  the  unknown  quan- 
tities d and  to  appear  in  the  equation.  The  approximate 
values  of  d and  to  for  the  given  velocity  can  be  taken  from 
the  tables  and  inserted  in  the  right-hand  side  of  the  equa- 
tion, and  a close  value  of  d worked  out  for  a first  approxi- 
mation, and  then  the  operation  repeated  for  a closer  value 
of  d , if  necessary. 

27S.  Equations  of  v,  7i,  d,  and  q,  for  long  pipes.— 

When  pipes  exceed  one  thousand  diameters  in  length  the 
following  simple  formulas  may  be  used,  taking  values  of  to 
from  table  61,  page  242,  and  value  of  2 g = 64.4. 


252 


FLOW  OF  WATER  THROUGH  PIPES. 


V = 

j 2 g7i"d  l 
l Ami  \ 

*=  8.025 

( Ami ) 

(14a) 

7i"  = 

Amlv 2 
2 gd 

- .01553 

d 

(14J) 

d = 

Amid1 

w 

= .01553  4^2 
h 

(14c) 

q = .785Ad2  | l *=  6.302 

( A ml  ' 


j fi/W ) i 
l Ami  1 


(14<2) 


in  which  v,  7i",  and  d,  are  in  feet,  and  q in  cubic  feet  per 
second.  For  equivalent  values  of  d in  inches  and  in  feet, 
see  table  104,  p.  504. 

279.  Many  Popular  Formulas  Incomplete. — The 

fact  that  the  majority  of  popular  formulas  for  flow  of  water 
in  pipes,  as  usually  quoted  in  cyclopedias  and  text-books, 
refer  to  It  + h",  or  in  some  cases  to  7i"  only,  and  not  to  IT. 
has  led  us  to  treat  the  subdivisions  of  H more  minutely  in 
detail  than  would  otherwise  have  been  necessary. 

Serious  errors  are  liable  to  result  from  the  application 
of  such  hydrodynamic  formulae  by  persons  not  familiar 
with  their  origin,  especially  when  the  problem  includes  a 
high  head  of  water  and  short  length  of  pipe. 

280.  Formula  of  M.  Chezy.  — The  formula  of 
M.  Chezy,  proposed  a century  ago,  and  into  which  nearly 
all  expressions  for  the  same  object,  since  introduced,  can  be 
resolved,  refers  to  7i  only,  or  7t  +7i",  and  not  to  H*  When 


stated  in  the  symbols  herein  used,  it  becomes  v = 


* Since  the  value  of  » must  here  he  found  before 


and  h'  are 


known,  h"  has  sometimes  been  assumed  for  simplicity,  to  be  identical  with  U, 

jj 

but  y may  give  a very  erroneous  value  of  i and  consequently  of  v. 


SUB-HEADS  COMPARED. 


253 


As  g is  introduced  in  place  of  2g  in  our  equation,  m'  will 

, m 
equal  — • 

£ 

281.  Various  Popular  Formulas  Compared.— The 

value  of  treating  the  question  of  flow  of  water  in  pipes  in 
detail  may  perhaps  best  be  illustrated  by  computing  the 
velocity  of  flow  from  our  pipe  P , Fig.  35,  as  it  is  extended 
to  different  lengths,  from  5 feet  to  10,000  feet,  by  a complete 
formula,  with  m at  its  legitimate  value,  and  then  computing 
the  same  by  several  prominent  formulas,  in  the  form  in 
which  they  are  usually  quoted.  (See  Table  No.  63,  p.  254.) 

282.  Sub-lieads  Compared. — If  we  compute  the  total 
head,  to  which  the  velocities,  found  by  the  first  formula  of 
the  table,  are  due,  we  shall  have  the  sub-heads,  as  follows ; 
when  d — 1 foot. 


H=  1 +.505  + 


Lengths  in  Feet. 

5- 

s°- 

IOO. 

IOOO. 

10,000 

Velocities  in  Ft. 
per  Second. 

63.463. 

51. III. 

43-111- 

17.386. 

5-392- 

h 

62.542 

40.568 

28.863 

4.694 

•451 

h 

31- 583 

20.487 

H-575 

2.370 

.228 

Id 

5.878 

38-945 

56-57i 

92.941 

99-33° 

H 

100 .0 

100.0 

100.0 

loo . 0 

100.0 

It  is  here  shown  that  the  values  of  ft  and  ft'  cannot  be 
neglected  until  the  length  of  the  pipe  exceeds  one  thousand 
diameters,  under  the  ordinary  conditions  of  public  water 
supplies. 

In  our  first  length  of  five  feet,  ft  is  about  ten  and  one- 
half  times  ft",  and  li  is  about  five  and  one-half  times  ft". 


254 


FLOW  OF  WATER  THROUGH  PIPES. 


TABLE  No-  63. 

Results  given  by  Various  Formulas  for  Flow  of  Water  in 
Smooth  Fipes,  under  Pressure,  Compared. 

Data.— To  find  the  velocity,  given  : Head , H — 100  feet ; Diameter , d = i foot ; and  Lengths. 
/,  respectively  as  follows : 


Authority. 


Equation  (12)  .. 

Chezy 

Du  Buat  

Prony  (a) 

“ w 

Eytelwein  (a) . . 

“ (*)•• 

£aint  Vennant.. 
D’Aubuisson  (a) 

“ m 

Neville  (a)  . . 

“ (*).. 

Blackwell 

D’Arcy 

Leslie 

Jackson  

Hawksley 


Equations. 


1 i 


(1.5)  + 4 m 

( ghS  i J 

1 \mlC  1 

83.5 (r*  — .03)  „ , i 

* .084c?-*— .03) 


(/,)'- hyp-iog.  (Si+.-e)} 

= (9419.75?-/  + .00665)* — .0816 
= (9978-76  ri  + .02375)*—  .15412 
= (11703.95?-/  + .01698)* — .1308 

= 50  | TT^*/  s 

11 

= 105.926  (r/)11  

= (9579?-/ + .00813)*— .0902  ... 
= 95.6  V ri  


-b 


Hr 


,0234?-  + .0001085/ 
140  (W)1 — 11  {riy  .. 


P 


: 47-9x3 


'tY 


ri 


.00007726  4- 
100  V ri  .... 


.00000162 


1! 


v = 50 c(diy 


v = 48.045 


dh 


/ + 5+^ 


Lengths. 


5 

50 

100 

1000 

10, 00a 

feet 

feet. 

feet. 

feet. 

feet. 

Veloc. 

Veloc. 

Veloc. 

Veloc. 

Veloc • 

63.463 

51. Ill 

43. m 

17.386 

5-392 

223.607 

7O.7IO 

50.000 

15.810 

5.000 

102.918 

81.510 

13.662 

3.9781 

216.94 

68.54 

48.446 

15.258 

4.770 

223.214 

7O.480 

49.792 

15.641 

4.842 

241.778 

76.367 

53.960 

16.975 

5.280 

67.40 

50.00 

40.82 

x5-427 

4-985 

246.171 

73.682 

51.247 

15.232 

4-592 

218.758 

69.II4 

48.845 

15-384 

4.800 

213.761 

67.589 

t 

00 

t>» 

■r 

I5-1I4 

4.780 

62.540 

47.080 

38-75° 

14.780 

4.780 

294.650 

90.263 

63.070 

18.917 

5-5<>7 

214.267 

67-7I5 

47-9x3 

15-140 

4-791 

244. 120 

77-133 

54.640 

17.279 

5-464 

223.607 

70.710 

50.000 

15.810 

5.000 

223.607 

70.710 

50.000 

15.810 

5.000 

62-555 

47.084 

38.724 

14-797 

4-804 

In  which  C = contour  of  pipe,  in  feet ; / = length  of  pipe,  in  feet. 

c = unity  for  smooth  pipes,  and  m = coefficient  of  flow. 

is  reduced  for  rough  pipes.  r = hyd.  mean  radius,  in  feet,  = — • 

4 

d = diam.  of  pipe,  in  feet.  S'  = sectional  area  of  pipe,  in  square  feet 

A" 

H = entire  head,  in  feet.  / = sine  of  inclination,  in  feet,  = — • 

h"  — resistance  head,  in  feet.  v = velocity  of  flow,  in  feet  per  sec. 


PRONY’S  ANALYSIS. 


255 


In  long  pipes,  sufficient  velocity  is  converted  into  pres- 
sure to  reduce  somewhat  the  contraction  of  the  jet  at  its 
entrance  into  the  pipe.  In  very  long  pipes  the  effect  of  this 
contraction  becomes  insignificant  when  compared  with  the 
effect  of  reaction  from  the  walls  of  the  pipe. 

283.  Investigations  by  Dn  Buat,  Colomnb,  and 
Prony. — The  investigations  of  Du  Buat  and  Coloumb  led 
them  to  the  conclusion  that  the  velocity  of  the  fluid  occa- 
sioned a resistance  to  flow,  in  addition  to  that  arising  from 
the  wet  perimeter  of  a channel  or  pipe,  which  is  propor- 
tional to  the  simple  velocity ; and  afterwards  Prony,  coin- 
ciding with  tins  view,  undertook  the  investigation  of  the  two 
coefficients  thus  introduced  into  the  formula  of  resistance  to 
flow. 

Since  their  new  coefficient,  (3,  applied  to  the  simple  velo- 
city and  not  to  the  square  of  the  velocity,  as  does  the  co- 
efficient m,  their  expression,  in  our  symbols,  became 

If—^  = m(^(vt+(3v)-,  (15) 

in  which 

= ovh'  + K') 

284.  Prony’s  Analysis. — Prony  analyzed  the  results 
of  fifty-one  experiments  to  determine  the  values  of  m and  (3, 
including  eighteen  experiments  by  Du  Buat  with  a tin 
pipe  of  about  one  inch  diameter  and  sixty-five  feet  long ; 
twenty-six  experiments  by  Bossut  with  pipes  of  about  oue, 
one  and  one-quarter,  and  two-inch  diameters,  and  varying 
in  length  from  thirty-two  to  one  hundred  and  ninety -two 
feet ; and  seven  experiments  by  Couplet.  Six  of  these  last 
experiments  were  made  with  a five  and  one-quarter  inch 
pipe,  under  a head  less  than  two  and  one-quarter  feet,  and 


256 


FLOW  OF  WATER  THROUGH  PIPES. 


one  witli  a nineteen-inch  pipe  with  a head  of  about  twelve 
and  one-lialf  feet. 

We  have  quoted  above  (§  269)  eight  of  the  experiments 
by  Du  Buat,  nine  of  those  by  Bossut,  and  the  full  seven 
by  Couplet,  and  in  the  first  two  included  the  extremes  so 
as  to  cover  their  entire  range. 

This  was  a limited  foundation  upon  which  to  build  a 
theory  of  the  flow  of  water  in  pipes,  nevertheless  the  attain- 
ments of  this  eminent  investigator  enabled  him  to  deduce 
from  the  limited  data  hypotheses  which  were  valuable  con- 
tributions to  hydrodynamic  science. 

From  these  experiments  Prony  deduced  the  values,  as 
reduced  to  English  measures,  m = .0001061473  ; and  (3  = 
.16327. 

285.  Eytelwein’s  Equation  of  Resistance  to  Flow. 

— Eytelwein,  investigating  the  question  anew,  and  believing 
the  contraction  of  the  vein  at  the  entrance  to  the  pipe  should 
not  be  overlooked,  soon  afterward  modified  the  equation  to 
the  form, 

fi7 

H~^gd  = •000085434  O’  + -2756  v\  (16) 

in  which  c'  refers  to  the  effect  of  the  contraction. 

286.  D’Aubuissoii’s  Equation  of  Resistance  to 
Flow. — D’Aubuisson,  more  than  a half-century  later,  hav- 
ing regard  more  particularly  to  the  experiments  of  Couplet, 
gave  to  m and  (3  values  as  follows  : 

07 

= -000104392  s (tf  + .180449  v).  (17) 

287.  Weisbaeli’s  Equation  of  Resistance  to  Flow. 

— Weisbach,  availing  himself  of  eleven  experiments  of  his 
own  with  high  velocities,  and  one  by  M.  Grueymard.  in  ad- 


UNINTELLIGENT  USE  OF  PARTIAL  FORMULAS.  257 


dition  to  the  titty-one  above  referred  to,  proposed  the  fol- 
lowing formula  as  coinciding  better  with  the  results  of  his 
observations : 


i3\  l v 2 


(.014312 


+ 


.0171 55\  l jf 
Vv  ) d2g‘ 


(18) 


This  coefficient  (a  +—!=-),  which  replaces  4 m in  our  sym- 
' V v' 

bols,  is  founded  upon  the  assumption  that  the  resistance  of 
friction  increases  at  the  same  time  with  the  square  and  with 
the  square  root  of  the  cube  of  the  velocity. 

288.  Transpositions  of  an  Original  Formula. — 
That  Chezy’ s formula  has  been  generally  accepted  as  one 
founded  upon  correct  principles,  we  readily  infer  by  its  fre- 
quent adoption,  transposition  and  modification  in  the  writ- 
ings of  many  philosophers  and  hydraulicians.  Note,  for 
instance,  the  second  formulas  (v)  of  Eytelwein  and  D’Au- 
buisson  in  the  above  table  (No.  63),  and  the  formulas  of 
Beardmore,  Blackwell,  Downing,  Hawksley,  Jackson,  Box, 
Storrow,  and  others,  which  may  be  resolved  into  this  orig- 
inal form. 

289.  Un intelligent  Use  of  Partial  Formulas. — 

That  serious  errors  may  arise  from  an  unintelligent  and 
improper  use  of  these  formulas  is  conspicuously  apparent 
in  the  above  table  of  results,  computed  upon  conditions  in 
the  very  midst  of  the  range  of  conditions  of  ordinary  muni- 
cipal water  supplies.  A full  knowledge  of  the  origin  of  a 
formula  is  essential  for  its  safe  practical  application. 

A solid  body  falling  freely  in  a vacuum  through  a height 
of  100  feet,  acquires  a rate  of  motion  of  only  about  80.3  feet 
per  second,  yet  some  of  the  formulas  appear  to  indicate  a 
velocity  of  flow  exceeding  200  feet  per  second,  through  five 
feet  of  pipe,  under  100  feet  head  pressure. 

17 


258 


FLOW  OF  WATER  THROUGH  PIPES. 


290.  A Formula  of  more  General  Application.— 

Weisbacli  lias  suggested  a more  compreliensive  form  of 
expression  which  includes  the  head  generating  the  velocity 
of  flow  and  the  head  equivalent  to  the  dynamic  force  lost  at 
the  entry  of  the  jet  into  the  pipe,  as  well  as  the  head  balanc- 
ing the  resistance  to  flow  in  the  pipe,  and  therefore  his 
equation  presents  the  equality  between  the  total  head  H. 
and  the  sum  of  the  velocity  and  resistance  heads,  equal 
to  h + 1i  + 7i ". 

Weisbacli  has  also  developed  a portion  of  the  values 
of  m,  varying  with  v,  but  neglecting  the  influence  of  r. 

291.  Value  of  v for  Given  Slopes. — We  have  here- 
tofore insisted  that  m,  as  introduced  into  the  equation,  shall 
approximate  near  to  its  legitimate  value  for  the  given  condi- 
tions. Its  value  for  each  given  diameter,  or  hydraulic  mean 
radius,  r,  depends  upon  the  velocity  of  flow,  and  therefore 
upon  the  slope,  s,  generating  the  velocity. 

To  aid  in  the  selection  of  m from  the  tables  of  m, 
page  242,  we  have  plotted  the  several  velocities  as  ordinates 
with  given  sines  of  slopes,  i,  as  abscissas  for  such  experi- 
mental data  as  was  obtainable,  and  have  taken  the  interme- 
diate approximate  values  of  v from  their  parabolic  curves 
thus  determined  from  the  experimental  data,  and  have 
arranged  the  following  table  of  v ; which  of  course  refers  to 
the  head  A",  balancing  the  resistance  in  the  slope  s. 


Head,  in  feet  per  1,000  feet  length. 


Velocity,  in  feet  per  second. 


FRICTION  HEAD,  PER  1,000  FEET  LENGTH, 
in  smooth,  coated  Cast-iron  Pipes,  for  given  Velocities. 


VELOCITIES  FOR  GIVEN  SLOPES  AND  DIAMETERS.  259 


T A B L E No.  6 4. 


Velocities,  v,  for  given  Slopes  and  Diameters, 
for  Long  Clean  Iron  Pipes. 


H 

/ 

I 

or  v - 

_ /2 gri 

\ VI 

)*■ 

V 2 gH 

\(i  + 

cr ) + m 

L)  s 

Diameters. 

Sine  of 

Slope. 

Slope. 

Yl  inch. 

H" 

I7/ 

iK" 

I V\" 

2" 

.O4I7  ft. 

.0625'. 

.0834'. 

.1250'. 

.1458'. 

.1667'. 

h" 

Velocity. 

Velocity. 

Velocity. 

Velocity. 

Velocity. 

Velocity. 

‘ l 

Ft.  per  sec. 

Ft . per  sec. 

Ft. per  sec. 

Ft.  per  sec. 

Ft. per  sec. 

Ft.  per  sec. 

I 

in 

IOOO 

.OOI 

■23 

•30 

■36 

.46 

.50 

• 54 

I 

t < 

500 

.002 

•34 

•44 

• 53 

.66 

-73 

•79 

I 

333 

.003 

•43 

.55 

.66 

-83 

•90 

.99 

I 

250 

.004 

• 50 

.65 

■ 77 

■97 

1.06 

1. 15 

I 

200 

.005 

.58 

•73 

.87 

I. IO 

1.20 

1.30 

I 

167 

.006 

.64 

.8l 

•95 

1.20 

i-33 

1.44 

I 

143 

.007 

.69 

•87 

1.03 

1. 31 

1-44 

1.56 

I 

125 

.008 

•74 

•95 

I.  II 

1. 41 

1-54 

1.68 

I 

III 

.OO9 

.78 

I.  OO 

1. 18 

1. 51 

1.65 

1.79 

I 

100 

.OIO 

.82 

1.06 

1.26 

1.60 

i-74 

1.88 

I 

( < 

83-3 

.012 

.91 

1. 18 

1.38 

i-75 

1.92 

2.07 

I 

7i-4 

.014 

.99 

1.28 

1. 5i 

1.90 

2.08 

2.24 

I 

62.5 

.016 

1.07 

1.38 

1.63 

2.04 

2.23 

2.4I 

I 

55-6 

.018 

1. 15 

1.47 

1.74 

2.17 

2.38 

2.57 

I 

50.0 

.02 

1.23 

1.56 

1.84 

2.30 

2.52 

2.72 

I 

33-3 

•03 

1.52 

1.96 

2.28 

2.88 

3.  IO 

3-40 

I 

25.0 

.04 

1.78 

2.29 

2.68 

3-40 

3-68 

3-97 

I 

20.0 

.05 

2.00 

2.56 

3.00 

3-83 

4.16 

4.48 

I 

16.6 

.06 

2.20 

2.83 

3-33 

4.22 

4.62 

4-95 

I 

14.3 

.07 

2.40 

3.08 

3.62 

4-59 

5.02 

5.38 

I 

12.5 

.08 

2.58 

3-30 

3-88 

4.88 

5-37 

5.80 

I 

II. I 

.09 

2.75 

3-50 

4-15 

5-20 

5-74 

6.20 

I 

10.0 

.10 

2.9O 

3-74 

4.38 

5-5o 

6.08 

6.56 

I 

8.33 

.12 

3.21 

4.14 

4-83 

6.06 

6-73 

7.27 

I 

7-14 

■ 14 

3-50 

4.48 

5-24 

6.60 

7.32 

7.92 

I 

6.25 

.16 

3-76 

4-83 

5.64 

7-i4 

7.88 

8.55 

I 

5-55 

.18 

4.04 

5.i6 

6.03 

7.60 

8-39 

9. 12 

I 

5.00 

.20 

4.28 

5-48 

6-37 

8.06 

8.92 

9.64 

I 

4.00 

■25 

4-85 

6.23 

7.21 

9.07 

10.07 

10.83 

I 

3-33 

•30 

5-35 

6.85 

8.00 

10.00 

II. IO 

n.95 

I 

2.50 

.40 

6.26 

7-97 

9-33 

11.68 

12.80 

13-70 

I 

2.00 

.50 

7.10 

9.00 

10.50 

13.18 

14.40 

15-34 

I 

1.66 

.60 

7-85 

9.92 

H-54 

14-44 

15.80 

16.83 

I 

1-43 

.70 

8.60 

10.82 

12.60 

15.68 

17.14 

18.30 

I 

1.25 

.80 

9.26 

11.63 

I3-48 

16.78 

18.40 

19.64 

I 

I. II 

.90 

9.84 

12.34 

14-34 

17-83 

19-55 

20.90 

I 

I. OO 

I. OO 

10-35 

13.00 

15-15 

18.83 

20.56 

22.00 

Area  r = .7854 d^,  and  volume  q = vs,  For  table  (104)  of  sectional  areas  see  page  504. 


260  VELOCITIES  FOR  GIVEN  SLOPES  AND  DIAMETERS 


TABLE  No.  64  — (Continued). 
Velocities,  v,  for  given  Slopes  and  Diameters, 
for  Long,  Clean  Iron  Pipes. 


Slope. 

Sine  of 
Slope. 

Diameters. 

3 inch. 

4" 

•3333' • 

6" 

•5'. 

8" 

.6667'. 

10" 

•8333'. 

12" 

1'. 

. h” 

Velocity. 

Velocity. 

Velocity. 

Velocity. 

Velocity. 

Velocity. 

Ft.  per  sec. 

Ft. per  sec. 

Ft. per  sec. 

Ft.  per  sec. 

Ft. per  sec. 

Ft. per  sec. 

I 

in 

IIII 

.0009 

.66 

• 79 

1.00 

1.20 

1. 41 

1.56 

I 

IOOO 

.OOIO 

.70 

.83 

1.05 

1.28 

1.49 

1.65 

I 

< < 

gag 

.OOII 

■ 74 

.88 

I.II 

i-34 

1.56 

i-74 

I 

i « 

§33 

.0012 

• 77 

■92 

I.l6 

1.40 

1.62 

1.82 

I 

( 4 

769 

.0013 

.81 

.96 

1 . 21 

1.46 

1.68 

1.90 

I 

714 

.0014 

.84 

1.00 

1.26 

i-53 

i-75 

1.97 

I 

4 4 

667 

.0015 

.87 

1.04 

1.32 

i-57 

1.82 

2.04 

I 

4 4 

625 

.0016 

.90 

1.07 

1.36 

1.63 

1.88 

2. II 

I 

4 4 

588 

.0017 

•93 

I.II 

I.40 

1.6S 

i-93 

2.18 

I 

4 4 

556 

.0018 

.96 

1.14 

i-45 

i-73 

2.00 

2.25 

I 

526 

.OOI9 

•99 

x- 1 7 

1.49 

1.7S 

2.05 

2.31 

I 

500 

.0020 

I.OI 

1.20 

i-54 

1.S3 

2.10 

2.37 

I 

4 4 

455 

.0022 

1.06 

1.26 

1.62 

1.92 

2.22 

2.49 

I 

4 4 

4i7 

.0024 

I.  II 

i-33 

1.69 

2.01 

2.32 

2.60 

I 

4 4 

385 

.0026 

1. 16 

1.38 

1.76 

2.10 

2.42 

2.72 

I 

4 4 

357 

.0028 

1 . 21 

1.44 

1:83 

2.1S 

2.51 

2.83 

I 

333 

.0030 

1-25 

1.50 

1.90 

2.26 

2.60 

2.94 

I 

286 

.0035 

1.36 

1.62 

2.05 

2.45 

2.82 

3-19 

I 

250 

.004 

L47 

i-75 

2.21 

2.63 

3.02 

3-42 

I 

4 4 

200 

.005 

1.65 

1.96 

2.50 

2.97  ' 

3-4i 

3-84 

I 

4 4 

167 

.006 

1.82 

2.16 

2.76 

3-27 

3-77 

4-23 

I 

4 4 

143 

.007 

1.98 

2-35 

2.99 

3-55 

4.10 

4. 58 

I 

125 

.008 

2.13 

2.52 

3-21 

3.S2 

4.40 

4.92 

I 

4 4 

III 

.OO9 

2.26 

2.68 

3-42 

4.06 

4.68 

5-24 

I 

4 4 

IOO 

.010 

2-39 

2.83 

3.62 

4.30 

4-94 

5-54 

I 

4 4 

83-3 

.012 

2.63 

3-D 

3.98 

4-74 

5-42 

6.0S 

I 

4 4 

71.4 

.OI4 

2.87 

3.40 

4-33 

5-i5 

5-SS 

6.58 

I 

4 4 

62.5 

.016 

3.08 

3-65 

4.65 

5-53 

6.29 

7.0S 

I 

4 4 

55-6 

.018 

3.29 

3-89 

4-95 

5-88 

6.69 

7-52 

I 

4 4 

50.0 

.020 

3-48 

4.13 

5.24 

6.22 

7.08 

7-95 

I 

4 4 

33-3 

•03 

4-30 

5-13 

6.52 

7-75 

8.78 

9.7S 

I 

4 4 

25.0 

.04 

5-03 

5-95 

7-57 

8.94 

10.18 

11.38 

I 

4 4 

20.0 

.05 

5.64 

6.72 

8.50 

10.00 

H-45 

12.73 

I 

4 4 

16.6 

.06 

6.23 

7.42 

9-32 

11. 00 

12-54 

14.05 

I 

4 4 

14-3 

.07 

6. 79 

8.08 

10.12 

11.92 

13.60 

15-22 

I 

4 4 

12.5 

.08 

7-30 

S.69 

10.88 

12.S3 

14.58 

16.28 

I 

4 4 

II. I 

.09 

7.80 

9.24 

11.56 

13.66 

15.70 

17-30 

I 

4 4 

10.0 

.10 

8.25 

9-75 

12.20 

14.40 

16.36 

IS.26 

I 

4 4 

8.33 

.12 

9.10 

10.70 

I3-4° 

15.88 

1S.00 

20.06 

I 

4 4 

7-14 

• 14 

9.84 

11.58 

14.52 

17.16 

19-45 

21.70 

I 

4 4 

6.25 

.16 

10.56 

12.40 

15.58 

18.S6 

20.88 

23.24 

I 

4 4 

5-55 

.18 

11.25 

13.20 

16.56 

19.50 

22.  20 

24.68 

I 

5-00 

.20 

II.9O 

14.00 

17.50 

20.64 

23.50 

26.10 

I 

4 4 

4.00 

.25 

13.36 

15-72 

19.68 

23.30 

26.51 

29.40 

I 

4 4 

3-33 

•30 

14-63 

17-30 

21.65 

25.64 

29.18 

32.45 

VELOCITIES  FOR  GIVEN  SLOPES  AND  DIAMETERS.  261 


TABLE  No.  64  — (Continued). 
Velocities,  v,  for  given  Slopes  and  Diameters, 
for  Long,  Clean  Iron  Pipes. 


Slope. 

Sine  of 
Slope. 

Diameters. 

14  inch. 
1.1667  ft. 

l6" 

I-3333'- 

l8" 

I.SO'- 

2C>" 

1.667'. 

24" 

2'. 

27" 

2.25'. 

h" 

Velocity. 

Velocity. 

Velocity. 

Velocity. 

Velocity. 

, Velocity. 

1 1 

Ft. per  sec. 

Ft . per  sec. 

Ft. per  sec. 

Ft.  per  sec. 

Ft.  per  sec. 

Ft. per  sec. 

I in 

IOOOO 

.OOOI 

.54 

•59 

•65 

.70 

•79 

.86 

I “ 

5000 

.0002 

• 78 

.85 

•94 

I. OI 

I-I4 

1.24 

I “ 

3333 

.0003 

.96 

1.05 

1.15 

1.24 

I-4I 

1-53 

I “ 

2500 

.0004 

1. 12 

I.23 

i-33 

1.44 

1.63 

1.76 

I “ 

2000 

.0005 

1.26 

1.39 

1.50 

1. 6l 

1.82 

1.97 

I “ 

1667 

.0006 

1.38 

i-53 

1.65 

1.77 

2.00 

2.17 

I “ 

1428 

.0007 

1.50 

1.65 

1.78 

I.92 

2.17 

2-35 

I “ 

1250 

.0008 

1.62 

i-77 

1.92 

2.06 

2.33 

2.51 

I “ 

IIII 

.OOO9 

1.72 

1.89 

2.04 

2.19 

2.48 

2.67 

I “ 

1000 

.OOIO 

1. 81 

r-99 

2.15 

2.31 

2.62 

2.82 

I “ 

9°9 

.OOII 

I.9O 

2.09 

2.26 

2.43 

2.75 

2.96 

I “ 

833 

.0012 

1.99 

2.19 

2.36 

2.54 

2.88 

3-io 

I “ 

769 

.0013 

2.08 

2.28 

2.46 

2.64 

3.00 

3.22 

I “ 

7N 

.0014 

2. 16 

2.36 

2.56 

2.74 

3-12 

3-35 

I “ 

667 

.0015 

2.23 

2.45 

2.65 

2.84 

3-23 

3-47 

I “ 

625 

.0016 

2.31 

•2.53 

2.74 

2.94 

3-33 

3.58 

I “ 

588 

.0017 

2.38 

2.61 

2.83 

3-03 

3-43 

3.70 

I “ 

556 

.0018 

2.45 

2.69 

2.91 

3.12 

3-54 

3-8i 

I “ 

526 

.OOI9 

2.52 

2.77 

2.99 

3.22 

3-64 

3-92 

I “ 

500 

.0020 

2.58 

2.85 

3.08 

3-30 

3-74 

4-03 

I “ 

455 

.0022 

2.72 

3-00 

3-23 

3-47 

3-92 

4-23 

I “ 

417 

.0024 

2.86 

3.13 

3-38 

3-63 

4.10 

4-43 

I “ 

385 

.0026 

2.98 

3.27 

3-52 

3-78 

4.27 

4.61 

I “ 

357 

.0028 

3.10 

3-39 

3-65 

3-93 

4-43 

4.80 

I “ 

333 

.0030 

3.22 

3.52 

3-79 

4-07 

4-60 

4.98 

I “ 

286 

.0035 

3-49 

3.82 

4.U 

4.42 

4-99 

5-38 

I “ 

250 

.0040 

3-75 

4.10 

4.42 

4-73 

5-34 

5-74 

I “ 

222 

.0045 

4.00 

4.36 

4.70 

5-04 

5-67 

6.10 

I “ 

200  • 

.0050 

4-23 

4.61 

4-97 

5-33 

5-99 

6.45 

I “ 

182 

.0055 

4-45 

4.85 

5.22 

5-59 

6.29 

6. 78 

I “ 

167 

.0060 

4.66 

5.07 

5-46 

5-86 

6.58 

7.09 

I “ 

154 

.0065 

4.86 

5.29 

5.68 

6.10 

6.85 

7-38 

1 “ 

143 

.007 

5.05 

5.5i 

5-9i 

6-34 

7-io 

7.66 

I “ 

125 

.008 

5.40 

5.90 

6.35 

6.78 

7.60 

8.21 

I “ 

III 

.OO9 

5-74 

6.26 

6.74 

7.19 

8.08 

8.72 

I “ 

100 

.OIO 

6.08 

6.61 

7.12 

7.58 

8.52 

9.19 

I “ 

83.3 

.012 

6.69  ■ 

7.25 

7.82 

8-33 

9-38 

IO.  IO 

I “ 

71.4 

.014 

7-23 

7.85 

8.44 

9.01 

10.15 

10.94 

I “ 

62.5 

.016 

7-74 

8.41 

9.04 

9.64 

10.88 

11.70 

I “ 

55.6 

.018 

8.24 

8.95 

9.61 

10.25 

II-54 

12.43 

I “ 

50.0 

.02 

8.70 

9-45 

10.14 

10.80 

12.15 

13.10 

I “ 

33-3 

•03 

10.72 

11. 61 

12.50 

13-30 

14.96 

16. 10 

I “ 

25.0 

.04 

12.46 

13-50 

14-52 

I5-48 

17.32 

18.70 

I “ 

20.0 

.05 

14.00 

15.10 

16.25 

17-34 

19.40 

21.00 

I “ 

10.0 

. IO 

19.95 

21.65 

23.30 

24.76 

27.50 

29.80 

262  VELOCITIES  FOE  GIVEN  SLOPES  AND  DIAMETERS 


TABLE  No.  64  — (Continued). 
Velocities,  v,  for  given  Slopes  and  Diameters, 
for  Long,  Clean  Iron  Pipes. 


Slope. 

Sine  of 
Slope. 

Diameters. 

30  inch. 
2.5  ft. 

33" 

2.75'* 

36" 
3 • 

40" 

3-3333'- 

44" 

3.6667'. 

48" 

4'- 

ku 

Velocity. 

Velocity. 

Velocity. 

Velocity. 

Velocity. 

Velocity. 

1 1 

Ft. per  sec. 

Ft.  per  sec. 

Ft.  per  sec. 

Ft.  per  sec. 

Ft . per  sec. 

Ft.  per  sec. 

I 

in 

20000 

.00005 

.66 

.70 

.76 

.81 

.87 

■93 

I 

IOOOO 

.OOOI 

•94 

1. 00 

1.07 

1. 16 

1.23 

I.32 

I 

5000 

.0002 

1-34 

I.42 

i-53 

1.64 

i-74 

1.86 

I 

3333 

.0003 

1.64 

1-74 

1.87 

2.01 

2.13 

2.28 

I 

2500 

.0004 

1.89 

2.02 

2. 16 

2.32 

2.45 

2.62 

I 

2000 

.0005 

2.12 

2.26 

2.42 

2.61 

2.75 

2.93 

I 

1667 

.0006 

2.34 

2.48 

2.65 

2.86 

3.01 

3.22 

I 

1 1 

1428 

.0007 

2.53 

2.68 

2.87 

3.0s 

3-3i 

3-50 

I 

1250 

.0008 

2.71 

2.88 

3.07 

3-3° 

3-54 

3.76 

I 

IIII 

.OOO9 

2.8S 

3.06 

3-27 

3-50 

3-76 

4.00 

I 

1000 

.OOIO 

3-04 

3-25 

3-45' 

3-70 

3.96 

4.24 

I 

9°9 

.OOII 

3.20 

3.41 

3-63 

3.87 

4-15 

4-43 

I 

833 

.0012 

3-33 

3-56 

3-76 

4.07 

4-35 

4-65 

I 

769 

.0013 

3.48 

3-70 

3-94 

4.24 

4-52 

4.84 

I 

714 

.0014 

3.61 

3-85 

4.09 

4.40 

4.69 

5.02 

I 

667 

.0015 

3-74 

3.99 

- 4-24 

4-54 

4.S5 

5-19 

I 

625 

.0016 

3-87 

4.12 

+ 38 

4.72 

5-°3 

5-36 

I 

588 

.0017 

3-99 

4.25 

4.52 

4.85 

5.20 

5-53 

I 

556 

.0018 

4.11 

4-37 

4-65 

5-00 

5-36 

5-70 

I 

526 

.OOI9 

4.  22 

4-49 

4-  78 

5-14 

5.51 

5.85 

I 

500 

.0020 

4-33 

4.62 

4.91 

5.28 

5.67 

6.00 

I 

455 

.0022 

4-55 

4.84 

5.15 

5-45 

5.84 

6.30 

I 

4i7 

.0024 

4-75 

5.06 

5-36 

5.78 

6.22 

6.59 

I 

385 

.0026 

4-95 

5-27 

5-6o 

6.03 

6.47 

6.S7 

I 

357 

.0028 

5.14 

5-47 

5-82 

6.24 

6. 70 

7-14 

I 

333 

.0030 

5.32 

5-66 

6.04 

6.48 

6.94 

7.38 

I 

286 

.0035 

5-76 

6.14 

6-53 

7.00 

.7-50 

8.00 

I 

250 

.004 

6.16 

6.58 

6.97 

7-50 

S.00 

S-53 

I 

200 

.005 

6.90 

7.38 

7.7S 

8.40 

S.97 

9-55 

I 

167 

.006 

7.58 

8.09 

8-54 

9-23 

9.84 

10.49 

I 

143 

.007 

8.22 

8-75 

9.26 

9.96 

10.65 

11-35 

I 

125 

.008 

8.80 

9-35 

9-93 

10.66 

11.65 

12.13 

I 

III 

.OO9 

9-34 

9-93 

10.53 

H-34 

12. II 

12.88 

I 

IOO 

.OIO 

9.86 

10.47 

II. 12 

11.95 

12.73 

I3.4S 

I 

83-3 

.012 

10.80 

11.50 

12.  IS 

I3-II 

13-93 

14.S7 

I 

71.4 

.014 

1I.69 

12.45 

13-19 

14.17 

15.04 

16.10 

I 

62.5 

.016 

12.53 

13.30 

14.12 

15.16 

16.0S 

17.10 

I 

55.6 

.018 

13.28 

14.14 

15.00 

16.10 

17.42 

1S.1S 

I 

50.0 

.020 

14.00 

14-93 

15. So 

17.00 

1S.20 

19.30 

I 

45-4 

.022 

14.72 

15-70 

16.60 

17.84 

19. iS 

20.20 

I 

41-7 

.024 

15.42 

16.40 

17.40 

18.60 

20.0S 

21.12 

I 

38.5 

.026 

16.00 

17.19 

18.10 

19-34 

2O.9O 

21.95 

I 

« t 

35-7 

.028 

16.65 

17.70 

1S.80 

20.08 

21. 6S 

22. So 

I 

< « 

33-3 

.03 

17.24 

1S.40 

19-50 

20.84 

22.40 

23.66 

VELOCITIES  FOR  GIVEN  SLOPES  AND  DIAMETERS.  263 


TABLE  No.  64  — (Continued). 


Velocities,  v,  for  given  Slopes  and  Diameters, 
for  Long,  Clean  Iron  Pipes. 


Slope. 

Sine  of 
Slope. 

Diameters. 

54  inch. 
4.5  ft. 

60" 

5'- 

72" 

6'. 

84" 

7'- 

96" 

8'. 

h" 

Velocity . 

Velocity. 

Velocity. 

Velocity. 

Velocity. 

1 l 

Ft.  per  sec . 

Ft.  per  sec. 

Ft.  per  sec. 

Ft.  per  sec. 

Ft.  per  sec. 

I 

in 

1 0000 

.0001 

I.42 

1.56 

1.78 

2.01 

2.23 

I 

5000 

.0002 

2.02 

2.19 

2.51 

2.83 

3-15 

I 

3333 

.0003 

2.46 

2.69 

3-H 

3-46 

3-84 

I 

2500 

.0004 

2.85 

3.10 

3-55 

4.00 

4.46 

I 

2000 

.0005 

3.20 

3-48 

3-98 

4-50 

5.00 

I 

< < 

1667 

.0006 

3-53 

3.84 

4-36 

4.90 

5-47 

I 

< c 

1428 

.0007 

3.82 

4-i5 

4.72 

5-34 

5.89 

I 

« < 

1250 

.0008 

4.08 

4-45 

5.08 

5.69 

6.26 

I 

mi 

.OOO9 

4-3° 

4-73 

5.38 

6.03 

6.63 

I 

< < 

1000 

.OOIO 

4.60 

4-97 

5.60 

6-35 

6.98 

I 

< < 

909 

.OOII 

4.80 

5.23 

6.00 

6.66 

7-30 

I 

< < 

833 

.0012 

5.02 

5-44 

6.25 

6.98 

7.60 

I 

t < 

769 

.0013 

5.24 

5.67 

6.52 

7.28 

7.92 

I 

t < 

714 

.0014 

5-45 

5.88 

6-75 

7-58 

8.20 

I 

< < 

667 

.0015 

5.63 

6.09 

7.00 

7-83 

8.48 

I 

t < 

625 

.0016 

5.72 

6.30 

7.24 

8.10 

8.76 

I 

« t 

588 

.0017 

6.00 

6.50 

7-47 

8.35 

9.04 

I 

< < 

556 

.0018 

6.18 

6.69 

7.68 

8.63 

9-34 

I 

i < 

526 

.OOlg 

6.36 

6.86 

7.90 

8.82 

9.62 

I 

500 

.0020 

6-53 

7.04 

8. 10 

9-°4 

9.88 

I 

455 

.0022 

6.86 

7-38 

8.50 

9.50 

10.40 

I 

417 

.0024 

7.17 

7.70 

8.88 

9-95 

10.88 

I 

385 

.0026 

7-47 

8.03 

9.22 

10.36 

n-33 

I 

357 

.0028 

7-75 

8-34 

9.58 

10.78 

11.76 

I 

333 

.0030 

8.03 

8.64 

9-91 

11. 15 

12.18 

I 

286 

.0035 

8.68 

9-35 

10.72 

12.05 

13.16 

1 

250 

.004 

9.29 

10.01 

11.48 

12.87 

14.10 

I 

i t 

200 

.005 

10.42 

11.24 

12.86 

14.42 

15.80 

I 

167 

.006 

11.42 

12.32 

14.00 

15-92 

17.20 

I 

143 

.007 

12.35 

13-33 

15.10 

17.00 

18.50 

292.  Values  of  h and  h'  for  Given  Velocities. — 

In  Table  65  are  given  tlie  values  of  h and  7i  for  given 
velocities,  wliicli  are  to  be  subtracted  from  II  to  compute 
the  height  of  the  slope  balancing  the  resistance  R. 

The  velocity  being  known  approximately,  its  correspond- 
ing m for  any  given  diameter  may  be  taken  from  the  table 
of  m,  page  242,  and  inserted  in  the  formula : 

1 \ 

v = V2gH  . ( 7)  * 

\1.5  + m -I 

nr 


264 


FLOW  OF  WATER  THROUGH  FIRES. 


TABLE  No.  6 5. 

Tables  of  h and  Ji  due  to  Given  Velocities,  h and  h being 

IN  FEET  AND  V IN  FEET  PER  SECOND, 


Velocity. 

k 

k' 

h + hr 

.80 

.010 

.0050 

.0150 

.98 

.015 

.0075 

.0225 

I-I3 

.020 

.OIOI 

.0301 

1.27 

.025 

.0126 

.0376 

i-39 

.030 

.0151 

.0451 

1.50 

.035 

.0177 

.0527 

1.60 

.040 

.0202 

.0602 

1.70 

.045 

.0227 

.0677 

1.79 

.050 

.0252 

.0752 

1.88 

•055 

.0278 

.0828 

1.97 

.060 

.0303 

.0903 

2.04 

.065 

.0328 

.0978 

2.12 

.070 

•0353 

• 1053 

2.20 

■075 

.0379 

.II29 

2.27 

.080 

.0404 

.1204 

2.34 

.085 

.0429 

.1279 

2.41 

.OgO 

.0454 

•1354 

2.47 

•095 

.0480 

• 1430 

2.54 

.100 

.0505 

•1505 

2.60 

.105 

.0530 

.1580 

2.66 

.110 

.0555 

• 1655 

2.72 

.115 

.0580 

•1730 

2.78 

.120 

.0606 

.1806 

2.84 

.125 

.0631 

.1881 

2.89 

.130 

.0656 

.1956 

2.95 

•135 

.0672 

.2022 

3.00 

.140 

.0707 

.2IO7 

305 

.145 

.0732 

.2182 

311 

.150 

•0757 

.2257 

316 

•155 

.0772 

.2322 

3-21 

.160 

.0808 

.2408 

3.26 

.165 

.0833 

.2483 

3.31 

.170 

.0858 

.2558  ! 

3.36 

•175 

.0883 

.2633 

3.40 

.180 

.O9O9 

.2709 

3.45 

.185 

•0934 

.2784  1 

3-5o 

.I90 

.0959 

.2859 

3-55 

•195 

.0984 

• 2934 

3-59 

.200 

.IOIO 

.3010 

3-68 

.21 

.1060 

.3160 

3.76 

.22 

.1111 

• 3311 

3.85 

•23 

.1161 

• 3461 

3-93 

.24 

.1212 

.3612 

4.01 

•25 

.1262 

.3762 

4.09 

.26 

• 1313 

•3913 

4-17 

•27 

.1363 

.4063 

4-25 

.28 

.1414 

.4214 

4-32 

•29 

.1464 

.4364 

4-39 

•30 

.1515 

.4515 

Velocity. 

h 

h' 

h + h' 

4-47 

•31 

•1565 

• 4665 

4-54 

•32 

.1616 

.4816 

4.61 

•33 

.1666 

.4966 

4.68 

•34 

.1717 

•5117 

4-75 

•35 

.1767 

•5267 

4.81 

•3^ 

.1818 

54i8 

4.87 

•37 

.1868 

•5568 

4-94 

•38 

•I9I9 

5719 

5-01 

•39 

.1969 

• 5869 

5-07 

.40 

.2020 

.6060 

5-14 

.41 

.2070 

.6170 

5-20 

•42 

.2121 

.6321 

5 26 

•43 

.2172 

.6472 

5-32 

•44 

.2222 

.6622 

5.38 

•45 

.2272 

.6772 

5-44 

.46 

.2323 

.6923 

5-50 

•47 

•2373 

.7073 

5-56 

.48 

•2424 

• 7224 

5.62 

•49 

•2474 

•7374 

5.67 

•50 

•2525 

7525 

5-73 

•5i 

•2575 

•7675 

5-79 

•52 

.2626 

.7826 

5.85 

•53 

.2676 

.7976 

5-9° 

•54 

•2727 

.8127 

5-95 

•55 

.2777 

.8277 

6.00 

•56 

.2S28 

.8428 

6.06 

•57 

.2S78 

.8578 

6. ii 

•58 

.2929 

• 8729 

6.17 

•59 

•2979 

.8879 

6.22 

.60 

.3030 

.9030 

6.28 

.6l 

.3080 

.9180 

6.32 

.62 

•3131 

•9331 

6-37 

■63 

.3181 

.0481 

6.42 

.64 

.3232 

.9632 

6.47 

•65 

.3282 

■9782 

6.52 

.66 

•3333 

•9933 

6-57 

.67 

•3383 

1.00S3 

6.61 

•6S 

•3434 

1-0434 

6.66 

.69 

.3484 

1.03S4 

6.71 

•70 

•3535 

1-0535 

6.76 

•7i 

• 35S5 

1.06S5 

6.81 

•72 

.3636 

1 .0S36 

6.86 

•73 

.36S6 

1.09S6 

6.91 

•74 

•3737 

III37 

6-95 

•75 

• 3787 

1.1287 

6.99 

.76 

.3838 

1.1438 

7.04 

•77 

.3SS8 

1.1588 

7.09 

.78 

• 3939 

I-I739 

TABLES  OF  7i  AND  h’, 


265 


TABLE  No.  6 5— (Continued). 

Tables  of  h and  h due  to  Given  Velocities,  h and  h ' being 

IN  FEET  AND  V IN  FEET  PER  SECOND. 


Velocity. 

k 

h' 

h + h' 

Velocity. 

k 

h> 

h + h' 

7-13 

•79 

•3989 

I . 1889 

22.34 

7-75 

3-914 

1 1 . 664 

7.18 

.80 

.4040 

I . 2040 

22.70 

8 

4.O4O 

12.040 

7.22 

.81 

.4090 

I. 2190 

23-05 

8.25 

4. 166 

12.666 

7.26 

.82 

.4141 

1-2341 

23.40 

8.50 

4.292 

12.792 

7.31 

■83 

.4191 

I. 2491 

23-74 

8-75 

4.419 

13.169 

7-35 

.84 

.4242 

I . 2642 

24.07 

9 

4-545 

13-545 

7.40 

.85 

.4292 

1.2792 

24.41 

9-25 

4.671 

13.921 

7-44 

.86 

•4343 

1.2943 

24-73 

9-50 

4-797 

14.297 

7.48 

.87 

•4393 

1-3093 

25.06 

9-75 

4.924 

14.674 

7-53 

.88 

•4444 

I • 3244 

25-38 

IO 

5.050 

15-050 

7-57 

.89 

• 4494 

1-3394 

25-69 

10.25 

5-I76 

15.426 

7.61 

.90 

• 4545 

1-3545 

26.00 

10.50 

5.302 

15.802 

7-65 

.91 

•4595 

I-3695 

26.32 

10.75 

5-492 

16.242 

7.70 

.92 

.4646 

1.3846 

26.62 

II 

5-555 

16.555 

7-74 

•93 

.4696 

1.3996 

26.91 

11.25 

5.681 

16.931 

7.78 

•94 

•4747 

1.4147 

27.21 

11.50 

5.807 

17-307 

7.82 

•95 

• 4797 

1.4297 

27-51 

H-75 

5-934 

17.684 

7.86 

.96 

.4848 

1.4448 

27.8 

12 

6.060 

18.060 

7.90 

•97 

.4898 

1.4598 

28.4 

12.5 

6.186 

18.686 

7-94 

.98 

•4949 

1-4749 

28.9 

13 

6.565 

19-565 

7.98 

•99 

•4999 

1.4899 

29-5 

I3-5 

6.817 

20.317 

8.03 

I 

•505 

1-505 

30.0 

14 

7.070 

21.070 

8.97 

1.25 

.631 

1. 881 

30.5 

14-5 

7.322 

21.822 

9-83 

1.50 

•757 

2.257 

3i-i 

15 

7-575 

22.575 

10.60 

i-75 

.884 

2.634 

31.6 

15-5 

7.827 

23.327 

11. 4 

2 

I. OIO 

3.010 

32.1 

l6 

8.080 

24.080 

n-35 

2.25 

1.136 

3.386 

32.6 

16.5 

8-332 

24.832 

12.6 

2.50 

1.362 

3.862 

33-i 

17 

8.585 

25-585 

13-30 

2.75 

1.389 

4-139 

33-6 

17-5 

8.837 

26.337 

13-9 

3 

I-5I5 

4-515 

34-o 

18 

9.090 

27.O9O 

14.47 

3-25 

1.641 

4.891 

34-5 

18.5 

9-342 

27.842 

15.0 

3-50 

1.767 

5.267 

35-0 

19 

9-595 

28.595 

15-54 

3-75 

1.894 

5.644 

35-4 

19-5 

9.847 

29-347 

16.05 

4 

2.020 

6.020 

35-9 

20 

10.100 

30. IOO 

16.54 

4-25 

2.146 

6.396 

36.8 

21 

10.352 

31-352 

17.02 

4-50 

2.272 

6.772 

37-6 

22 

II. no 

33-no 

17.49 

4-75 

2-399 

7-149 

38-5 

23 

11.615 

34-615 

17.94 

5 

2.525 

7-525 

39-3 

24 

12.120 

36.120 

18.39 

5-25 

2.651 

7.901 

40.1 

25 

12.625 

37  625 

18.82 

5-50 

2.777 

8.277 

40-9 

26 

13- r30 

39  130 

19.24 

5-75 

2.904 

8.654 

41.7 

27 

I3-635 

40.635 

19.66 

6 

3.030 

9.030 

42-5 

28 

14.140 

42.14c 

20.06 

6.25 

3-I56 

9.406 

43-2 

29 

14.645 

43-645 

20.46 

6.50 

3.282 

9.782 

43-9 

30 

15.150 

45-150 

20.85 

6-75 

3-409 

1 10.159 

47-4 

35 

I7-675 

52.675 

21.23 

7 

3-535 

I 10-535 

50-7 

40 

20.200 

60.200 

21.61 

7-25 

3.661 

IO.9II 

53-8 

45 

22.725 

67.725 

21.98 

7-50 

3-787 

11.287 

56.7 

50 

25.250 

75*250 

266 


FLOW  OF  WATER  THROUGH  PIPES. 


293.  Classified  Equations  for  Velocity,  Head. 
Volume,  and  Diameter. — The  coefficients  of  How  for  the 
given  slopes  and  diameters  being  determined,  they,  with 
the  coefficients  of  resistance  of  entry  for  different  forms  of 
entrance,  may  be  introduced  into  the  classified  equations 
for  velocity,  and  their  resolutions  for  head,  volume,  and 
diameter  completed  ; when  the  equations  will  become,* 


r 

I*  , 

t i 

| 1.054  + m^ 

- for  pipes  with  well-rounded  entrances.  (c£) 

r 

* 

| 1.50 5 + ml 
l r J 

- for  pipes  with  square-edged  flush  entrances!  o)  *■ 

f -j 

i 

. 1 1.9 56+m^ 

for  pipes  with  square-edged  entrances  pro-  / 
jecting  into  the  reservoir.  ' J , 

294.  Coefficients  of  Entrance  of  Jet. — Other  values 
of  cr,  for  other  conditions  of  pipe  entrance,  or  other  coef- 
ficients of  velocity  cv,  may  be  taken  from,  or  interpolated 
in  the  following  table,  computed  from  the  formulas, 


TAB  LE  No.  66. 
Values  of  c,  and  c for  Tubes. 


cv  or  c. . 

.980 

•974 

•950 

•925 

.900 

•875 

.850 

.825 

.815 

.800 

•750 1 715 

.700 

cr 

.041 

•054 

.109 

.169 

•25s 

.306 

•383 

.469 

•505 

•563 

.778  ■ .956 

1.041 

1 4 • C .. 

1. 041 

1.054 

1. 109 

1.169 

1-235 

1.306 

1-383 

1.469 

1-505 

1.563 

1.778  j 1.956 

2.041 

* Vide  formulas  for  q and  d in  §486,  page  499. 


TRANSPOSITIONS  OF  FORMULAS. 


267 


295.  Transpositions  of  Formulas.  — In  the  for- 
mulas for  v in  long  pipes  we  have  v = \Z^L  x 

m 4Z 

Since  the  value  of  2 g(=  64.4)  may  be  taken  as  constant  for 
all  usual  pipe  computations,  we  may  take  c as  the  symbol  of 

and  write  v — c\  -yy-  ^ 
m ( 4 l 

for  v and  its  transpositions  as  follows  : 


and  also  several  expressions 


v — c Vri  — \/~-L  x Vri 
m 

V = j/%L  x\*x%  f*=  4.0124] 

m (4  7 ) ( 


dh" ) i 
. ml 


A"  = \ m X 


2^7 


X 


Z 


V'l 


= .06211^8  = 

,2o<$  cZ  .2ocd 


d — j 4m  X 


X - = 06211  ^ 

XA  Ti" 


v"l 


.25e2A' 


l = 


2 g dll' 
4 m-w2 


= 16.1- 


cZA"  .25c- did 


mv 


_ \h"  1 

g = .7854cZ2r  = .3927c  CcZ5  X j-j- j 


(20) 

(21) 

(22) 

(23) 

(24) 


In  which  cZ,  A",  and  Z are  in  feet,  the  rate  v in  feet  per 
second  and  the  volume  5 in  cubic  feet  per  second,  and  values 
of  m may  be  selected  from  Table  No., -61,  .page  242,  and 
values  of  c from  Table  66a,  page  268,  for  the  given  values 
of  d and  v. 

Equivalent  formulas  for  A",  v,  cl,  and  Z,  with  fractional 
exponents,  are  given  in  §298,  page  271. 

A table  of  coefficients,  c,  for  clean,  smooth,  cast-iron 
pipes,  of  Class  C in  roughness,  for  different  diameters  and 
velocities,  is  given  on  page  268  following. 


268 


COEFFICIENTS  FOR  SMOOTH  PIPES. 


TABLE  No.  66a. 

Coefficients  of  Flow  (<r)  of  Water  in  Smooth-Coated,  Cast- 
Iron  Pipes,  under  Pressure,  at  Different  Velocities  and  in 

Pipesof  Different  Diameters.  c = 


Velocity. 

Diameters. 

3A" 

Yz  inch. 

i" 

i Vi” 

.I2S'. 

1 K" 

2" 

.0417  feet. 

.0625'. 

.0833'. 

•1458'. 

.1667'. 

Feet  per 
Second. 

Coefficient. 

Coefficient. 

Coefficient . 

Coefficient . 

Coefficie7it . 

Coefficient. 

. I 

.... 

78. 00 

79.00 

. 2 

78.75 

79-75 

80.80 

■3 

77-50 

78.75 

80.30 

81.25 

82.40 

•4 

79. 00 

80.30 

81.65 

82.60 

83-5° 

•5 

78.35 

80. 10 

81.40 

82.75 

83.70 

84. 60 

.6 

79-25 

81.10 

O 

"f 

00 

83-75 

84.63 

85-50 

•7 

80. 15 

81.90 

83-35 

84. 60 

85-45 

86.40 

.8 

80.86 

82. 70 

84.  I 2 

85-35 

86.  2 1 

87. 10 

•9 

81.51 

83-38 

84. 81 

86.00. 

86. 90 

87-75 

1.0 

82.35 

83-93 

85-47 

86.65 

87-55 

88.35 

1. 1 

82.86 

84.5° 

86.05 

87-25 

88.11 

88.85 

I.  2 

83.40 

85.00 

86. 60 

87.80 

88.61 

89-35 

i-3 

83-93 

85-49 

87. 10 

88.30 

89. 1 1 

89.85 

i-4 

84-43 

85-95 

87-55 

88.75 

89. 60 

90.30 

I-5 

84. 90 

86. 40 

88.00 

89. 20 

90.  02 

90.70 

i.6 

85-35 

86.81 

88. 40 

89. 60 

90.42 

91.  IO 

i-7 

85.80 

87.  20 

88.80 

90.00 

90. 80 

91.45 

i.8 

86.  20 

87.61 

89. 12 

90.39 

91.16 

91.80 

i 9 

86.60 

88. 00 

89.50 

90.74 

91-50 

92.12 

2.0 

87. 00 

88.36 

89.85 

9I-I4 

91.85 

92.46 

2.25 

87.90 

89.  22 

90.  70 

91.90 

92.70 

93.26 

2-5 

88.  70 

90.  OO 

9i-4i 

• 92-65 

93-40 

94.00 

2-75 

89-45 

90. 80 

92.  I I 

93-35 

94.10 

94-65 

3.o 

9°-  T5 

9i-47 

92-75 

94.00 

94.66 

95-36 

3-5 

91  46 

92-75 

93-92 

95  - 1 5 

95.80 

96-33 

4 

92.63 

93-93 

95-0° 

96.15 

96-75 

97- 3 1 

5 

94-74 

95-85 

96. 82 

97-94 

98.50 

99.09 

6 

96.58 

97.62 

98.31 

99.40 

99-95 

100.45 

7 

98.  20 

98-95 

99.70 

100. 63 

IOI.IO 

101.65 

8 

99-5° 

100. 17 

100. 80 

101.80 

102.  26 

102.  70 

9 

100. 58 

101.20 

101. 70 

102.70 

IO3.  12 

103.63 

IO 

101.43 

102.  OO 

102.  60 

103.49 

I03-85 

104-33 

I 2 

102.85 

103.38 

IO3.70 

IO4.  JO 

104-93 

105.40 

14 

103-85 

IO4.  20 

IO4.  70 

105.40 

IO5.7O 

106.  IC 

16 

104. 66 

105.00 

IO5.4O 

106. 00 

106.32 

106. 68 

18 

1 °5 - 35 

105.67 

106.  OO 

106. 50 

106.75 

107. 16 

20 

i°5-75 

106.35 

I06.  36 

106. 80 

XO7.  IO 

107.56 

a/?L  = 

“ in 


V 


d/i" 


For  values  of  m see  Table  Nj  01,  page  242. 


COEFFICIENTS  FOE  SMOOTH  PIPES. 


26Sa 


TABLE  No.  6 6a  — (Continued.) 


Coefficients  of  Flow  (<:)  of  Water  in  Clean  Cast-Iron 


Pipes,  under  Pressure. 


Velocity. 

Diameters. 

3 inch 

4,, 

6 " 

8" 

IO" 

„ 

.25  feet. 

•3333'- 

•5  • 

.6667'. 

•8333'- 

I7. 

Feet  per 
Second. 

Coefficient. 

Coefficient . 

Coefficient. 

Coefficient . 

Coefficient . 

Coefficient . 

. i 

80.75 

82. 00 

84.00 

87. 00 

89.50 

92.  OO 

. 2 

82.50 

83.70 

85.80 

89-50 

92.  IO 

94-5° 

•3 

83.90 

85.20 

87-75 

91.30 

93.60 

96. 22 

• 4 

85.10 

86. 40 

89.25 

92.50 

94-75 

97-35 

•5 

86. 16 

87-54 

90.40 

93-44 

95-75 

98.25 

.6 

87.02 

88.45 

91.40 

94.22 

96-55 

99-  °5 

•7 

87-75 

89.30 

92.25 

95.00 

97-25 

99.72 

.8 

88.54 

90.  IO 

93.00 

95-65 

97.90 

100.33 

•9 

89.25 

VO 

O 

00 

0 

93.68 

96.  28 

98-55 

100. 89 

1.0 

89. 84 

91-43 

94-3° 

96.85 

99.16 

101. 40 

1. 1 

90.41 

92.05 

94. 86 

97-35 

99-65 

101. 89 

X.  2 

90. 96 

92.63 

95-4° 

97.88 

100. 1 7 

102.33 

1-3 

91.42 

93-  J5 

95-9° 

98.36 

100. 63 

102.75 

1.4 

91-  93 

93-63 

96-35 

98. 80 

101.08 

103-23 

i-5 

92-37 

94. 08 

96.77 

99-23 

101.48 

103-55 

i.6 

92-73 

94-5° 

97-17 

99. 61 

101.87 

103. 88 

i-7 

93-25 

94.90 

97-57 

99-97 

102.  20 

104.24 

i.8 

93-63 

95-27 

97.92 

100.  30 

102-55 

i°4-55 

1.9 

94.  OO 

95-65 

98.25 

100. 62 

102. 87 

104.85 

2.0 

94-33 

96. 00 

98.61 

100.  92 

103-15 

105.16 

2.25 

95-12 

96.78 

99-35 

101.61 

103. 80 

105. 80 

2-5 

95-77 

97-45 

IOO.  04 

102.  20 

104.40 

106. 32 

2-75 

96.41 

98. 1 1 

100. 63 

102.65 

104-95 

106. 85 

3-o 

97. 00 

98.63 

101. 16 

103-25 

105.40 

107.30 

3-5 

98.05 

99-63 

102. 1 1 

104. 18 

106. 24 

108. 10 

4 

99.  OO 

100.45 

102.93 

105.00 

106.95 

108. 80 

5 

100. 65 

102.  OO 

IO4.4O 

106.40 

108. 20 

IO9.  9O 

6 

101.79 

io3-  35 

1 °5 - 5 5 

I07-  55 

109. 20 

110.85 

7 

IO3.  OO 

104.50 

106.53 

108. 50 

110.05 

1 1 1. 60 

8 

IO4.  OO 

1 °5 - 35 

107.32 

109.  20 

110.77 

112.25 

9 

104.  76 

106. 10 

108. 03 

109. 72 

in-35 

112.72 

IO 

105.40 

106. 66 

108. 50 

1 10. 1 2 

in-75 

1 13- IO 

12 

106. 40 

i°7-45 

109.38 

no.  90 

112.37 

113.82 

14 

107.03 

108. 10 

109. 90 

III. 50 

112.90 

114.40 

l6 

107.30 

108. 65 

110.50 

I 12.00 

113.40 

115.00 

18 

107. 96 

IO9.  20 

110.85 

II2.50 

113.90 

US-36 

20 

108. 40 

109. 60 

1 1 1. 20 

I 13.  OO 

”4-35 

115.70 

2685 


COEFFICIENTS  FOE  SMOOTH  PIPES, 


TABLE  No.  6 6 a — (Continued.) 


Coefficients  of  Flow  (c)  of  Water  in  Clean  Cast-Iron 
Pipes,  under  Pressure. 


Velocity. 

Diameters. 

14  inch. 

16" 

18" 

20" 

24" 

27" 

1.6667  feet. 

I-3333'- 

1*5/* 

1.666^'. 

2'. 

2.2^'. 

Feet  per 
Second. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

. I 

95.00 

97-5° 

99-5° 

101.50 

106. 00 

IO9.  OO 

. 2 

97. 00 

99.  OO 

IOI.  20 

103-50 

107-75 

no.40 

•3 

98.25 

100.45 

102. 60 

104.75 

108.75 

in. 30 

•4 

99.40 

IQI- 55 

103.70 

1 °5 - 7 5 

109. 67 

I 12.  IO 

•5 

iQO-35 

102.45 

104-45 

i°6-45 

no.40 

112.75 

.6 

IOI.IO 

103. 20 

105. 20 

107. 16 

I 1 1.  OO 

113-30 

• 7 

101.80 

103-85 

105. 80 

107.70 

in-57 

113.80 

.8 

102.37 

104. 42 

106.40 

108.25 

112.05 

114.25 

•9 

102.  92 

104.95 

106. 90 

108.75 

112.50 

114.70 

1.0 

103-45 

105.46 

107.36 

109.  20 

112.93 

H5- IO 

I.  I 

103.90 

105.90 

107. 80 

109.65 

113-25 

115.48 

1.2 

104.40 

106. 30 

108. 20 

I 10. 00 

113.60 

115.82 

1-3 

104. 78 

106. 65 

108.55 

no.  36 

113. 91 

116.13 

1.4 

105.18 

107. 00 

108. 90 

110.  70 

114.23 

116.43 

i-5 

105-50 

107.30 

109. 20 

I II.  00 

114.50 

116. 70 

i.6 

i°5-85 

107. 60 

109.50 

III. 30 

114.76 

116.95 

i-7 

106. 1 7 

107. 90 

109.75 

iri-55 

115.00 

117.20 

i.8 

106.45 

108. 20 

no. 00 

1 1 1. 80 

115.20 

117.40 

1.9 

106.73 

108.45 

110.25 

I 12.  03 

115.40 

117.60 

2.0 

107. 00 

108. 70 

1 10. 50 

1 12. 26 

1 15. 60 

117.78 

2.25 

107.63 

109.25 

1 1 1. 08 

1 12.80 

1 16.02 

1 18. 21 

2-5 

108. 16 

io9-75 

in-53 

113.20 

1 16.46 

118. 60 

2-75 

108.62 

I IO.  2 I 

I I 2.  OO 

113-65 

1 16. 81 

118.93 

3-° 

109.00 

110.65 

1 12. 36 

I I4.OO 

I 17.  I I 

I 19.  22 

3-5 

109. 80 

in-45 

1 13- 1 1 

1 x4-  56 

117.70 

119-73 

4 

110.47 

112.12 

113-73 

115. 10 

1 18. 20 

120.13 

5 

1 1 1. 60 

113-12 

114-75 

1 16. 04 

119.07 

120.85 

6 

112.45 

H3-97 

115-45 

116.75 

119. 60 

121.40 

7 

113.20 

114.63 

1 16. 03 

117.36 

120.  20 

m.85 

8 

H3-75 

ri5-i5 

116.45 

H7-75 

120. 60 

122.20 

9 

1 14. 18 

H5-55 

116.75 

118. 10 

120.85 

122.50 

IO 

114.5° 

115.86 

117.05 

118.45 

121.10 

122.85 

12 

1 x5- 25 

116.47 

117.66 

I I9.  OO 

121.60 

I23-35 

14 

115.80 

1 1 7.00 

118.25 

119.50 

122.00 

123-75 

l6 

116.32 

H7-45 

118.65 

119.90 

122.  25 

124.09 

r8 

116.65 

1 1 7. 80 

119. 06 

120.35 

122.  50 

124.40 

20 

I I 7.  OO 

118.25 

119-45 

1 20. 60 

122.75 

124.70 

COEFFICIENTS  FOE  SMOOTH  PIPES. 


268c 


TABLE  No.  6 6a  — (Continued.) 


Coefficients  of  Flow  (<r)  of  Water  in  Clean  Cast-Iron 
Pipes,  under  Pressure. 


Velocity. 

Diameters. 

30  inch. 

33" 

36" 

3'- 

40" 

44" 

48" 

a'  ' 

2.5  feet. 

2.75'- 

3-3337- 

2.6667'. 

Feet  per 
Second. 

Coefficient. 

Coefficient . 

Coefficient . 

Coefficient. 

Coefficient. 

Coefficient. 

. i 

HI. 5° 

114.5° 

I 17.  OO 

I 2 I.  OO 

I 24.  OO 

127.00 

. 2 

I 13.  OO 

H5-75 

118.25 

122.00 

125.20 

128.00 

•3 

I I4.  OO 

1 16. 70 

I 19.  12 

122. 70 

I25-85 

128. 70 

•4 

114.83 

117.40 

120.00 

123.30 

126.40 

i29-33 

•5 

ii5-4o 

1 18. 00 

120. 63 

123-85 

126.85 

1 29. 67 

.6 

1 16. 00 

118.45 

I 2 I . IO 

124.3° 

127.25 

I30.  OO 

•7 

116.50 

1 18. 90 

121. 60 

124. 70 

127.60 

130.30 

.8 

1 16. 90 

119.3° 

122.  OO 

125.04 

127.90 

130.60 

•9 

H7-33 

119.63 

122.36 

125-33 

128. 20 

130-83 

T.O 

117.70 

120.00 

122.65 

125-65 

128.50 

1 3 1. 00 

1. 1 

1 18. 00 

1 20. 25 

122.93 

125.90 

128. 70 

131.20 

1.2 

118.30 

1 20. 50 

123.18 

126. 12 

128.86 

i3I-36 

i-3 

1 18. 60 

120.75 

123.40 

1 26. 30 

I29.  O4 

131-5° 

1.4 

118.85 

121.00 

123. 60 

126.47 

I29.  20 

i3I-63 

i-5 

I I9.  IO 

121.25 

123-75 

1 26. 63 

129.32 

I3I-  76 

i.6 

119.30 

121.43 

123.90 

126.76 

129.42 

131.86 

I-  7 

119.50 

121.60 

124. 05 

126.88 

I29-  55 

131.96 

i.8 

1 19.  70 

121.80 

1 24. 20 

127.00 

129.64 

132.06 

1.9 

1 19. 86 

121. 96 

124.31 

127. 1 1 

129.72 

132-15 

2.0 

120.  04 

122.  I I 

124.43 

127.21 

129.80 

132.24 

2.25 

120.  32 

122.42 

124. 70 

127.48 

130.  OO 

132.46 

2-5 

120.51 

122.75 

124.92 

127.67 

I30.  20 

132-65 

2-75 

120.90 

I23.  OO 

125. 11 

127. 86 

i3°-35 

132.82 

3-o 

121. 12 

123.25 

125.29 

1 28. 00 

i3°-5° 

i33-oo 

3-5 

121. 60 

123.60 

125.63 

128.32 

130. 82 

I33-36 

4 

122.0  O 

I24.  OO 

125-93 

128.60 

131-1° 

1 33- 5 1 

5 

122. 60 

1 24. 5 5 

126. 50 

129.03 

131-5° 

133-9° 

6 

123.20 

125.07 

126.95 

129.41 

131-85 

134.20 

7 

123.62 

125.50 

127.40 

129.70 

132.16 

i34-5o 

8 

I24.  OO 

125.85 

127-75 

130.  CO 

132-45 

134.80 

9 

124.30 

126. 12 

1 28. 00 

I3°-  3° 

132-75 

i35-o5 

10 

124. 60 

126.40 

128.25 

J3°-  55 

133-0° 

135-26 

12 

125. 20 

126.90 

128.73 

131.00 

133-40 

I35-65 

14 

125. 60 

127.30 

129. 16 

131.40 

133-80 

136.00 

l6 

126.00 

127.60 

129.50 

1 3 1 - 7 5 

134.10 

136-25 

18 

126. 30 

128. 00 

129.80 

132.10 

134-3° 

136.42 

20 

126.54 

128.25 

I30.  OO 

132-5° 

134-5° 

136.65 

t 


268cZ 


COEFFICIENTS  FOK  SMOOTH  PIPES. 


TABLE  No.  66a.  — (Continued). 

Coefficients  of  Flow  ( c ) of  Water  in  Cast-Iron  Pipes,  or 
Smooth  Masonry,  under  Pressure. 


Velocity. 

Diameters. 

54  inch. 

60" 

72" 

84" 

l'  • 

96" 

8'. 

4.5  feet. 

s' • 

6'. 

Feet  per 
Second. 

Coefficient. 

Coefficient . 

Coefficient. 

Coefficient. 

Coefficient. 

. i 

I3I-4° 

134-5° 

140.5° 

145.80 

i5°-5° 

" . 2 

132.  20 

135-36 

141.5° 

146. 80 

1 5 1 - 75 

•3 

132. 80 

136.00 

I42.  20 

147-5° 

152-65 

•4 

133-3° 

136.48 

142.  70 

148. 00 

i53-4° 

•5 

I33-65 

136.91 

143.18 

148.45 

i53-9° 

.6 

134.00 

137-3° 

x43-  55 

148.  78 

i54-3° 

•7 

r34-25 

137.60 

x43-85 

149. 10 

154-65 

.8 

134-49 

137-84 

144. 12 

I49-36 

154.9° 

•9 

134-7° 

138-05 

x44- 35 

149.60 

I55-I5 

I.  o 

134.86 

138. 22 

144-55 

149.76 

I55-32 

1. 1 

i35-°2 

138.40 

144-65 

149-95 

155-42 

1.2 

I35-I5 

138-52 

144-75 

150.09 

I55-52 

i-3 

135-27 

138-65 

144.9° 

150. 18 

i55-6o 

1.4 

135-4° 

I38-75 

145-°° 

150. 28 

155-65 

i-5 

I35-48 

138-83 

145. 10 

i5°-36 

i55-7° 

i.6 

135-55 

138.91 

145.20 

x5°-43 

155-74 

i-7 

135-63 

x38- 98 

I45-27 

x5°-5° 

x55- 77 

i.8 

135-7° 

139.04 

x45-  S2 

x5°-57 

i55-8o 

1.9 

135-77 

139.1° 

145-37 

x5°-63 

155-83 

2.0 

I35-83 

139. 16 

145-41 

150.70 

155-87 

2.25 

136. 00 

x39-3i 

1 45  - 5 7 

i5°-85 

155-95 

2-5 

136. 16 

1 39-45 

i45-7° 

151.°° 

156-05 

2-75 

136-32 

139.60 

145-87 

I5I-  x5 

156. 18 

3-o 

136-47 

139-72 

146. 00 

i5i-3° 

156-25 

3-5 

I36-75 

139.92 

146. 26 

151-56 

156.40 

4 

137.00 

140.  I 2 

146.5° 

1 5 x-  80 

156.5° 

. 5 

I37-42 

140. 46 

146. 90 

152.20 

156-65 

6 

137-75 

140. 70 

147-25 

x52-  5° 

156.80 

7 

138. 00 

140. 96 

147-5° 

152-75 

i56-9i 

8 

138.21 

141. 2 I 

147-75 

x53-°° 

157.08 

9 

138.40 

141.46 

147. 91 

153- J5 

157.20 

IO 

138. 60 

141. 66 

148.03 

x53-3° 

157-3° 

I 2 

138.96 

I 42.  IO 

148. 22 

153-52 

157-52 

14 

139.28 

142.40 

148.32 

x53-67 

i57-7° 

16 

139-55 

142. 70 

148. 40 

153-73 

157.80 

18 

139-7° 

I 42. 9O 

148.45 

t53-8o 

157.9° 

20 

139.82 

143.00 

148. 50 

153-9° 

158.00 

COEFFICIENT  “ C ” FOR  PIPES,  CLASSIFIED  IN  ROUGHNESS, 

for  a Velocity  of  about  three  feet  per  second. 


CLASSIFIED  RESISTANCES. 


269 


296.  Frictional  Resistances  Classified. — The  co- 
efficients m given  in  Table  No.  61,  and  c in  Table  No.  66a, 
are  adapted  to  computations  of  how  in  clean,  smooth- 
coated  cast-iron  pipes  as  ordinarily  used  in  public  water- 
supply  systems.  Some  new  smooth-metal  varnished  pipes 
have  coefficients  of  less  values  of  m and  greater  values  of 
c,  and  some  rougher  pipe  materials  have  coefficients  vary- 
ing in  the  opposite  directions.  When  pipes  are  tested  for 
how  and  their  coefficients  developed  the  respective  coeffi- 
cients show  with  much  precision  the  relative  roughnesses 
of  the  pipes. 

The  large  pipes  most  commonly  used  are  as  follows, 
with  classihcation  designated  by  letters  : 

A.  Yery  smooth  metal  pipes  asplialtum  varnished. 

B.  Thin  riveted  or  cast-iron  pipes,  smoothly  varnished. 

C.  Clean,  smooth,  coated  cast-iron  pipes.  (Standard  of 
Roughness. ) 

D.  Cement-lined  iron  pipes. 

E.  Yitrihed  stoneware  pipes. 

F.  Wood  stave  pipes. 

G.  Slightly  tuberculated,  or  rough-coated  cast-iron 
pipes,  and  large  steel  pipes  with  boiler  rivets. 

H.  Beton  Coignet  pipes. 

I.  Brick  and  brick-linecl  pipes. 

J.  Rough  brick-lined  pipes. 

K.  Foul  tuberculated  cast-iron  pipes. 

L.  Yery  foul  pipes  with  bends  and  valves. 

Table  No.  665  gives  approximate  coefficients  c for  these 
several  classes  of  pipes,  A to  L,  for  medium  velocities  of 
how  and  for  the  several  standard  diameters  from  four  to 
ninety-six  inches. 

The  coefficients  c may  be  used  in  the  above  formulas  for 
v,  h,  d , and  l,  Nos.  20  to  24,  inclusive. 


269a 


FLOW  OF  WATER  THROUGH  PIPES, 


TABLE  No.  66b. 

Coefficients  for  Pipes  of  Classified  Roughness. 


For  medium  velocities  of  about  three  feet  per  second. 


Diara. 
in  inches. 

d 

in  feet. 

A. 

c 

B. 

c 

c. 

c* 

D. 

c 

E. 

c 

F. 

c 

4 

•333 

105.40 

103. 1 

98.6 

94.8 

91.4 

88.3 

6 

•5 

108.25 

106. 1 

101. 1 

97-7 

94-4 

9I.2 

8 

.667 

no.75 

108.7 

103-3 

100.3 

97.0 

93-8 

IO 

•833 

112.85 

1 1 1.0 

105-3 

102.3 

99.2 

96.0 

12 

1.0 

115.00 

113.0 

107  2 

104-3 

I0I.2 

9S.1 

14 

1.167 

1 17.20 

II5.0 

IO9.O 

106.2 

103.0 

100.0 

l6 

1-333 

119.15 

117.0 

110.6 

107.8 

104.7 

101.7 

18 

i-5 

121.25 

118.9 

112.3 

109.5 

106.4 

103.4 

20 

1.667 

123.  IO 

120.  7 

II3-9 

III. I 

108.0 

105.0 

22 

1-833 

124.90 

122.4 

H5-4 

II2.5 

109.4 

106.6 

24 

2.0 

126. 70 

124. 1 

117.0 

II4.0 

1 1 0.9 

10S.1 

27 

2.25 

129.30 

126  5 

I 19.2 

116.3 

113-1 

1 10.3 

30 

2.50 

131.80 

128.8 

121.3 

118.4 

II5.2 

II2.4 

33 

2.75 

134-30 

131-1 

123.3 

120.4 

117.2 

114-5 

36 

3-0 

136.70 

133-3 

125.3 

122.4 

II9.2 

1 16.5 

40 

3-333 

139-70 

136-1 

127.9 

125.0 

121.8 

II9.O 

44 

3.667 

142.60 

138.9 

130.5 

127.5 

124.2 

121.6 

48 

4.0 

145-20 

I4I-4 

133.0 

129.9 

126.S 

123.8 

54 

4-5 

149-15 

145-2 

136.4 

133-3 

130.3 

127.2 

60 

5-0 

152.70 

148.6 

139.6 

136.6 

133-7 

130.5 

72 

6.0 

159-50 

155-3 

145.8 

142.6 

1 39- 7 

136.6 

84 

7.0 

165.80 

161.8 

I5I-3 

14S.0 

I45-I 

I42.O 

96 

8.0 

172.00 

168.0 

156.2 

i53-o 

149-8 

146.8 

* The  corresponding  values  of  m — for  Class  C will  be  found  in  Table 
No.  61,  page  243,  in  the  line  of  velocity  = 3. 


If  tlie  coefficient  is  desired  for  some  otlier  than  the  three 
feet  per  second  to  which  the  above  table  is  adjusted,  then 
let  v'  and  c'  be  the  new  velocity  and  coefficient.  We  have 
then  their  proportionate  values 

c & 

: : — = : — — , from  which  we  have  in  like  diameter, 
Vri  Vr'i' 


c'  = c—  X 

V 


vr 

Vi 


and 


c = 


c,vVi^ 

v'  Vi' 


v : v 


COEFFICIENTS  CLASSIFIED. 


2695 


TABLE  No.  66  b— (Continued). 

Coefficients  for  Pipes  of  Classified  Roughness. 


Diam. 
in  inches. 

d 

in  feet. 

G. 

c 

H. 

c 

I. 

c 

J- 

c 

K. 

c 

L. 

c 

4 

•333 

81.8 

75.8 

67:8 

58.0 

45-6 

38.0 

6 

•5 

85.6 

80.3 

71.8 

6l.O 

51.0 

42.0 

8 

.667 

88.4 

83-3 

75-0 

64.0 

55-o 

46.0 

10 

.833 

90.7 

85.8 

77-5 

67.0 

58.2 

49-3 

12 

1.0 

93-o 

88.2 

8 0.0 

69.2 

6l.O 

5i-7 

14 

1.167 

94-9 

90.3 

82. 1 

71-5 

63-5 

53-5 

16 

1-333 

96.6 

92.0 

84.1 

73-5 

65-5 

55-1 

is 

1-5 

98.4 

93-8 

85-9 

75-3 

67-3 

56.8 

20 

1.667 

100.0 

95-5 

87.6 

77.0 

69.0 

58.2 

22 

1-833 

101.4 

97.0 

89. 1 

79.0 

70.6 

59-5 

24 

2.0 

103.0 

98.7 

90.6 

80.5 

72.0 

61.0 

27 

2.25 

'105.2 

IOI.O 

92.6 

82.4 

74  0 

62.1 

30 

2 5 

107.3 

103.2 

94-7 

84.0 

75-9 

63-3 

33 

275 

109.3 

105.3 

96.6 

86.0 

77.6 

65.0 

3& 

3-0 

III. 3 

107.3 

9S.4 

87.7 

79-2 

66.5 

40 

3-333 

114.0 

IIO.O 

100  7 

90.0 

81.3 

68.0 

44 

3.667 

116.6 

112.4 

103  0 

92.0 

83.2 

69.6 

48 

4.0 

1:8.8 

1 14.8 

105.2 

94.0 

85.0 

71.0 

54 

4-5 

122.2 

118.3 

108.5 

96. 2 

S7-3 

73-4 

60 

5-0 

125-5 

121.6 

m. 3 

99-o 

89.6 

75.0 

72 

6.0 

131.8 

127.8 

117.0 

103-3 

93-9 

78-5 

84 

7.0 

137-5 

133.2 

122.2 

107.5 

97.6 

81.6 

96 

8.0 

142.8 

138.0 

126.8 

III. 2 

IOI.O 

85.0 

The  table  and  diagram  of  classified  coefficients,  c,  illus- 
trate also  the  transitions  of  pipes  from  class  to  class  and 
reductions  of  c with  increasing  age  of  each  pipe.  There  is 
a gradual  increase  in  roughness  of  Pipe  Walls,  as  their 
tubercles  grow  in  soft  water  or  lime  incrustations  increase 
in  hard  water  from  Class  B,  through  the  successive  rougher 
classes  C,  D,  E,  F,  Gr,  and  many  pipes  in  process  of  time 
reach  the  decided  roughness  of  Class  L. 


270 


FLOW  OF  WATER  THROUGH  PIPES. 


296a.  Modified  Chezy  Formula. — The  discussions 


of  velocities  of  flow  in  channels,  pages  315  and  329,  indicate 
that  the  Chezy  factors  of  resistance  head,  in  pipes  (pages 
229,  233),  may  be  more  precisely  stated  as  follows  : 


The  effects  of  the  reactions  from  a given  unit  area  of  the 
contour  are  not  alike  upon  all  the  particles  of  water  in  the 
section.  Experiments  indicate  that  the  reactions  from  any 
point  of  contour  upon  any  given  particle  of  water  varies 
between  the  cube  root  and  the  square  root  of  the  distance  of 
the  particle.  The  resultant  reactions  from  a unit  length  of 
(7''5/C 

pipe  are  nearly  as  and  their  frictional  effect  in* 

creases  nearly  with  the  square  of  the  velocity  of  flow. 

The  corresponding  formula  for  velocity  in  a Class  C,  or 
smooth  pipe,  is 


Symbols  may  be  used  as  before  for  the  compound  fac- 


to diameter  d in  feet.  Then,  since  r in  circular  pipes  is  in 
all  cases  equal  one-fourtli  d , 


(24) 


(25) 


v = n(i . 4r 


(28) 


MODIFIED  COEFFICIENTS. 


270 a 


also,  v —f(i  . r Vr)^  = cirif 


(28a) 


The  effect  of  the  additional  factor,  as  above,  is  to  greatly 
reduce,  except  in  small  pipes,  the  variableness  of  the  co- 
efficient n,  as  compared  with  m and  c. 

To  illustrate  the  relative  values  of  the  coefficients, 
assume  l = 1000  feet  and  v — 3 feet  per  second,  and  vary 
diameter. 


d 

1.0  ft. 

2.0  ft. 

4.0  ft. 

8.0  ft. 

m 

.00560 

.00468 

.00364 

.00264 

c 

107.30 

1 1 7. 1 1 

133.00 

i56-25 

n 

53-^5 

49-5° 

46.9 

46.45 

f 

I5  :-^9 

140.00 

133.00 

131.4° 

h 

3-I27 

1.312 

•5°9 

.184 

with  diameter  constant  at  1 foot  and  velocity  varied,  the 
values  of  n for  different  velocities  are 

v — 0.5  v — 3 v — io  v = 20 

n — 49-I25  « = 53-65  ^ = 56.55  n — 57.85 

In  Class  C pipes,  n and  f are  nearly  constant,  for 
medium  velocities,  in  all  pipes  exceeding  3 feet  diameter. 

A general  approximate  formula  for  such  pipes  is 


In  smaller  pipes  the  values  of  n and  f for  medium 
velocities  increase  as  d is  reduced,  as  follows : 

diam.  I 36,;  I 30 n I 27''  I I 20"  I 18"  I 16"  I 12"  ior/  I 8/;  I 6/; 

n 47.6  48.3  48.8  49.5  50.5  51. 1 51.8  I 53.7  55-°  56.7  59-5 

/ I 134.6  I 136.6  | 138.0  I 140.0  | 142.8  | 144.5  I t46-5  I 151.9  155-5  I x6o.4  I 168.2 


(29) 


or 


v — 133(f  . r V r)K 


(29  a) 


LOGARITHMIC  DIAGRAM  OF  VELOCITIES, 


'270& 


LOGARITHMIC  DIAGRAM. 


LOGARITHMIC  DIAGRAM. 


271 


If  the  frictional  resistance  varied  truly,  in  pipes  of  one 
class  of  roughness,  as  r2  and  d'-\  then  the  value  of  n would 
be  constant  at  about  50. 

297.  Constant  Coefficients. — Tne  desirability  of  a 
general  formula,  for  flow  of  water  in  pipes,  that  is  con- 
veniently useful  without  an  assisting  diagram  of  coefficients 
has  long  been  recognized.  Searches  for  such  expressions 
have  been  made  by  prominent  engineers,  and  the  most 
useful  expressions  have,  perhaps,  been  those  in  which  the 
variable  relations  of  diameter,  d,  and  velocity,  v,  to  a given 
inclination,  i,  of  the  pipe  have  been  indicated  by  the  ex- 
ponents given  to  those  terms,  leaving  a coefficient  b,  con- 
stant or  approximately  constant. 

These  exponential  formulas  as  written  by  Hagen,  Prof. 
Unwin,  M.  Flamant,  and  other  eminent  mathematicians 
have  been  reduced  to  the  following  form  by  Win.  E.  Foss, 
C.E.,  viz., 

vn 

l = (30) 

This  class  of  formulas  is  very  useful  for  approximate 
computations.  The  writer  found  the  constant  exponents 
and  coefficients  to  be  applicable  in  pipes  only  within 
limited  ranges  of  velocities  and  diameters,  and  constructed 
a table  of  b,  n,  and  m,  adapting  one  set  to  each  standard 
diameter  of  pipe,  as  in  Table  Ho.  66c,  following. 

298.  Logarithmic  Diagram.  — A logarithmic  di- 
agram of  velocities  of  flow  in  Class  C pipes,  for  given  in- 
clinations and  diameters,  may  be  readily  constructed  from 
Table  No.  64,  page  260,  of  velocities,  or  from  the  diagram 
opposite,  of  velocities  for  given  heads  per  1000  feet,  thus : 

On  a sheet  ruled  in  squares  (say  one  inch  each)  start 
with  zero  near  the  left-hand  lower  corner  and  write  the 


271a 


FLOW  OF  WATER  THROUGH  PIPES. 


logarithmic  scale  for  inclinations,  or  sines  of  slope,  as 
abscissas  horizontally,  and  from  the  same  zero  point  the 
logarithmic  scale  for  diameters  as  ordinates  on  the  per- 
pendicular line.  Then  for  each  given  diameter  plot  each 
given  sine  of  slope  as  an  abscissa  and  each  corresponding 
velocity  as  an  ordinate.  The  series  of  plotted  points  for 
velocities  in  each  given  diameter  will  lie  approximately  in 
a straight  line.  A straight  line  for  each  diameter  may  be 
thus  placed  on  the  logarithmic  diagram  and  the  logarithms 
of  velocities  read  from  it  for  the  logarithms  of  any  inclina^ 
tions  chosen.  The  diagram  Avill  thus  solve  at  sight  ques- 
tions of  inclinations  for  given  velocities  and  of  velocities 
for  given  inclinations  in  any  one  pipe  of  Class  C,  or  pipes 
of  like  degree  of  roughness  of  the  same  diameter. 

The  ratio  of  inclination  of  each  diameter  line  gives  the 
value  of  the  exponent  n of  v,  and  may  be  readily  found 
from  the  scale  diagram.  The  logarithm  of  the  inclination 
■i,  that  gives  velocity  equal  one  foot  per  second  in  any 
given  pipe,  is  found  at  the  intersection  of  the  line  for  that 
diameter  with  the  horizontal  line  0,  which  is  the  logarithm 
of  1. 

Plot  upon  the  diagram  diameter  points,  taking  as 
abscissas  the  logarithms  of  i corresponding  to  v = 1 for 
each  of  the  series  of  diameters,  and  as  ordinates  the  loga- 
rithms of  the  same  respective  diameters,  and  draw  a line 
through  these  diameter  points.  This  line  will  be  curved. 
Draw  a tangent  from  the  curve  at  each  diameter  point, 
letting  the  tangent  cut  the  horizontal  line  0,  of  the  scale. 
The  ratio  of  inclination  of  each  tangent  line  to  line  0 will 
give  the  exponent  m of  the  corresponding  d,  and  the  point 
of  intersection  of  the  tangent  with  line  0 will  indicate  the 
logarithm  of  the  natural  number  b,  the  coefficient. 


LOGARITHMIC  FORMULAS. 


2716 


It  is  observed  that  the  diameter  lines  for  velocity  are 
not  parallel,  therefore  the  exponents  n are  not  precisely 
alike  for  like  velocities  in  different  diameters.  It  is  ob- 
served that  the  line  through  the  diameter  points  is  curved, 
therefore  the  exponents  m for  d and  the  coefficients  b for 
different  diameters  are  not  precisely  alike  for  like  inclina- 
tions. The  exponents  as  thus  taken  from  the  diagram  in- 
crease from  n — 1.82  and  m = 1.055  for  one-lialf  inch 
smooth,  coated  cast-iron  pipes  to  n = 1.9854  and  m = 1.54 
for  96-inch  pipes.  The  coefficients  b decrease  from  .0043065 
for  one-half  inch  to  .0003887  for  12-inch  and  then  increase 
to  .000512  for  96-incli  smooth  pipes. 

Table  No.  66c  gives  a series  of  exponents  and  coeffi- 
cients adapted  to  the  series  of  stated  diameters  of  smooth, 
coated,  cast-iron  pipes  from  .25  foot  to  8 feet  diameters. 
Each  diameter  has  its  own  formula  and  exponents,  and 
selections  may  be  made  for  each  diameter  applicable  to  the 
following  formulas : 


*=(»£)  ** 

(31) 

n/dmll 

(32) 

II 

(32a) 

dmfi 
^ ~~  bvn 

(326) 

In  which  d equals  diameter  in  feet,  v equals  velocity  of 
flow  in  feet  per  second,  li  equals  the  head  in  feet,  balancing 
resistance  to  flow,  and  l is  the  length  of  pipe,  in  feet. 

The  table  of  exponents  No.  66c  shows  that  the  relation 
of  friction  head  to  velocity  of  flow  does  not,  in  the  small 


271c 


FLOW  OF  WATER  THROUGH  PIPES. 


pipes,  vary  with  the  square  of  the  velocity  as  is  usually 
assumed,  but  in  a four-inch  pipe  as  the  1.85  power,  but  the 
relation  aproaches  nearer  to  the  second  power  as  diameter 
approaches  six  feet.  Also,  the  relation  of  the  friction  head 
to  diameter  approaches  the  ratio  of  1 -p  Vd*  as  6 feet  di- 
ameters are  reached,  but  has  lesser  exponents  in  smaller 
pipes. 

TABLE  No.  66c. 


Table  of  Values  of  b,  n,  and  m,  for  Given  Diameters. 


Diameter 
in  inches. 

d 

in  feet. 

Expo. 

b 

Expo,  of 

V — 71 

Expo,  of 
d — m. 

3 

•25 

.0004224 

1.8450 

I . I42 

4 

•3333 

.0004170 

1.8510 

1 .160 

6 

■ 5 

.OOO4085 

1.8630 

1-195 

8 

.6667 

.000^010 

1.8735 

1.224 

10 

•8333 

.OOO3954 

1. 8816 

1.24S 

12 

1 .0 

.OOO3887 

1 . 8900 

1.272 

14 

1 . 1667 

.0003943 

1.8993 

1.294 

16 

1-3333 

.OOO3986 

1. 9051 

1-313 

18 

i-5 

,000_|029 

1.9126 

1 -331 

20 

1.6667 

. 0004064 

1-9195 

1-347 

22 

1-8333 

. 0004099 

1.9256 

1.362 

24 

2.0 

.0004133 

1-9340 

1-375 

27 

2.25 

.0004185 

1.9440 

1-394 

30 

2.5 

.0004235 

I .9520 

I. 410 

33 

2-75 

.0004280 

1.9576 

1.424 

36 

3-o 

.0004327 

1.9620 

1.436 

40 

3-3333 

.0004383 

1 . 9660 

1.44S 

44 

3.6667 

.0004437 

1.9700 

1-459 

4s 

4.0 

.0004492 

1.9725 

1.470 

54 

4-5 

.0004570 

1.9760 

1-483 

60 

5-o 

.0004647 

I-9783 

1-494 

72 

6.0 

. 0004SOO 

1.9815 

I-5I3 

84 

7.0 

.0004955 

I-9835 

1 . 52S 

96 

8.0 

.0005120 

1.9854 

1.540 

The  assumptions  that  these  exponents  were  constant 
has  necessitated  a wide  range  of  values  of  the  coefficients 
such  as  m and  c in  all  those  formulas  that  have  heretofore 
been  in  general  use.  Giving  truer  values  to  the  exponents 
brings  the  coefficient  b nearly  constant  for  one  given  class. 


CLASSIFIED  EXPONENTS. 


271J 


The  construction  of  similar  diagrams  for  rougher  classes 
of  pipes  shows  that  their  logarithmic  velocity  lines  are 
moved  to  the  left  on  the  diagram,  and  have  slightly  in- 
creased ratios  of  inclinations  and  exponents.  The  lines 
through  the  diameter  points  are  moved  to  the  left  also,  and 
are  more  curved  ; hence  the  exponent  m for  diameter  and 
coefficient  b have  slightly  increasing  values  as  roughness 
increases.  Such  slight  modifications  of  m and  b lead  to  a 
series  of  formulas  adapted  to  approximate  computations  in 
pipes  classified  in  roughness  as  above  suggested.  The  fol- 
lowing formulas,  one  for  each  class  of  roughness,  apply  to 
a wide  range  of  velocities,  and  to  diameters  from  six  to 
ninety-  six  inches1: 


.523 


and  Ti  = v523 


.000379 l 


~ (33) 


<< 


(34) 


u 


(34a) 


(345) 


(34c) 


(34  d) 


a 


(34c) 


(34/) 


(34 g) 


272 


FLOW  OF  WATER  THROUGH  PIPES. 


Class  L.  V — 


d^Ti 
.0012  <ol 


.5 


(34  h) 


BENDS  AND  BRANCHES. 


299.  Bends. — The  experiments  with  Tends,  angles,  and 
contractions  in  pipes,  so  far  as  recorded,  have  been  with 
very  small  pipes,  and  the  deductions  therefrom  are  ot 
uncertain  value  when  applied  to  the  ordinary  mains  and 
distribution  pipes  of  public  water  supplies. 

Our  pipes  should  be  so  proportioned  that  the  velocity 
of  flow,  at  an  extreme,  need  not  exceed  ten  feet  per  second. 
Our  bends  should  have  a radius,  at  axis,  equal  at  least  to 
four  diameters. 

Under  such  conditions,  the  loss  of  head  at  a single  bend 
will  not  exceed  about  one-tenth  the  height  to  which  the 
velocity  is  due  (not  including  height  balancing  resistance 
of  pipe-wall). 

In  such  case,  we  may  for  an  approximation  take,* 


According  to  this  equation,  if  a pipe  is  1 foot  diameter, 
1000  feet  long,  and  flowing  with  free  end  under  100  feet 
head,  the  loss  at  one  90°  bend,  whose  axial  radius  of  curva- 
ture equals  4 diameters,  will  be  .47  feet  of  head.  If  there 
are  two  bends,  the  total  head  remaining  constant,  the  loss 


v 


(33) 


(34) 


* Tlie  mean  value  of  (1  + cr)  for  short  pipes  is  1.505. 


BENDS. 


273 


at  both  will  not  be  double  this  amount,  for  the  velocity 
through  the  first  will  be  reduced  by  the  resistance  in  the 
second,  and  therefore  the  resistance  in  the  first  will  be 
reduced  proportionally  with  the  square  of  the  reduction  of 
the  velocity  ; and  a similar  proportional  reduction  of  resist- 
ance will  take  place  in  the  first  and  second  bends  when  a 
third  is  added. 

Let  v be  the  velocity  due  to  the  given  head  and  length 
of  pipe  without  a bend,  and  vl  the  velocity  after  the  bend  is 
inserted,  then  the  height  of  head  lost,  7ib,  in  consequence  of 

the  bend  is  hb  = — — and  -S'  — 7ib  is  the  effective  remain- 


ing head. 


2g 


After  computing  the  new  value  of  H beyond  the  first 
bend,  we  may  substitute  that  in  the  equation  to  find  the 
new  value  of  vly  and  proceed  to  deduce  the  value  of  H'' 
beyond  the  second  bend,  etc.,  or  raise  the  subdivisor  to  a 
power  whose  index  equals  the  number  of  bends  ; thus, 


No.  of  Bends 

I 

2 

3 

4 

5 

6 

7 ! 8 

9 

IO  II 

12 

Subdivisors. 

■9 

,8i 

.656 

•591 

•531 

.478 

■43°|  -387 

•349 

.314I  .282 

.254 

Reciprocals. 

I.II 

1.23 

1.52 

1.68 

1.88 

2.09 

2.33  2.58 

2.87 

3-i8  3-55 

394 

For  larger  pipes,  or  for  larger  radius  of  curvature,  or 
reduced  velocity,  the  value  of  the  subdivisor  may  rise  to  .94 
or  .96,  or  even  near  to  unity. 

When  pipes  exceed  one  thousand  diameters  in  length, 
the  term  (1  + c,)  may  be  neglected,  and  the  equations 
assume  the  following  more  simple  forms,  in  which  the 
reciprocals  of  the  above  table,  according  to  the  number  of 
bends,  become  the  coefficients  of  m. 


j %gh"r  j* 
t l.lllmZ  f 


(35) 


h"  = 


1.111  mlv2 

2gr- 


(36) 


In  which  v = the  rate  of  flow,  in  feet  per  second  ; h"  = the 
frictional  head ; and  i = the  sine  of  the  inclination. 


274 


FLOW  OF  WATER  THROUGH  PIPES. 


T = the  hydraulic  mean  radius  = -ec^lon . 

contour 

m = a coefficient  ( vide  table  of  m,  page  242). 

2 g — 64.4. 

The  experiments  by  Du  Buat,  Venturi,  and  other  of  the 
early  experimentalists,  with  pipes  varying  from  one-half  to 
two  inches  diameter,  and  more  recent  experiments  by  Weis- 
bacli,  have  been  fully  and  ably  discussed  by  the  latter,  in 
“Mechanics  of  Engineering”  and  elsewhere. 

Weisbach’s  formula  for  additional  height  of  head,  kb, 
necessary  to  overcome  the  resistance  of  one  bend,  is 


, _ <£  v2 

‘ ~ 1 80 ; * Yg' 


(37) 


in  which  z is  a coefficient  of  resistance,  <f>  the  arc  of  the  bend 
in  degrees,  and  hh  the  additional  head  required. 

The  value  of  z he  deduces  by  an  empirical  formula : 


z = .131  + 1.847  (r)1, 


in  which  r is  the  radius  or  semi-diameter  of  the  pipe,  and  R 
the  axial  radius  of  curvature  of  the  bend. 

For  given  ratios  of  r to  i?,  z has  the  following  values, 
for  pipes  with  circular  cross- sections. 


TABLE  No.  67. 
Coefficients  of  Resistance  in  Bends. 


r 

~R 

.1 

•V 

.2 

•25 

•3 

•35 

•4 

•45 

•5 

•55 

z 

•I31 

•!33 

.138 

• 145 

.158 

00 

.206 

.244 

.294 

•35° 

r 

R 

.6 

•65 

•7 

•75 

.8 

•85 

•9 

•95 

I 

— 

z 

•44° 

•540 

.661 

.806 

•977 

1. 177 

1.408 

1.674 

r-978 

— 

BRANCHES. 


275 


300.  Branches. — In  branches,  the  sums  of  the  resist- 
ances due  to  the  deflections  of  the  moving  particles,  the 
contractions  of  sections  by  centrifugal  force,  and  the  con- 
tractions near  square  edges,  if  there  are  such,  will  for  each 
given  velocity  vary  inversely  as  the  diameters  of  the 
branches. 

Until  reliable  data  for  other  than  small  pipe  branches  is 
supplied,  we  may  assume  in  approximate  preliminary 
estimates  of  head  required,  when  the  velocity  of  flow,  under 
pressure,  is  ten  feet  per  second,  a reduction  of  that  portion 

of  the  head  to  which  the  velocity  is  due  ( = at  a right- 

angled  branch,  equal  to  about  fifty  per  cent,  in  branches  of 
three  to  six  inches  diameter  and  thirty  to  forty  per  cent,  in 
larger  branches. 

The  equations  then  take  the  following  form  : 


The  value  of  the  subdivisor  will  be  changed  according 
to  the  special  conditions  of  the  given  case,  and  the  effects 
of  a series  of  branches  will  be  similar  to  those  above 
described  for  a series  of  bends,  but  enhanced  in  degree. 

For  long  pipes,  equivalent  equations  will  be, 


2 gH 


(38) 


(39) 


(40) 


1.333raZ*2 


(41) 


276 


FLOW  OF  WATER  THROUGH  PIPES. 


301.  How  to  Economize  Head. — The  losses  of  head 
and  of  energy  due  to  frictions  of  pipe- wall  and  to  resistances 
of  angles,  contractions,  etc.,  increase  with  the  square  of  the 
velocity,  and  they  occasionally  consume  so  much  of  the 
head  that  a very  small  fraction  of  the  entire  head  only 
remains  to  generate  the  final  velocity  of  flow. 

The  losses,  other  than  those  due  to  the  walls  of  the  pipes, 
originate  chiefly  about  the  square  edges  of  the  pipes, 
orifices,  and  valves,  where  contractions  and  their  resulting 
eddies  are  produced,  or  are  due  to  the  centrifugal  force  of 
the  particles  in  angles  and  bends. 

These  losses  about  the  edges  may  be  modified  materially, 
even  near  to  zero,  by  rounding  all  entrances  to  the  form  of 
their  rend  contractd , and  by  joining  all  pipes  of  lesser 
diameter  to  the  greater  by  acutely  converging  or  gently 
curved  reducers  (Fig.  102),  so  that  the  solidity  and  sym- 
metrical section  of  the  column  of  water  shall  not  be  dis- 
turbed, and  so  that  all  changes  of  velocity  shall  he  gradual 
and  without  agitation  among  the  fluid  p articles. 

It  is  of  the  utmost  importance,  when  head  and  energy 
are  to  be  economized,  that  the  general  onward  motion  of 
the  particles  of  the  jet  be  maintained,  since  wherever  a 
sudden  contraction  occurs  an  eddy  is  produced,  and 
wherever  currents  of  different  velocities  and  directions 
intermingle  an  agitation  results,  both  of  which  divert  a 
portion  of  the  forward  energy  of  the  particles  to  the  right 
and  left,  and  convert  it  into  pressure  against  the  walls  of 
the  pipe,  from  whence  so  much  reaction  as  is  across  the 
pipe  is  void  of  useful  effect,  and  the  energy  of  the  jet  to  a 
like  extent  neutralized,  and  so  much  as  is  back  into  the 
approaching  column  is  a twofold  consumption  of  dynamic 
force. 


WEIR,  FOR  A TURBINE  TEST  AT  LOWELL,  BY  JAS.  B.  FRANCIS, 


CHAPTER  XIV. 


MEASURING  WEIRS,  AND  WEIR  GAUGING. 

302.  Gauged  Volumes  of  Flow. — A partially  sub- 
merged measuring  orifice  or  notch  in  one  of  the  upright 
sides  of  a water  tank,  or  a horizontal  measuring  crest  with 
vertical  shoulders,  in  a barrier  across  a stream,  equivalent 
to  a notch,  is  termed  a weir. 

Weirs,  as  well  as  submerged  orifices  (§  206)  are  used 
for  gauging  the  flow  of  water,  and  in  their  approved  forms 
give  opportunity  to  apply  the  constant  force  and  accelera- 
tion of  gravity,  acting  upon  the  water  that  falls  over  the 
weir,  to  aid  in  determining  the  volume  of  its  flow. 

The  volume  of  flow,  Q,  equals  the  product  of  the  section 
of  the  jet  upon  the  weir,  S,  into  its  mean  velocity,  V. 

Q = SV.  (1) 

303.  Form  of  Weir. — For  convenience  in  practical 
construction  and  use,  liydraulicians  usually  form  their 
measuring  weirs  with  horizontal  crests,  CD,  and  vertical 
ends  AC  and  BD,  Fig.  41. 

Fig.  40.  Fig.  41. 


278 


MEASURING  WEIRS,  A^'D  WEIR  GAUGING. 


The  theory  of  How  over  weirs  of  this  description  is  more 
accurately  established  by  numerous  experimental  and  posi- 
tive measurements,  than  for  any  other  form  of  notch. 

The  head  of  water  upon  rectangular  weirs  is  measured 
from  the  crest  CD  of  the  weir  to  the  surface  of  still  water,  a 
short  distance  above  the  weir,  instead  of  from  the  centre  of 
pressure  or  centre  of  gravity  (§  206)  of  the  aperture,  as  in 
the  case  of  submerged  orifices. 

The  weir  is  placed  at  right  angles  to  the  stream,  -with  its 
upstream  face  in  a vertical  plane. 

The  crest  and  vertical  shoulders  of  the  weir  are  cham- 
fered so  as  to  flare  outward  on  the  discharge  side  at  an 
angle  not  less  than  thirty  degrees.  The  thin  crest  and 
ends  receiving  the  current  must  be  truly  horizontal  and 
vertical,  and  truly  at  right  angles  to  the  upper  plane  of  the 

weir,  and  sharp-edged,  so 
as  to  give  a contracted  jet 
analogous  to  that  flowing 
through  thin,  square-edged 
plate. 

The  edges  are  common- 
ly formed  of  a jointed  and 
chamfered  casting,  or  of  a 
jointed  plate  not  exceeding 
one-tenth  inch  thickness,  as  shown  in  Fig.  42. 

304.  Dimensions.  — The  dimensions  of  the  notch 
should  be  ample  to  carry  the  entire  stream,  and  yet  not  so 
long  that  the  depth  of  water  upon  a sharp  crest  shall  be  less 
than  five  inches,  and  if  contraction  is  obtained  at  the  up- 
right ends,  the  section  of  the  jet  in  the  notch  should  not 
exceed  one- fifth  the  section  of  the  approaching  stream,  lest 
the  stream  approach  the  weir  with  an  acquired  velocity  that 
will  appreciate  the  natural  volume  of  flow  through  the  notch. 


Fig.  42. 


END  CONTRACTIONS. 


279 


305.  Stability.— Care  is  to  be  taken  to  make  the  foun- 
dation of  the  weir  firm,  the  bracing  substantial,  and  the 
planking  rigid,  so  there  shall  be  no  vibration  of  the  frame- 
work or  crest,  and  its  sheet  piling  is  to  go  deep,  and  well 
into  the  banks  on  each  side,  when  set  in  a stream,  so  that 
there  shall  be  no  escape  of  water  under  or  around  it,  and  a 
firm  apron  is  to  be  provided  to  receive  the  falling  water  and 
to  prevent  undermining. 

306.  Varying  Length. — Upon  mountain  streams,  it  is 
frequently  necessary  to  provide  for  increasing  or  shortening 
the  length  of  the  weir,  so  that  due  proportions  of  notch  to 
volume  may  be  maintained.  This  may  be  accomplished  by 
the  use  of  vertical  stop-planks  with  fiared  edges,  placed  at 
one  or  both  ends  of  the  weir,  as  at  ff,  Fig.  41. 

Sometimes  it  is  necessary  to  make  the  notch  of  the  entire 
width  of  the  stream,  when  there  will  be  crest  contraction 
only,  and  no  end  contractions,  in  which  ca^e  partitions  B 
(Fig.  44)  should  be  placed  against  the  upper  side  of  the 


Fig.  43.  Fig.  44. 


weir  flush  with  its  shoulders  and  at  right  angles  to  ita 
plane.  On  other  occasions  the  weir  may  be  so  long  as  to 
require  intermediate  posts,  F (Fig.  44),  in  its  frame-work, 
when  intermediate  contractions,  one  to  each  side  of  a post, 
will  be  obtained,  in  addition  to  the  crest  and  end  contrac- 


280 


MEASURING  WEIRS,  AND  WEIR  GAUGING. 


tions  ; each  of  which  exert  an  important  diminishing  influ- 
ence upon  the  volume  of  flow. 

307.  End  Contractions.— A short  weir  may  be  de- 
fined, one  which  is  appreciably  affected  by  end  contractions 
throughout  its  entire  length ; practically,  when  the  length 
of  unbroken  opening  is  less  than  about  four  times  the 
depth  of  water  flowing  over. 

The  end  contractions  affect  a nearly  constant  length  at 
each  end,  for  each  given  depth,  on  long  weirs,  and  such 
length  increases  with  the  depth  of  water  upon  the  weir. 

To  obtain  perfect  end  contractions,  the  distance  from 
the  vertical  shoulder  to  the  side  of  the  channel  should 
not  be  less  than  double  the  depth  of  the  water  upon  the 
weir. 

If  there  is  no  end  contraction,  the  volume  for  any  given 
depth  is  proportional  to  the  entire  length  of  the  weir. 

The  flow,  for  a given  length,  on  long  weirs,  or  on  weirs 
without  end  contractions,  is  proportional  to  a power  of  the 
depth  on  the  weir. 

308.  Crest  Contractions.  — To  obtain  perfect  crest 
contractions,  the  depth  of  water  above  the  weir  should  not 
be  less  than  about  double  the  depth  upon  the  weir,  especi- 
ally when  the  depth  flowing  over  is  less  than  one  foot ; and 
the  clear  fall  below  the  crest  to  the  surface  of  tail  water 
should  be  sufficient  to  maintain  a perfect  circulation  of  air 
in  the  crest  contraction,  d (Fig.  42),  under  the  jet,  all  along 
the  crest.  Such  supplies  of  air  are  to  be  provided  for  at 
ends,  and  at  central  posts,  F (Fig.  44),  since  a vacuum 
under  the  jet  would  defeat  the  application  of  the  ordinary 
formula. 

309.  Theory  of  Flow  over  a Weir.— To  illustrate 
the  deduced  theory  of  flow  through  rectangular  notches,  we 
will  first  consider  a case  independent  of  contraction : 


THEORY  OF  FLOW  OVER  A WEIR. 


2S1 


Let  a,  b,  c,  d,  e,  f,  etc.  (Fig.  45),  be  orifices  in  the  side 
of  a reservoir,  at  depths  below  the  water  surface,  respec- 
tively of  1,  2,  3,  4,  5,  6,  etc.,  feet. 

Then  the  velocity  of  issue  of  jet  from  each  orifice  will  be 

V=  V2 JH, 


according  to  its  depth,  H,  below  the  surface,  viz.  : 


For  orifice  5,  V = \'2gl  = 8.03  feet  per  second. 

“ « c,  V = V2g2  — 11.40  “ 

“ “ d,  V = V2g8  = 13.90  “ 

“ “ e,  V = V2gl  = 16.00  “ 

“ “ f,V=  V2g5  = 17.90  “ 

« “ i,  V = V2g0  = 19.70  “ 

“ Jc,  V = V2g7  = 21.20  u 

“ n,  V = V'2g8  — 22.70  “ 

“ o,  V = \'2g9  = 24.10  “ 


p,  V = V2gl0  = 25.40 


U 

a 

u 

u 

a 

a 

u 

a 

a 


u 

Ci 

€i 

ii 

M 

u 

«< 

u 


Plot  each  of  these  depths,  a,  b,  c,  etc.,  to  scale  upon  the 
same  vertical  line  as  abscisses  and  their  corresponding 
velocities  of  issue,  bb',  cc',  dd\  etc. , horizontally  to  the  same 


282 


MEASURING  WEIRS,  AND  WEIR  GAUGING. 


scale  as  ordinates ; tlien  the  extremities  of  the  horizontal 
lines  will  touch  a parabolic  line,  a , b ',  d,  p,  whose  vertex 
is  at  a,  abscissa  is  ap,  ordinates  are  bb',  cc',  pp , etc.,  and 
whose  parameter  equals  2 g. 

Suppose  now  the  lintels  separating  the  orifices  are  in- 
finitely thin,  then  the  volume  issuing  per  second  from  each 
orifice  will  equal  a prism,  whose  length  and  height  equals 
that  of  the  orifice,  and  whose  mean  projection  is  equal  to 
its  ordinate,  bb’,  cc',  dd,  etc.,  or  equals  in  feet,  the  feet  per 
second  of  velocity  of  issue  from  the  orifice. 

Again,  suppose  the  partitions  to  be  entirely  removed 
and  the  fluid  veins  to  be  infinitely  thin  and  infinite  in  num- 
ber as  respects  height,  tlien  the  velocities  of  the  veins  plot- 
ted to  scale,  will  touch,  as  before,  the  parabolic  line  ah’ dpi, 
and  the  volume  of  issue  per  second  will  equal  a prism  whose 
end  area  equals  the  notch  ap,  and  whose  area  of  projection 
equals  the  area  of  the  parabolic  segment,  app'da,. 

According  to  well  known  properties  of  the  parabola,  the 
segment  app'da  is  equal  to  two-thirds  its  circumscribing 
parallelogram  Aapp'. 

Let  l be  the  length  of  the  notch,  II  the  height  = op,  and 
V2gH  the  length  of  the  segment  =pg>  ; then  the  area  of  the 
circumscribing  parallelogram  equals  E x V2gE  and  the 
area  of  the  segment  equals  Ex  § V2gE  and  the  volume  of 
issue  Q = l x E x § V2gE.  (2) 

Let  V be  the  velocity  of  the  film  of  mean  velocity. 
Since  the  volume  of  the  segmental  prism  app'da  equals 
two  thirds  of  the  parallelopiped  Ap  of  equal  height,  length, 
and  projection,  it  follows  that  the  volume  of  the  segment 
equals  the  volume  of  a parallelopiped  of  equal  height  and 
length  and  of  § the  projection  = pp',  and  the  mean  velocity 
of  issue,  V — pp"  = | V2gH. 

The  volume  Q = l x E x V —l  x E x | Y/2gE. 


FLOW  WITHOUT  AND  WITH  CONTRACTIONS. 


283 


If  the  crest  of  the  weir  is  raised  to  f,  then  let  the  height 
af  he  h,  and  the  velocity  of  issue  of  the  film  at  the  crest  f 
will  he  V2gh,  and  the  volume  of  issue  q from  the  notch  af 
will  he,  q = \l  x h x Vh  x V2g. 

If  the  volume  q of  this  segmental  prism  aff'b'a , he  sub- 
tracted from  the  volume  Q of  the  segmental  prism  app'cl'a , 
the  remainder  will  equal  the  volume  of  the  prism  fppf ' — 
Q — q = (f l x H x VH  x V2 g)  — (fZ  x Ti  x Vh  x V2 g)  = 

§ l V2g  (HVH-  Ti  Vh).  (3) 

310.  Formulas  for  Flow  without  and  with  Con- 
tractions. — The  formula  (2),  Q = l x H x § V2g  x VH 
may  take  the  form  Q — V2g  x l x f Hi.  (4) 

Taking  into  consideration  the  complete  contraction  in  a 
rectangular  weir,  we  observe  first,  that  in  addition  to  the 
crest  and  end  contractions,  the  surface  of  the  stream,  Fig.  42, 
begins  to  lower  at  a short  distance  above  the  weir,  and  the 
jet  assumes  a downward  curve  over  the  weir. 

Experiments  demonstrate  that  the  measurements  are 
facilitated,  both  in  accuracy  of  observations  and  in  ease  of 
calculations,  by  taking  the  height  of  water  upon  the  weir 
to  the  true  surface  level  a short  distance  above  the  weir, 
instead  of  to  the  actual  surface  immediately  over  the  crest. 
In  such  case  the  top  contraction  has  no  separate  coefficient 
in  the  formula  of  volume. 

Experiments  demonstrate  also,  that  a perfect  end  con- 
traction, when  depths  upon  the  weir  are  between  three  and 
twenty-four  inches,  and  length  not  less  than  three  times  the 
given  depth,  will  reduce  the  effective  length  of  the  weir  a 
mean  amount,  approximately  equal  to  one-tentli  of  the 
depth  from  still  water  surface  to  crest. 

If  H is  this  depth  from  surface  to  crest,  and  l the  full 
length  of  the  weir,  and  T the  effective  length  of  the  weir, 
then  one  end  contraction  makes  l—  (l  — 0.1  H)\  and  two 


284 


MEASURING  WEIRS,  AND  WEIR  GAUGING. 


end  contractions  make  l'—  (l  — 0.2 H) ; and  any  number, 
n,  of  end  contractions  make  l'—  (l  — 0.1  nH). 

The  reduction  of  volume  by  the  crest  contraction  is  com- 
pensated for  by  a coefficient  m introduced  in  the  formula 
for  theoretical  volume,  as  above  deduced.  This  coefficient 
(m)  is  to  be  determined  for  the  several  relative  depths  and 
lengths  by  experiment. 

If  we  insert  the  factors  relating  to  end  and  crest  contrac- 
tions, the  formula  for  volume  becomes  : 

Q - | m x V2g  x (l  — 0.1nH)HK  (5) 

The  factors  § and  V2g  are  constants,  and  for  approximate 
calculations  within  limits  of  3 to  24  inches  depths  upon  the 
weir,  m may  be  taken  as  constant. 

Let  C represent  the  product  of  these  three  factors,  then 
C = §m  x V2g. 

The  admirable  experiments  with  wens  * upon  a great 
scale,  which  were  conducted  by  James  B.  Francis,  C.  E., 
with  the  aid  of  the  most  perfect  mechanical  appliances,  in  a 
most  thorough  and  careful  manner,  give  to  C a mean  value 
of  3.33,  and  we  have  3.33  = § m x V2g. 

Transposing  and  assigning  to  V2g  its  numerical  value, 
we  have, 

3.33  3.33 

m = 2 — uxxu  — r o?  ~ -622  as  a mean  coefficient. 

^ X o.U^O  O.oO 

The  formula  for  volume  of  flow  may  take  the  following 
forms : 

Q = | V2g  x m{l  — 0.1  nH)H*  = 5.35 m(l  — 0.1  (6) 

or  for  approximate  results. 

Q = 0(1  — 0.1  nH)m  = 3.33(Z  - 0.1  nH)H\.  (7) 

This  last  formula,  suggested  by  Mr.  Francis,  assumes 


* Lowell  Hydraulic  Experiments  ; Van  Nostrand,  New  York,  1868. 


INCREASE  OF  VOLUME  DUE  TO  INITIAL  VELOCITY.  285 


that  the  discharge  is  from  a reservoir  infinitely  large,  so  that 
the  water  approaching  has  received  no  initial  velocity. 

311.  Increase  of  Volume  due  to  Initial  Velocity 
of  Water. — When  there  is  appreciable  velocity  of  approach, 
let  S be  the  section  of  stream  in  the  channel  of  approach, 
and  V the  mean  velocity  of  flow  in  the  section  S',  and  It  the 
height  to  which  the  velocity  V is  due,  and  Q the  volume 
eulianced  by  the  initial  velocity.  Then 


SV  - Q',  and  V=  and  7i  — 

If  the  mean  velocity,  V,  is  to  be  determined  from  the 
surface  motion  of  the  water  in  the  channel  of  approach,  let 
V1  be  the  surface  motion ; then,  as  will  be  shown  in  the 
consideration  of  flow  of  water  in  channels  (§  332),  the  mean 
velocity  is,  approximately,  eight-tenths  of  the  surface  ve- 

(.8  77 


looity,  and  V — .8  V',  and  it  = 


2g 


Fig.  46. 


Referring  again  to  a parabolic  segment  of  length  equal 
to  the  unit  of  length  of  weir, 

Rig.  46,  and  let  H — ap,  and 
It  — sa,  and  V2gH = pp'  and 
V 2g{  II  + Ji)  = pt. 

The  ordinate  pp'  of  the  seg- 
ment app'  is  the  projection  of  a 
parabolic  segment  whose  volume 
equals  the  volume  of  flow  when 
the  depth  upon  the  weir  equals 
ap. 

When  the  flow  has  no  initial 
velocity  the  ordinate  at  a — 0, 

but  when  the  flow  has  an  initial  velocity  due  to  the  height 
sa  = 7i , the  ordinate  at  a equals  V 2gh  — a, a',  and  the  ordi- 
nate at  p — V2g{ll  + h)  =pt,  and  any  ordinate  f,  at  a 


'286 


MEASURING  WEIRS,  AND  WEIR  GAUGING. 


depth  It  — sf,  equals  V2gJt  — ff",  therefore  the  increase 
of  volume  of  flow  clue  to  iuitial  velocity  is  represented  by 
the  volume  aa’tpf and  the  whole  volume  of  flow  by  the 
volume  apla'. 

This  last  volume  is  the  volume  spt  less  the  volume  saa\ 
and  equals,  for  unit  of  length, 


{1  (H  + h)  ‘V2g(HJr7i)\  — \%h  V2 gh\  = f Vty \(H+h)i - 7ii\. 


Let  Q'  be  the  enhanced  volume,  and  let  H'  be  some 
depth,  yp,  upon  the  weir,  that  substituted  for  II  in  the 
ordinary  formula  for  Q would  give  the  value  of  Q'. 

The  formula  then,  if  there  are  no  end  contractions,  is 


or,  for'  approximate  measures,  including  end  contractions, 
if  any, 

Q = 3.33  ( l - 0 .InW)  H'K  (10) 

To  determine  the  value  of  II'  from  (II  + 7i),  substitute 
the  value  of  Q in  the  equation  (8)  of  volume  for  one  unit  of 
length,  and  we  have 


If  the  volume  of  flow  (Q  = \ml  R)  is  known,  and  it 
is  desired  to  find  the  depth  II  upon  a weir  of  given  length, 
then  by  transposition  we  have, 


Q'  = \ml  \/2 ~g  H 


(9) 


iV¥g\(E+h)*-M\  = 
and  reducing,  we  have 
IT  = 


(11) 


(12) 


COEFFICIENTS  FOR  WEIR  FORMULAS. 


287 


or,  in  case  of  initial  velocity  in  the  approaching  water, 


The  first  of  these  two  values  of  II  will  give  results  suf- 
ficiently near  for  all  ordinary  practice,  if  the  initial  velocity 
does  not  exceed  one-lialf  foot  per  second. 

In  the  above  formulas  of  volume  the  symbols  represent 
values  as  follows : 

Q — volume  due  to  natural  flow,  in  cubic  feet  per  second. 
I — length  of  weir,  in  feet. 

I — effective  length  of  weir,  in  feet. 

m = coefficient  of  crest  contraction,  determined  by  exper- 
iment. 

H=  observed  depth  of  water  upon  the  weir,  in  feet. 

JS  = section  of  channel  leading  to  the  weir,  in  square  feet 
V = mean  velocity  of  water  approaching  the  weir,  in  feet 
per  second. 

h = head  to  which  this  velocity  is  due,  in  feet. 

2g  — 64.3896,  or  64.4  for  ordinary  calculations. 

H — head  upon  the  weir,  when  corrected  to  include  effect 
of  initial  velocity  of  approaching  water. 

Q'  = volume  of  flow,  including  effect  due  to  initial  velocity 


312.  Coefficients  for  Weir  Formulas.  — The  con- 
trolling influence  of  the  contractions  entitle  them  to  a 
detailed  study. 

In  Mr.  Francis’  formula  for  volume,  quoted  above,  the 
end  contraction  is  assumed  to  be  a function  of  the  depth, 
and  the  crest  contraction  to  be  compensated  for  by  the 
coefficient  C,  of  which  m is  the  variable  factor  dependent 
upon  the  depth. 


(13) 


of  approaching  water. 


288 


MEASURING  WEIRS,  AND  WEIR  GAUGING. 


In  the  following  table  the  quantities  in  columns  A,  B, 
1),  E,  F have  been  selected  from  Mr.  Francis’  table,  the 
column  C reduced  from  its  corresponding  column,  and  the 
column  G computed.  Each  of  the  columns  are  means  of  a 
number  of  nearly  parallel  experiments,  and  they  are  here 
arranged  according  to  depth  upon  the  weir. 

TABLE  No.  68. 

Experimental  Weir  Coefficients. 


• A. 

B. 

c. 

D. 

E. 

F. 

G. 

Length  of  weir  = /, 
in  feet. 

Corrected  depth 
upon  weir  = //', 
in  feet. 

Quantity  of  water 
passing  weir,  in 
cu.  ft.  per  sec. 

= Q 

Quantity  computed 
by 

\m  V *g  (/— 0.  mH')  H'* 
in  cu.  ft.  per  sec. 

Quantity  computed 

by 

3.33  (/ — o.i nil')  II'1 
in  cu.  ft.  per  sec. 

- !| 
O N 

> II 

Value  of  tit. 

9-997 

.62 

16.2148 

16.0382 

16.0502 

3-3275 

.622 

9-997 

•65 

17.3401 

17.1990 

17.2187 

3.3262 

.622 

9-995 

.80 

23-7905 

23.8821 

23.8156 

3-3393 

.624 

9-997 

.80 

23-4304 

23.4OU 

23-4391 

3-3246 

.621 

9-997 

-S3 

25.0410 

24-83I3 

24.7548 

3-3403 

.624 

9-995 

.98 

32-563° 

32.3956 

32.2899 

3-3409 

.624 

9-995 

I. OO 

33-4946 

33-2534 

33-2833 

3-327° 

.622 

9-997 

I. OO 

32.5754 

32.5486 

32.6240 

3-3223 

.621 

9-997 

I.06 

36.0017 

35.8026 

35-56o2 

3-3527 

.627 

9 997 

J-25 

45-5654 

45-4I25 

45.3608 

3-3338 

.623 

9-997 

1.56 

62.6019 

62.6147 

62.8392 

3-3i8i 

.620 

7-997 

.68 

14.5478 

14.4581 

14.4247 

3-3368 

.624 

7-997 

1.02 

26.2756 

26.2686 

26.0333 

3-36oi 

Mean, 

.628 

.623 

Mr.  Francis  points  out  the  necessity  of  caution  in  apply- 
ing the  above  formula  for  Q beyond  the  limit  covered  by 
the  experiments,  but  it  occasionally  becomes  necessary  to 
use  some  formula  for  depths  both  less  and  greater  than  is 
included  in  the  above  table. 

After  plotting  with  care  the  results  obtained  in  various 


DISCHARGES  FOR  GIVEN  DEPTHS. 


289 


experiments  by  different  experimentalists,  we  suggest  the 
following  coefficients  for  the  respective  given  depths,  until  a 
series  of  equal  range  shall  be  established  by  experiments 
■with  a standard  wen-  gauge.  At  the  same  time,  we  advise 
that  weirs  be  so  proportioned  that  the  depths  upon  them 
shall  conform  to  the  limits  already  covered  by  experiment, 
or  at  least  between  6 and  48  inches  depths,  and  with  length 
equal  to  four  times  the  depth. 


TABLE  No.  69. 

Coefficients,  C,  for  given  Depths  upon  thin  Weirs. 
(Q  = C/Hi) 


Depth,  feet 

0.2 

•4 

.6 

.8 

1.0 

1.2 

i-4 

1.6 

1.8 

2.0 

Value  of  m 

.628 

.625 

.625 

.623 

.622 

.621 

.620 

.620 

.619 

.619 

Value  of  C 

3-  361 

3-352 

3-342 

3-334 

3.328 

3-323 

3-3I9 

3-315 

3-312 

3-312 

Q,  for  / — i 

.301 

.848 

i-553 

2.386 

3.328 

4.368 

5.498 

6.703 

7-998 

9.362 

Depth,  feet 

2.5 

3-o 

3-5 

4.0 

4-5 

5-o 

5-5 

6.0 

7.0 

8.0 

Value  of  7 n 

.618 

.618 

.618 

.619 

.620 

.'621 

.622 

.623 

.625 

.627 

Value  of  C 

3 .306 

3-306 

3.308 

3-311 

3'3X5 

3-32i 

3 327 

3-332 

3-334 

3-355 

Q,  for  l — 1 

13.086 

17.1:8 

21.660 

26.488 

21.645 

37-13° 

42.914 

48.97° 

61.913 

75-915 

313.  Discharges  for  Given  Depths. — The  following 
table  of  approximate  how  over  each  foot  in  length  of  a 
sliarp-crested  rectangular  weir  has  been  prepared  to  aid  in 
adjusting  the  proportions  of  weirs  for  given  streams.  End 
contractions  are  not  here  allowed  for.*  The  coefficients  C 
(in  Clll'i)  are  taken  from  table  above,  and  l equals  unity. 

The  proportions  of  weir  and  its  ratio  to  section  of  chan- 
nel are  here  supposed  to  conform  to  the  general  suggestions 
given  above. 

* To  compensate  for  a single  end  contraction,  in  long  weirs,  deduct  from 
the  total  length,  in  feet,  an  amount  equal  to  one-tenth  the  head  upon  the  weir, 
in  feet.  Reduce  the  total  length  a like  amount  for  each  end  contraction. 

19 


290 


MEASURING  WEIRS,  AND  WEIR  GAUGING. 


TABLE  No.  70. 

Discharges,  for  Given  Depths  over  each  Lineal  Foot  of  Weir 


Head  from 
still  water 
in  ft.=W. 

H*‘. 

Cu.  ft.  per 
second  for 
1 ft.  length 

= cm  . 

Head. 

3 

H \ 

Cubic  feet. 

Head. 

Cubic  feet. 

.04 

.0080 

.0261 

.46 

.3120 

1.0386 

1.2 

1-3145 

4-3Q°4 

.05 

.0112 

.0365 

.48 

.3326 

I . 1072 

1.3 

1 .4822 

4.9506 

.06 

.0147 

.0480 

.50 

■3536 

I-I77I 

1.4 

1.6565 

5-5327 

.07 

.0185 

.0604 

.52 

•3750 

1.2483 

i-5 

1.8371 

6.1341 

.08 

.0226 

.0738 

■54 

.3968 

I.3209 

1.6 

2.0239 

6.7576 

.09 

.0270 

.0881 

■56 

.4191 

I-395I 

i-7 

2.2165 

7-3987 

.IO 

.0316 

. 1032 

•58 

•4417 

1.4724 

1.8 

2.4150 

8. 061 1 

.11 

.0365 

•1195 

.60 

.4648 

1-5475 

1.9 

2 6190 

8.7421 

. 12 

.0416 

■ 1361 

.62 

.4882 

1.6286 

2.0 

2.8284 

9-4413 

• 13 

.0469 

■1536 

.64 

.5120 

1.7080 

2.1 

3.0432 

10. 1581 

.14 

.0524 

. 1718 

.66 

.5362 

1.7888 

2.2 

3.2631 

10.8924 

• 15 

.0581 

. 1906 

.68 

.5607 

1.8705 

2-3 

3-48SI 

11.6280 

.16 

.0640 

.2102 

.70 

•5857 

1.9540 

2.4 

3.7181 

1 2 . 3960 

• 17 

.0701 

.2303 

•72 

.6109 

2.0380 

2.5 

3-9528 

13. 17&S 

.18 

.0764 

.2510 

• 74 

.6366 

2.1237 

2.6 

4.1924 

13-9773 

.19 

.0828 

.2721 

.76 

.6626 

2.2104 

2.7 

4.4366 

14.7915 

.20 

.0894 

.2938 

.78 

.6889 

2 . 2996 

2.8 

4-6S53 

15.6208 

.22 

.1032 

•3407 

.80 

•7155 

2.3SS3 

2.9 

4-9385 

16.8486 

.24 

.1176 

.3882 

.82 

.7426 

2.4788 

3-° 

5 . 1962 

17.3230 

.26 

.1325 

•4377 

.84 

.7699 

2.5699 

3-i 

5-458i 

18.1809 

.28 

. 1482 

.4892 

.86 

■7975 

2.6620 

3-2 

5-7243 

19.0676 

•30 

• 1643 

•5445 

.83 

•8255 

2-7557 

3-3 

5-994S 

19.9687 

•32 

.1790 

•5999 

.90 

.8538 

2.8500 

3-4 

6.2693 

20.8833 

•34 

.1983 

.6572 

.92 

.8824 

2 9455 

3*5 

6-5479 

21  .S110 

•36 

.2160 

•7158 

•94 

.9114 

3.0432 

3-6 

6.8305 

22.7525 

• 33 

.2342 

.7761 

.96 

.9406 

3.1407 

3-7 

7-II7I 

23.7071 

.40 

.2530 

.8384 

.98 

.9702 

3-2395 

3-8 

7.4076 

24-571° 

.42 

.2722 

.9020 

I .OO 

I . OOOO 

3-339° 

3-9 

7.7019 

25-54/2 

.44 

.2919 

.9672 

I . I 

I-I537 

3.8522 

4.0 

8.0000 

26.5360 

The  coefficients  derived  from  the  experiments  of  Cast  el 
and  D’Aubuisson,  Du  Buat,  Poncelet  and  Lebros,  Smeaton 
and  Brindley,  and  Simpson  and  Blackwell,  have  been 
deduced  by  those  eminent  experimentalists  to  compensate 
for  all  contractions.  In  such  cases,  the  ratio  of  length  of 
weir  to  depth,  especially  where  depth  exceeds  one-fourth 
the  length,  and  the  ratio  of  length  to  breadth  of  channel  by 
which  water  approaches,  exert  controlling  influences  upon 
the  coefficient. 


WEIR  COEFFICIENTS. 


291 


The  following  table  of  coefficients,  deduced  by  Castel, 
show  the  influence  of  depth  and  length. 

In  these  experiments,  Castel  used  for  channel  a wooden 
trough  2 feet  5}  inches  wide,  and  the  weir  placed  upon  its 
discharging  end  was  in  each  case  of  thin  copper  plate. 


TABLE  No.  71. 

Weir  Coefficients,  by  Castel. 


Canal,  2.427  feet  wide.  Coefficients,  the  lengths  of  the  overfall  being  respectively 


Dej: 

upor 

crc 

Ft. 

2.42 

Ft. 

2.23 

Ft. 

1.96 

Ft. 

1.64 

Ft. 

i-3i 

Ft. 

0.98 

Ft. 

0.65 

Ft. 

0.32 

Ft. 
0. 16 

Ft. 

0.09 

Ft. 

0.06 

Ft. 

0.03 

Ft. 

0.78 

o-595 

0.615 

0.639 

.72 

•594 

.614 

•e39 

•65 

0.596 

-594 

.614 

0.629 

.640 

0.670 

•5Q 

•595 

•594 

.613 

.628 

.641 

.672 

•52 

■595 

•592 

.613 

.628 

.642 

.674 

•45 

0.603 

•593 

•592 

.612 

.628 

643 

.675 

•39 

0.621 

.604 

•592 

.591 

.612 

.628 

■645 

.678 

•32 

0.657 

0.644 

0.631 

.621 

.604 

•593 

■59i 

.612 

.627 

.648 

.687 

.26 

0.662 

.656 

.644 

.632 

.620 

.606 

•595 

•592 

.612 

.627 

.652 

.698 

• x9 

.662 

.656 

.645 

.632 

.622 

.610 

.604 

•595 

.612 

628 

.648 

•713 

.16 

.662 

.656 

.644 

•633 

.626 

.616 

.611 

•597 

.613 

.629 

.663 

.13 

.662 

.656 

■645 

.636 

.632 

.623 

.619 

.604 

.614 

669 

.09 

.663 

.660 

.651 

.642 

.636 

.631 

. 624 

.618 

If  we  plot  certain  series  of  experiments  by  Smeaton  and 
Brindley,  Poncelet  and  Lesbro,  Du  Buat,  and  Simpson  and 
Blackwell,  and  take  the  corresponding  series  of  coefficients 
from  the  resulting  curves,  we  have  the  following  results  for 
the  given  depths  and  lengths. 


TABLE  No.  72. 

Series  ob-  Weir  Coefficients. 


Experimenters. 

Lengths  of 
weir,  in  feet. 

Depths  upon  Weir,  in  Feet. 

Ft. 

0.075 

Ft. 

0.1 

Ft. 
0 15 

Ft. 

0.2 

Ft. 

0.25 

Ft. 

0.3 

Ft. 

0.4 

Ft. 

0.5 

Ft. 

0.6 

Ft. 

0.7 

Ft. 

0.8 

Ft. 

0.9 

Smeaton  and  Brindley 

Poncelet  and  Lesbros 

Du  Buat 

Simpson  and  Blackwell..  . 

0- S 
.646 

1- 533 
3.0 

10.0 

.682 

.625 

•673 

.740 

•615 

.66  7 
.618 
.662 

•725 

.638 

.640 

.608 

.645 

.700 

•673 

.623 

.600 

■635 

.678 

.700 

.613 

•597 

.629 

•657 

.718 

.605 

•593 

.624 

.638 

•735 

.596 

•59o 

.622 

.608 

•754 

•593 

.488 

.628 

•592 

.767 

•485 

•635 

•577 

.780 

.482 

.560 

•793 

.480 

.478 

292 


MEASURING  WEIRS,  AND  WEIR  GAUGING. 


Within  the  limits  of  depths  covered  by  the  above  experi- 
ments the  coefficients  all  increase  as  the  depths  decrease, 
except  in  the  last  series  belonging  to  the  10  foot  weir.  The 
curves  in  each  instance  begin  to  bend  rapidly  at  depths  of 
about  three-tenths  feet.  In  the  two  last  series  above,  the 
convexities  of  the  curves  are  opposed  to  each  other,  and  the 
curves  cross  at  a depth  of  .275  feet. 

314.  Vacuum  under  the  Crest. — If  the  partitions  E 
(Fig.  44)  are  prolonged  below  the  wen-  so  as  to  close  the 
ends  of  the  crest  contraction,  and  the  fall  is  slight  to  surface 
of  tail  water,  the  moving  current  will  withdraw  sufficient 
air  from  under  the  fall  to  produce  a vacuum  in  the  crest 
contraction,  from  which  will  result  an  increased  flow  over 
the  weir.  Such  vacuum  will  take  place  if  the  surface  of 
the  tail  water  rises  to  the  level  of  the  crest  when  there  is 
two  and  one-half  or  more  inches  depth  flowing  over  the  weir. 

The  tail  water  may  rise  near  to  the  crest  of  the  weir,  if 
no  vacuum  is  produced,  without  materially  affecting  the 
volume  of  flow. 

315.  Examples  of  Initial  Velocity. — Mr.  Francis 
found  that  with  a half  foot  depth  upon  the  weir,  a half  foot 
per  second  initial  velocity  of  approach  increased  the  dis- 
charge about  one  per  cent.,  and  with  one  foot  upon  the 
weir,  one  foot  per  second  initial  velocity  increased  the  dis- 
charge about  two  per  cent. 

When  initial  velocity  exists  in  the  approaching  water, 
and  the  flow  is  irregular,  with  eddies,  results  of  submerged 
obstructions  or  irregular  channel,  the  channel  should  be 
corrected,  and,  if  necessary,  a grating  placed  in  the  stream 
some  distance  above  the  weir,  so  that  the  water  will  ap- 
proach with  steady  and  even  flow  upon  each  side  of  the 
channel’s  axis,  so  that  correct  measurements  may  be  takei] 
of  the  height  of  the  surface  of  the  stream  above  the  wen. 


WIDE-CRESTED  WEIRS. 


293 


316.  Wide- Crested  Weirs. — If  the  crest  of  the  weir  is 
thickened,  as  in  the  case  of  an  nnchamfered  plank,  the  jet 
tends  to  cross  in  contact  with  its  full  crest  breadth,  and  the 
contraction  is  distorted.  This  is  especially  the  case  when 
the  depth  upon  the  weir  is  less  than  three  inches. 

If  the  edge  receiving  the  current  is  not  a perfect  angle 
not  greater  than  a light-angle,  that  is,  if  it  is  worn  or 
rounded,  the  jet  tends  to  follow  the  crest  surface  and  dis- 
tort the  contraction. 

In  such  cases  the  ordinary  formula  are  not  applicable, 
and  the  safest  remedy  is  to  correct  the  weir. 

When  the  web  crest  is  about  three  feet  wide,  and  level, 
with  a rising  incline  to  its  receiving  edge,  as  in  Fig.  47,  Mr. 
Francis  suggests  a formula  for  approximate  measurements, 
when  end  contractions  are  suppressed,  for  depths  between 
six  and  eighteen  inches,  as  follows : 


Q = 3.01208  l E15S 

The  coefficient  m is  here  .563  approximately. 

Fig.  47. 


(12) 


< 3—0 


10' 


0 


In  Mr.  Blackwell’ s experiments  on  weirs  three  feet  wide, 
both  level  and  inclined  downward  from  the  receiving  edge 
to  the  discharge,  coefficients  m were  obtained,  as  follows, 
applicable  to  the  formula 


Q = | m l V2g  EK 


(13) 


294 


MEASURING  WEIRS,  AND  WEIR  GAUGING 


TABLE  No.  73. 

Coefficients  for  Weir  Crests  Three  Feet  Wide. 


Depths  from 
still  water 
upon  the 
the  weir. 

3 feet  long, 
level. 

3 feet  long, 
inclined. 

1 in  18. 

3 feet  long, 
inclined. 

1 in  12. 

6 feet  long, 
level. 

10  feet  long, 
level. 

10  feet  long 
inclined. 

1 in  18. 

Feet. 

771. 

m. 

771. 

771. 

771. 

771. 

.083 

• 452 

■ 545 

.467 

.... 

.381 

.467 

.167 

.482 

• 546 

•533 

•479 

•495 

.250 

.441 

• 537 

• 539 

.492 

•333 

.419 

•431 

•455 

•497 

•515 

.417 

•479 

.516 

.518 

.500 

.501 

• 531 

• 507 

•513 

•543 

.533 

.488 

• 513 

• 527 

•497 

.667 

.470 

.491 

.468 

.507 

.750 

.476 

.492 

.498 

.480 

.486 

.833 

.... 

•465 

•455 

•9T7 
1. 000 

.467 

317.  Triangular  Notches. — Prof.  James  Thomson,  of 
the  University  of  Glasgow,  proposed,  in  a paper  read  before 
the  British  Association  at  Leeds,  in  1858,  a triangular  form 
of  measuring  weir.  In  his  experiments  with  such  weir,  the 
depths  of  water  varied  from  2 to  4 inches,  and  the  volumes 
from  .033  to  .6  cubic  feet  per  second.  From  his  experi- 
ments with  a right-angled  triangular  notch  he  derived  the 
formula  (with  It  in  inches  and  Q in  cubic  feet  per  minute!. 

Q = 0.317  hi.  (14) 

Tire  flow  for  all  depths  would  be  through  similar  til- 
angles,  therefore  an  empirical  formula  applies  with  greater 
reliability  to  varying  depths. 

Prof.  Thomson  claimed  that  “in  the  proposed  system 
the  quantity  flowing  comes  to  be  a function  of  only  one 
variable — namely,  the  measured  head  of  water — while  in 
the  rectangular  notches  it  is  a function  of  at  least  two  vari- 
ables, namely,  the  head  of  water,  and  the  horizontal  width 


obstacles  to  accurate  measures. 


295 


of  the  notch ; and  is  commonly  also  a function  of  a third 
variable,  namely,  the  depth  from  the  crest  of  the  notch 
down  to  the  bottom  of  the  channel  of  approach.” 

When  the  stream  is  of  such  magnitude  as  to  require  a 
considerable  number  of  triangular  notches  (say  of  90° 
angles,  or  isosceles  right-angled  triangles)  for  a single  gauge, 
the  greatest  nicety  will  be  required  to  place  the  inverted 
apices  all  in  the  same  exact  level,  so  one  measurement  of 
depth  only  may  suffice  for  all  the.  notches. 

The  angles  of  the  notches  in  each  weir  must  conform 
exactly  to  the  angles  of  the  notch  from  which  the  empirical 
formula,  or  series  of  coefficients  for  given  depths,  was  de- 
duced. 

For  large  volumes  of  water,  the  great  length  required 
for  a sufficient  number  of  notches,  as  well  as  depth  required 
in  each  notch,  are  often  obstacles  not  easily  overcome,  and 
the  mechanical  refinement  necessary  to  ensure  accuracy  of 
measurement  is  often  difficult  of  attainment. 

318.  Obstacles  to  Accurate  Measures. — A correct 
measurement  of  the  depth  of  water  upon  a weir  is  not  so 
easily  obtained  as  might  be  supposed  by  those  unpractised 
in  hydraulic  experiments. 

If  the  weir  is  truly  level  and  the  shoulders  truly  vertical, 
which  are  results  only  of  good  workmanship,  and  the 
length  intended  to  be  some  given  number  of  even  feet,  the 
chances  are  that  only  a skilled  workman  'will  have  brought 
the  length  within  one,  two,  or  even  three-thousandths  of  a 
foot  of  the  desired  length.  Again,  when  the  weir  is  truly 
adjusted  and  its  length  accurately  ascertained,  it  is  not 
easy  to  measure  the  depth  upon  the  crest  within  one  or  two 
thousandths  of  a foot,  without  excellent  mechanical  devices 
for  the  purpose. 

The  errors  due  to  agitation  or  ripple  upon  the  water  and 


296 


MEASURING  WEIRS,  AND  WEIR  GAUGING. 


tlie  capillary  attraction  of  the  measuring-rod  have  to  he 
eliminated. 

If  the  graduated  measuring-rod  is  of  clean  wood,  glass, 
steel,  copper,  or  any  metal  for  which  water  has  an  affin- 
ity, and  its  surface  is  moist,  or  is  wetted  by  ripple,  the 
water  'wall,  in  consequence  of  capillarity,  rise  upon  it  above 
the  true  water  level ; or  if,  on  the  other  hand,  the  rod  is 
greasy,  the  water  may,  in  consequence  of  molecular  repul- 
sion, not  rise  upon  it  to  the  true  surface  level. 

These  sources  of  error  may  not  be  of  much  consequence 
in  gaugings  of  mountain  streams,  when  the  only  object  is 
to  ascertain  approximately  the  flow  from  a given  watershed ; 
but  in  measurements  of  power,  and  in  tests  of  motors,  tur- 
bines, and  pumps,  they  are  of  consequence. 

Upon  a weir  ten  feet  long,  with  one  foot  depth  of  water 
flowing  over,  an  error  of  one-thousandth  of  a foot  in  meas- 
urement of  depth  will  affect  the  computation  of  flow  about 
0.30  cubic  feet  per  minute,  and  an  error  of  one-thousandth 
of  a foot  (about  -J-s  of  an  inch)  in  length  will  affect  the  com- 
putation about  two-tenths  of  a cubic  foot  per  minute. 

These  amounts  of  water  upon  a twenty-five  or  thirty  foot 
fall  would  have  quite  appreciable  effects  and  value. 

319.  Hook  Gauge. — A very  ingenious  and  valuable 
instrument  for  accurately  ascertaining  the  true  level  of  the 
water  surface,  and  depth  upon  a weir  to  still  water,  was 
invented  by  Uriah  Boy  den,  C.  E.,  of  Boston,  and  used  by 
him  in  hydraulic  experiments  as  early  as  the  year  1840. 

This,  shown  in  one  of  its  forms,  in  Fig.  48,  is  commonly 
termed  a Jioolc  gauge. 

This  gauge  renders  capillary  attraction  a useful  aid  to 
detect  error,  instead  of  being  a troublesome  source  of  error. 

The  instrument  is  firmly  secured  to  solid  substantial 
beams  or  a masonry  abutment,  so  that  it  will  be  suspended 


HOOK  GAUGE. 


297 


over  the  water  channel  a few  feet  up- 
stream from  the  weir,  and  where  the 
water  surface  is  protected,  naturally 
or  artificially,  from  the  influence  of 
wind  and  eddies.  The  gauge  is  here 
adjusted  at  such  a height  that  when  it 
reads  zero  the  point  of  the  hook  shall 
accurately  conform  to  the  level  of  the 
crest  of  the  wen ; or  the  vernier  reading 
is  to  be  taken,  with  the  hook  at  the 
exact  weir  level,  for  a correction  of 
future  readings. 

This  correction  is  to  be  verified  as 
occasion  requires  between  successive  ex- 
periments. 

When  the  full  flow  of  water  over  the 
weir  has  become  uniform,  the  hook  is 
to  be  carefully  raised  by  the  screw  mo- 
tion, until  the  point  just  reaches  the 
surface  of  the  water.  If  the  point  is 
lifted  at  all  above  the  water  surface,  the 
water  is  lifted  with  it  by  capillary  at- 
traction, and  the  reflection  of  light  from 
the  water  surface  is  distorted  and  reveals 
the  fact.  The  screw  is  then  to  be  re- 
versed and  the  point  slightly  lowered 
to  the  true  surface. 

In  ordinary  lights,  differences  of 
0.001  of  a foot  in  level  of  the  water  are 

easily  detected  by  aid  of  the  hook, 
= and  even  0.0001  of  a foot  by  an  expe- 
— rienced  observer  in  a favorable  light. 
Such  gauges  are  ordinarily  gradu- 


298 


MEASURING  WEIRS,  AND  WEIR  GAUGES. 


ated  to  hundredths  of  a foot  and  are  provided  with  a ver- 
nier indicating  thousandths  of  a foot,  and  fractions  of  tLis 
last  measure  may  he  estimated  with  reliability. 

320.  Rule  Gauge.  — For  rougher  and  approximate 
measures  a post  is  set  at  an  accessible  point  on  one  side  cf 
the  channel,  above  the  weir,  and  its  top  cut  off  level  at  the 
exact  level  of  the  weir  crest. 

The  depth  of  the  water  is  measured  by  a rule  placed 
vertically  on  the  top  of  this  post  and  observed  with  care. 

321.  Tube  and  Scale  Gauge. — For  summer  meas- 
ures, a pipe,  say  three-fourth  inch  lead,  is  passed  from  the 
dead  water  a little  above  the  weir,  through  or  around  the 
weir,  and  connected  to  a vertical  glass  water  tube  set  below 
the  weir  at  a convenient  point  of  observation.  In  such  case 
a scale  with  fine  graduations  is  fastened  against  the  glass 
with  its  zero  level  with  the  weir.  With  such  an  arrange- 
ment quite  accurate  observations  can  be  taken,  as  the 
water  in  a three-quarter  inch  tube  will  rise  to  the  level  of 
the  water  above  the  weir  over  the  open  mouth  of  the  tube, 
due  precautions  being  taken  to  keep  sediment  out  of  the 
tube. 

321a.  Weir  Volumes. — Table  No.  70,  page  290,  has 
been  computed  with  a variable  C,  as  in  table  69,  as  is  proper 
for  close  accuracy.  Table  73a  gives  results  more  in  detail, 
but  is  computed  with  a constant  coefficient,  by  formula  Xo.  7. 
page  284,  for  each  hundredth  of  foot-depth,  from  0.2  ft.  to 
3.0  ft.  The  intermediate  thousandths  of  a foot-depth  may 
readily  be  interpolated.  (See  Table,  Xo.  SO,  page  380. i 


WEIR  VOLUMES. 


298a 


TABLE  No.  73a. 

Computed  Weir  Volumes. 

On  sharp  crest,  Q = 3.33  (Z  — o.  1 n H)  H ’ (§  310,  p.  284),  for  each  lineal 
foot  of  weir. 

(See  also  foot  note  page  289,  for  effect  of  contractions.) 


Depth, 
in  feet. 

.00 

.01 

.02 

.03 

.04 

.05 

.06 

.07 

.08 

.09 

Discharge  Q,  in  cubic  feet  per  second. 

Length 

= 1 ft. 

n = 0. 

.2 

0.2078 

0.3205 

0.3436 

03673 

°-39I5 

0.4162 

0.4415 

0.4672 

0.4934 

0.5200 

•3 

0.5472 

05748 

0.6028 

0.6313 

0.6602 

0.6895 

0.7193 

0-7495 

0 7800 

0.8110 

•4 

0.8424 

O.8742 

0.9064 

0.9390 

°-97I9 

1.0052 

1.0389 

1.0730 

1 1074 

1.1422 

•5 

x-1773 

1.2128 

1.2487 

I.2849 

1-3214 

1.3583 

1-3955 

i-433° 

1.4709 

1. 5091 

.6 

1.5476 

1.5865 

1.6257 

I.6652 

1.7050 

x-745* 

1-7855 

1.8262 

1.8673 

1.9086 

•7 

1-9503 

1.9922 

2.0344 

2.O77O 

2.1198 

2.1629 

2.2063 

2.2500 

2.2940 

2.3382 

.8 

2.3828 

2.4276 

2.4727 

2.5180 

2.5637 

2 6096 

2.6558 

2.7022 

2.7490 

2-7959 

•9 

2.8432 

2.89O7 

2.9385 

2.9865 

3.0348 

3-0831 

3.1322 

3.1813 

3.2306 

3.2802 

1.0 

3-3303 

3.3801 

3-43°4 

3.4810 

3-5318 

3-5828 

5-6342 

3.6857 

3-7375 

3.7895 

1. 1 

3.8418 

3-8943 

3-9470 

4.OOOO 

4-0532 

4.1067 

4.1604 

4--I43 

4.2684 

4.3228 

1.2 

4-3774 

4.4322 

4.4873 

4-5426 

4.5981 

4.6538 

4.7098 

4.7660 

4.8224 

4.8790 

i-3 

4-9358 

4.9929 

5.0502 

77 

5 1654 

5-2233 

5.2814 

5-3398 

5-3984 

5-4572 

i-4 

5-5162 

5-5754 

5.6348 

5-6944 

5-7542 

58143 

5.8745 

5.9350 

5-9957 

6.0565 

i-5 

6.1176 

6.1789 

6.2404 

6.3320 

6.3639 

6.4260 

6.4883 

6.5508 

6.6135 

6.6764 

i.6 

6.7394 

6.8027 

6.8662 

6.9293 

6.9937 

7.0578 

7. 1221 

7.1865 

7.2512 

7.3160 

1-7 

7.3810 

7-4463 

7*5rI7 

7-5773 

7.6431 

7.7091 

7-7752 

7.8416 

7.9081 

7-9749 

1.8 

8.0418 

8.1089 

8.I762 

8.2437 

8-31 '3 

8.3792 

8.4472 

8.5154 

8.5838 

8.6524 

1.9 

8.7212 

8.7901 

8.8592 

8.9285 

8.9980 

Q.0677 

9-1375 

9.2075 

9.2777 

9 3481 

2.0 

9.4187 

9.4894 

9.5603 

9-6314 

9 7026 

9-7741 

9-8457 

9-9 '74 

9.9894 

10.062 

2.1 

10.134 

10.206 

10.279 

10.352 

10.425 

10.498 

IO-57I 

IO.645 

10.718 

10.792 

2.2 

10.866 

10.940 

II.OI5 

II.089 

11.164 

11.239 

11. 314 

11.389 

11.464 

11.540 

2'3 

11.615 

11.691 

n.767 

11  843 

11.920 

11.996 

12.073 

12.150 

12.227 

12.304 

2.4 

12.381 

12.459 

12.536 

I2.6l4 

12.692 

12.770 

12.848 

12.927 

13-005 

13.084 

2-5 

13.163 

13.242 

X3.32I 

13.401 

13.480 

13.560 

13.640 

13.720 

13.800 

13.880 

2.6 

13.96X 

14. 041 

14. 122 

14.203 

14.284 

14.365 

14.447 

14  528 

14.610 

14.692 

2.7 

H-774 

14.856 

14.938 

15.021 

16.103 

15.186 

15.269 

15-352 

15-435 

I5-5I9 

2.8 

15.602 

15.686 

15.769 

15.853 

15.938 

16.022 

16. 106 

I6.I9I 

16.275 

16.360 

2.9 

3-o 

16- 445 

17- 305 

16.530 

IO.616 

16.7OI 

16.787 

16.872 

16.958 

17.044 

I7-I3° 

17.217 

If  there  is  velocity  of  approach  (§  311,  p.  285)  divide  the 
weir  volume  as  above  by  section  of  channel,  in  square  feet, 
for  approximate  velocity  v.  Then  the  additional  depth  on 
weir  dne  to  this  velocity  is  h = ( [v 2 -r-  64.4).  Add  to  the 
measured  depth  1.5  h for  the  corrected  depth  on  weir,  and 
then  take  the  volume  from  the  above  table  for  the  corrected 
depth,  or  for  closer  accuracy  compute  by  formula  No.  10, 
page  286,  with  coefficient  from  table  69. 

The  coefficient  of  h (1.5)  becomes  2.05  approximately 
when  there  is  velocity  of  approach  with  end  contraction. 


Fig.  i 


Fig.  3. 


MODERN  CURRENT  METERS. 


CHAPTEB  XT. 


FLOW  OF  WATER  IX  OPEN  CHANNELS. 

322.  Gravity  the  Origin  of  Flow. — Gravity  tends  to 
pause  motion  in  all  bodies  of  water.  Its  effects  upon  the 
jiow  of  water  under  'pressure  have  been  already  discussed 
(Chap.  XIII),  as  have  also  the  effects  of  the  reactions  and 
cohesive  attractions  that  retard  its  flow. 

The  same  influences  control  the  flow  of  water  in  open 
channels. 

The  fluid  particles  are  attracted  toward  the  earth’s 
centre  along  that  path  where  the  least  resistance  is  op- 
posed. 

An  inclination  of  water  surface  of  one-thousandth  of  a 
foot  in  one  foot  distance  leaves  many  thousand  molecules 
of  water,  but  partially  supported  upon  the  lower  side,  and 
they  fall  freely  in  that  direction,  and  by  virtue  of  their 
weight  press  forward  the  advanced  particles  in  lower  planes. 


Fig.  49. 


If  water  is  admitted  from  the  reservoir  A,  into  the  open 
canal  B (Fig.  49),  until  it  rises  to  the  level  bb\  it  will  there 
stand  at  rest,  although  the  bottom  of  the  channel  is  in 
dined,  for  its  surface  will  be  in  a horizontal  plane.  The 


300 


FLOW  OF  WATER  IN  OPEN  CHANNELS. 


resistances  to  motion  upon  opposite  inclosing  sides,  and 
also  upon  opposite  ends,  balance  eacli  other.  The  alge- 
braic sum  of  horizontal  reactions  from  the  vertical  end  bd, 
is  exactly  equal  to  the  sum  of  the  horizontal  reactions  from 
the  inclined  bottom  db',  for  the  vertical  projection,  or  trace 
of  the  inclined  area,  db1,  exactly  equals  the  vertical  area  bd. 

The  same  equilibrium  would  have  resulted  if  the  bot- 
tom had  been  horizontal  or  inclined  downward  from  d to/’ 
and  a vertical  weir  placed  at  fb' , for  the  horizontal  reaction 
from  fb'  would  have  been  balanced  by  the  sum  of  the  hori- 
zontal reactions  from  bd  and  df. 

A destruction  of  equilibrium  permits  gravity  to  generate 
motion. 

If  a constant  volume  of  water  is  permitted  to  flow  from 
the  reservoir  A into  the  channel  B,  the  water  surface  will 
rise  above  the  level  bb , when  there  will  be  less  resistance  at 
the  end  b'  than  at  b,  and  the  fluid  particles,  impelled  by  the 
force  of  gravity,  will  flow  toward  b'.  When  motion  of  the 
water  is  fully  established,  and  the  flow  past  b has  become 
uniform,  there  will  result  an  inclination  of  the  surface  from 
a toward  a'.  This  inclination,  being  a resultant  of  a con- 
stant force,  gravity  may  be  used  as  a measure  of  the  por- 
tion of  that  force  that  is  consumed  in  maintaining  the 
velocity  of  flow. 

323.  Resistances  to  Flow. — Let  the  channel  be  ex- 
tended from  b'  (Fig.  49)  indefinitely,  and  with  uniform  in- 
clination, as  from  a'  to  A'  (Fig.  50).  Some  resistance  to  flow 
will  be  presented  by  the  roughness  and  attraction  of  the 
sides  and  bottom  of  the  channel. 

If  the  sides  and  bottom  are  of  uniform  quality,  as  re- 
spects smoothness  or  roughness,  the  amount  of  their  resist- 
ance in  each  unit  of  length  will  be  proportional  to  the  sum 
of  their  areas,  plus  the  water  surface  in  contact  whli  the 


EQUATIONS  OF  RESISTANCE  AND  VELOCITY. 


301 


air  reduced  by  an  experimental  fractional  coefficient ; and 
to  the  square  of  the  velocity  of  flow  past  them ; and  in- 
versely to  the  section  of  the  stream  flowing  past  them. 

The  exact  resistance  due  to  the  air* perimeter  has  yet  to 
be  separated  and  classified  by  a series  of  careful  experi- 
ments, but  we  may  assume  that  the  resistance  of  calm  air 
for  each  unit  of  free  surface  Avill  not  exceed  one  per  cent, 
of  that  for  like  units  of  the  bottom  and  sides  of  smooth 
channels,  and  will  bear  a less  ratio  for  rough  channels. 

The  air  perimeter  resistance  will  be  increased  by  oppos- 
ing, and  following  winds  may  enhance  the  velocity. 

Let  It  be  the  sum  of  resistances  from  the  sides,  bottom, 
and  surface,  in  foot  pounds  per  second  ; C,  the  contour,  or 
wetted  area  of  sides  and  bottom,  and  cs  the  width,  or  sur- 
face perimeter,  in  square  feet ; f,  a coefficient  of  cs ; S,  the 
sectional  area  of  the  stream,  in  square  feet;  and  v,  the 
mean  velocity  of  flow  of  the  stream,  in  feet  per  second  ; 
then  we  have  for  equation  of  resistance  to  flow,  from  sides, 
bottom,  and  surface,  for  one  unit  of  length : 


It  - 


C ±fcs 
S 


X (m)  — 
■2g 


and  for  any  length,  l,  in  lineal  feet, 


(1) 


M = 


C ±fcs 


S 


X l X 


mv 3 
2 g 


(21 


324.  Equations  of  Resistance  and  Velocity. — 

When  the  surface  of  the  water  is  level  the  entire  force  of 
gravity  acts  through  it  as  pressure,  but  when  the  surface  is 
inclined,  a portion  of  the  pressure  is  converted  into  motion. 
Motion  is  measured  by  its  rate  or  distance  passed  through 
in  the  given  unit  of  time,  and  the  rate  is  expressed  by  the 
term  velocity. 


302 


FLOW  OF  WATER  IN  OPEN  CHANNELS. 


In  Fig.  50,  let  a'k  be  the  inclination  of  the  water  surface 
in  a unit  of  length  of  the  stream,  then  a"k  will  be  its  ver- 
tical distance  and  k'k  its  horizontal  distance. 

The  effective  action  of  gravity  g to  maintain  motion,  or 
velocity  of  the  water,  is  dependent  on  this  slope,  and  the 
slope  is  usually  indicated  by  a ratio  of  the  vertical  distance 
to  the  horizontal  distance. 


Fig.  50. 


Let  7i"  be  the  vertical  distance  a"k  and  l be  the  hori- 
zontal distance  k'k , and  i the  slope,  or  sine  of  the  inclina- 


tion, then  the  ratio  of  slope  is  i = 


7T 

l • 


If  the  sides  and  bottom  of  the  channel  opposed  no  resist- 
ance to  flow,  then  the  velocity  v should  be  accelerated  in 
the  length  k'k  an  amount  equal  to  the  V2g7i",  but  the  flow 
being  uniform,  the  sum  of  the  resistances  in  l just  balance 
the  accelerating  force  of  gravity  g,  and  the  velocity  v con- 
tinues from  a'  to  k at  the  same  rate  that  had  already  been 
established  when  the  stream  reached  a',  which  was  due  to 

v2 

some  height  aa'  = 7i  = „ . 

2 g 

By  transposition,  we  have  v — V2 gli. 

If  the  sum  of  the  resistances  in  the  length  k'k  balance 
the  accelerating  force  due  to  the  head  a"k  = 7i",  then  we 
have 


h"  = a x 


0±fc, 


X lm. 


(3) 


v*  — 2g  x C±fc*  i 


X -r  X — . 


m 


(4) 


EQUATIONS  OF  RESISTANCE  AND  VELOCITY. 


303 


The  inverted  fractional  term 


S 


Section 


is 


C±fca  ~ Contour* 
termed  in  open  channels  the  hydraulic  mean  depth,  and 
the  letter  r is  used  to  express  it.  Since  i expresses  the 

h" 

value  of  the  sine  of  the  slope  = we  have 

c 


V = 


2gri ) 1 


h"  = 


m 

Imv1 

2gr 


Vri. 


lv' 


(5) 


(6) 


The  total  head  H equals  the  heights  aa!  + a"7c  = h + h", 


and 


h + h"=H= 


tt  . Imv1 


2g+  2gr 


L , tm)  v 

= |1  + 7-[ 


8/ 


(7) 


v — 


1 + m- 
r 


(8) 


In  long  canals  and  rivers,  with  slopes  not  exceeding 
three  feet  per  mile,  the  velocity  head  h is  usually  insig- 
nificant compared  with  the  frictional  head  h",  and  may  be 
neglected  in  the  equation. 

When  the  rate  of  flow  is  uniform,  h is  a constant  quan- 
tity, independent  of  the  length,  and  when  the  mean  velocity 
is  known  may  be  taken,  by  inspection,  from  the  table  of 
“Heads  (h)  due  to  given  Velocities,”  page  264. 

The  frictional  head  h"  increases  with  the  length,  hence 
the  term  Z in  the  equation  of  h". 


* In  full  pipes  — equals  the  sectional  area  divided  by  the  full  circumfer- 

G 

ence,  and  is  termed  the  hydraulic  mean  radius  (§  268),  hut  in  open  channels 
the  contour  is  the  wetted  perimeter  ; that  is,  the  sum  of  the  sides  and  bottom 


304 


FLOW  OF  WATER  IN  OPEN  CHANNELS. 


The  mean  velocity,  which  multiplied  into  the  sectional 
area  of  the  stream  will  give  the  volume  of  discharge,  is  a 
quantity  often  sought. 


Neglecting  the  value  of  h = 


which  has  given  the 


stream  its  resultant  motion,  and  taking  the  formula  for  h\ 
the  head  balancing  the  resistance  to  flow, 


h" 


lmv% 
2gr  ’ 


and  we  have  by  transposition, 


in  which  v = mean  velocity  of  all  the  films,  in  feet  per  sec. 


r — hydraulic  mean  depth 


8 

C±fcs 


in  feet. 


i = sine  of  inclination  = -j-  in  feet. 
g = 32.2. 


m — a comprehensive  variable  coefficient. 

C = wetted  earth  perimeter. 

cs  = surface  (air)  perimeter,  not  exceeding  ± .01 
for  smooth,  or  + .05  for  rough  channels. 

I = length,  referred  to  a horizontal  plane. 

Jl"  = vertical  fall  in  the  given  length. 


325.  Equation  of  Inclination. — If  the  flow  is  to  be 
at  some  predetermined  rate,  and  it  is  desired  to  find  the 
inclination,  or  slope  to  which  the  given  velocity,  for  the 
given  hydraulic  mean  radius,  is  due,  then  we  have,  by 
transposing  again, 


mv% 


(10) 


COEFFICIENTS  OF  FLOW  IN  CHANNELS. 


305 


The  member  v,  refers  to  the  mean  motion  of  all  the  fluid 
threads,  or  the  rate  which,  multiplied  into  the  section  of  the 
stream,  gives  the  volume  of  flow. 

326.  Coefficients  of  Flow  for  Channels. — The  value 
of  the  coefficient  of  flow  m,  and  its  dependent  c,  is  very 
variable  under  the  influences  of 

(a.)  Velocity  of  flow,  or  inclination  of  water  surface  ; 

(5.)  Hydraulic  mean  depth  ; 

(<?.)  Mean  depth  ; 

(d.)  Smoothness  or  roughness  of  the  solid  perimeter; 

(e.)  Direction  and  force  of  wind  upon  the  water  surface. 

A complete  theoretical  formula  for  flow  in  a straight, 
smooth,  symmetrical  channel  should  have  an  independent 
coefficient  for  each  of  these  influences,  and  other  coefficients 
for  influences  of  bends,  convergence  or  divergence  of  banks, 
and  eddy  influences ; but  such  mathematical  refinement 
belongs  oftener  to  the  recitation  room  than  to  expert  field 
practice. 

The  comprehensive  coefficient  m,  for  open  channels, 
which  includes  all  these  minor  modifiers,  is  inconstant  in  a 
degree  even  greater  than  the  coefficient  m for  full  pipes, 
which  we  have  already  discussed  (§  270.  Peculiarities  of 
the  Coefficient  of  Flow),  to  which  the  reader  is  here  referred. 

Experience  teaches  that  m is  less  for  large  or  deep,  than 
for  small  or  shallow  streams ; for  high  velocities,  than  for 
low  velocities ; and  for  smooth,  than  for  rough  channels. 

Kutter  adopted,*'  for  open  channels,  the  simple  formula 
v — c V ri,  and  divided  the  values  of  c into  twelve  classes, 
to  meet  the  varying  conditions,  from  small  to  great  velocities 
ana  sections  of  streams,  and  from  smooth  to  rough  sides 


* Vide  “ Hydraulic  Tables,”  trans.  by  L.  D.  A.  Jackson.  London,  1876. 


306 


FLOW  OF  WATER  IN  OPEN  CHANNELS. 


and  beds  of  channels.  His  c corresponds  to 


r m’ 


as  herein 


employed.  He  divides  c,  introducing  a factor  n varying 
with  degrees  of  roughness  of  the  channel  and  a factor 
m -T-  i covering  the  secondary  effect  upon  c by  change  of 

. I , m 
a -J — -4- 
1 n ' i 

( m\n* 

1+va+7  m 

in  which  a , Z,  and  m are  constants  whose  values  he  derives 
from  experiment.  Then 

1.811  , .00281 


velocity.  His  value  of  c then  becomes  c = 


41.6  + 


n 


c = 


1 + 41.6 


.00281 \ n 


% 


~w 


41.6  + 


1.811 


r 

.00281 


and 


= cVri  — 


n 


1+  41.6  + 


. 00281\ n 

i ‘Vr 


X V ri  (10a) 


Some  values  of  n for  different  channel  contours  are 
approximately  as  follows,  viz.:  .013  for  smooth  brickwork, 
.017  for  smooth  rubble,  .020  for  smooth,  clean  soil,  .025  for 
smooth  sandy  gravel,  .030  for  gravel  with  some  stones, 
.035  for  very  rough  channels. 

327.  Observed  Data  of  Flow  in  Channels. — 
We  deduce,  in  Table  74,  several  values  of  the  m of  the 
Cliezy  formula  from  various  actual  measures,  covering  a 
wide  range  of  values  of  cross-sections,  r,  and  velocities  of 
flow  v,  using  data  given  by  Messrs.  Humphreys  and  Abbott, 
1861 ; MM.  Darcy  and  Bazin,  1865  ; M.  Heinr.  Gerbenau, 
1867  ; and  in  sundry  reports  of  the  II.  S.  Engineer  Corps. 


TABLE  OF  COEFFICIENTS  FOR  CHANNELS. 


307 


Observed 


T A B L 
and  Computed 


i m i 


E No. 
Flows  in 
and  m — 


7 4. 


Canals  and  Rivers. 

m> 


Name  of  Stream. 

A. 

B. 

c. 

D. 

E. 

F. 

G. 

Area  = S. 

Wetted 
Perimeter 
= C 

Hy.  mean 
Depth  = r. 

V 

Inclination 
— i. 

Observed 
Velocity  1 
= v . 

Value  of 
Coefficient 
= m. 

Computed 

Velocity 

= V. 

Sq./t. 

Feet. 

Feet. 

Feet . 

Feet . 

Feet. 

Feeder  Chazilly 

9-5 

9-9 

O.96 

0.000792 

1.234 

•°32I5 

I-I33 

ir*3 

10.8 

1.04 

.000445 

0.962 

.03227 

O.966 

it  u 

14.9 

12.3 

I.2I 

.000808 

1.667 

.02265 

1-547 

u u . . 

18.1 

13.1 

I-38 

.000450 

1.296 

.02381 

1.275 

<t  o 

18.8 

13-3 

1.41 

.000993 

1.798 

.O2789 

1.926 

“ “ 

19.4 

13.8 

1.41 

.000858 

1.815 

.O2363 

1-794 

tt  tt 

22.2 

14.4 

i-54 

000986 

1-959 

.02548 

2.062 

It  u 

22.9 

14.7 

1.56 

.000842 

1.998 

.02Il3 

I*93° 

27.2 

159 

171 

.000441 

1.510 

.02130 

1.496 

Feeder  Grobois 

10. 1 

10.2 

0.98 

.000555 

0.984 

.036l7 

I.063 

U *k  ....  

11. 8 

“■3 

1.05 

.000310 

0.817 

.03155 

0.852 

17.2 

12.5 

i-38 

.000450 

1.326 

.02274 

I.278 

23.0 

14. 1 

I.63 

.000479 

1-434 

.02445 

1.502 

25-9 

14. 1 

1.71 

.000515 

1.746 

.01860 

I.6l7 

it  tt 

26.8 

I5*7 

1.71 

.000493 

1.683 

.OI9I7 

E5S5 

it  tt 

30.8 

173 

1.78 

.000275 

1.467 

.OI465 

I.23I 

“ “ 

32.0 

17-3 

1.85 

.000330 

1.411 

.01974 

1.381 

Speverbach 

30.2 

x9*7 

x-54 

.000407 

1.814 

.OI408 

1.422 

Canal 

50.; 

20.0 

2.40 

.000063 

1. 134 

•00757 

0.743 

Lauter  Canal 

56.4 

31.0 

1.82 

.000664 

2.106 

.01754 

r-934 

Saalach  

86.9 

6l.2 

x*38 

.001036 

2.155 

.OI982 

*•934 

“ 

96.7 

71.8 

i-34 

.001136 

1.970 

.02585 

I.98O 

ki  

119.0 

32-5 

3-7° 

.000698 

2.723 

.02243 

3-523 

C.  and  O.  C.  Feeder 

121.0 

32.7 

3-7° 

.000699 

3-°32 

.Ol8lI 

3-527 

River  Haine 

248.5 

50.5 

4.90 

.000165 

2.495 

.O0836 

2.I46 

Isaa 

3oo.i 

161.6 

1.85 

.00250c 

3-997 

.OI864 

3.8l2 

U 

306.4 

53-4 

5.70 

.000155 

2.558 

.OO869 

2.328 

Seine 

1978 

349 

5.70 

.000127 

2.C94 

.OIO63 

2.107 

B.  La  Fourche 

2868 

230 

15-7 

.000044 

2.789 

.00572 

3. no 

W ...  

3025 

232 

13.0 

.000037 

2.843 

.00383 

2.311 

k*  

3738 

238 

15.7 

.000045 

3.076 

.OO481 

3-145 

Seine 

4421 

405 

IO.9O 

.000140 

3-741 

.00702 

3.810 

,k  

6372 

439 

14.50 

.000140 

4.232 

.OO73O 

5.062 

kk  

8034 

5°4 

15.90 

.000172 

4.682 

.OO803 

6.326 

‘k  

9522 

5*8 

I8.4O 

.000103 

4.689 

.00268 

5.991 

Rhine 

14150 

I458 

9.72 

.000112 

2.910 

.OO828 

3-°37 

Upper  Mississippi  

159“ 

l6l2 

9.87 

.000074 

2.941 

.00544 

2-534 

328.  Table  of  Experimental  Flows,  and  Coef- 
ficients.— The  following  experiments,  in  Table  To,  quoted 
from  various  sources,  give  valuable  data  respecting  chan- 
nels of  various  sizes  and  degrees  of  roughness,  including 
their  respective  values  of  c 


308 


FLOW  OF  WATER  IX  OPEN  CHANNELS. 


TABLE  No.  75. 

Experimental  Data*  of  Flow  in  Channels  of  Earth. 


Locality  and  Roughness. 

Surface 

Width. 

Depth 

of 

Water. 

Hyd. 

Rad. 

r 

I 

1 Slope 
ft.  in  1000. 

. 

! 2 

Yeloc. 
ft.  per 
sec. 

V 

Coef. 

c 

Feet. 

Feet. 

\Ft./>enooo 

Fat. 

Mill  Race,  loamy  soil 

.69 

O.496 

4.1 

2.109 

46.8 

Creek 

.587 

1-3 

1-424 

51.2 

Mill  Race,  sandy . . . 

.72 

.596 

2-7 

1-934 

43.2 

Landquart,  coarse  detritus 

.62 

10.0 

1.738 

21.0 

Mill  Race 

.86 

• 703 

2.0 

2.199 

58.7 

Rhine,  detritus  and  coarse  gravel 

.76 

14.20 

4.526 

43-4 

Hockenbach.  

S8 

Visalia,  sandy  loam 

Mosa,  coarse  detritus 

•yy 

•99 

11.875 

3.867 

d-1  o7 
35*7 

Mill  Race 

14.8 

1. 11 

I 

2.20 

65.7 

Emme,  coarse  detritus 

1. 19 

5 

3-51 

45-4 

Plessur,  coarse  gravel 

1.25 

9.65 

6.C02 

54-7 

Rhine,  detritus  and  coarse  gravel 

1.32 

7-735 

47.0 

Lutschine,  coarse  detritus 

.... 

.... 

i-34 

3-325 

3-214 

48.0 

Mill  Race,  bed  fine  gravel  and 

earth 

1-387 

1-255 

3-139 

75-3 

Creek 

667 

CS  T 

Spyerbach 

1-54 

.4666 

1.814 

67.67 

Chazillv  Canal,  earth  stony 

13.00 

2.6 

1.34 

.986 

1.96 

50 

Grosbois  Canal,  some  vegetation 

13-3 

2.7 

1.56 

.S42 

2.00 

55-o 

Grosbois  Canal,  some  vegetation 

13-5 

2.9 

I. 71 

• 5 1 5 

i-75 

59 

Grosbois  Canal,  muddy  surface. . 

14.0 

2.9 

I. 71 

•493 

1.6S 

58 

Grosbois  Canal,  no  vegetation... 

15-7 

2.9 

1.78 

2.75 

t-47 

66 

Lauter  Canal,  earth., 

29.5 

1.S2 

.664 

2.  jo6 

6l 

Simme  Canal,  coarse  gravel 

I.S2 

6.50 

4.92 

45-1 

Grosbois  Canal,  some  vegetation 

15-5 

3-1 

1.S5 

■330 

1.41 

57-0 

River  Izar,  coarse  gravel 

153-0 

2.0 

r.86 

2.50 

4.021 

59 

Saalach,  earth  and  detritus 

1. 91 

1.242 

3-077 

63 

Marmel  Canal,  gravel 

Canal 

18 

4- 

2.43 

.0631 

1. 134 

9i-5 

Loch  Katrine,  some  vegetation.. 

2.525 

.1578 

r.7126 

S6.69 

Canal  du  Jard,  no  detritus 

2.5S 

.0651 

1.060 

S2.5 

Saare,  coarse  detritus 

2.70 

3-333 

4-559 

4S.I 

Realtore,  muddy  bottom 

19-7 

4-5 

2.S7 

■43 

2.54 

72.2 

Rhine,  coarse  detritus 

2.92 

6.00 

4- 25 1 

3X-9 

Henares,  sandy  gravel 

2-95 

.326 

2.296 

74.O4 

Tessin,  gravel  and  stones 

2.962 

.254 

1.663 

60.6 

Aar,  some  detritus 

3.12 

1.270 

4.19S 

66.6 

Limmot,  irregular  bed 

3.16 

2-75 

5-346 

57-4 

River  Lech  

153 

3-6 

3 16 

1. 15 

4-95 

Sr.S 

Engstlingen,  irregular  detritus. . . 

3-3i 

22.  2 

S.S56 

32.6 

3.386 

O 7 O 

“2.  II 

Salzach,  detritus 

3-53 

. 

j j j 

•94 

3-43 

60.3 

C.  and  O.  Canal  Feeder,  rough.. 

23 

7-6 

3-70 

.6985 

3-032 

59.6 

* From  Hering  and  Trautwine’s  Tables,  and  other  sources. 


FLOW  OF  WATER  IN  OPEN  CHANNELS. 


303« 


TABLE  No.  7 5.— (Continued.) 


Experimental  Data  of  Flow  in  Channels  of  Earth. 


Locality  and  Roughness. 

Surface 

Width. 

Dep  th 
of 

Water. 

Hyd. 

Rad. 

r 

Slope 
ft.  in  1000. 
i 

Veloc. 
ft.  per 
sec. 

V 

Coef. 

c 

Feet. 

Feet . 

Ft.penooc 

Feet . 

Escher  Canal,  gravel  and  detritus 
River  Main 

3.76 

3-94 

3.00 

.40 

6.986 

3-05 

65.7 

76.7 

Linth  Canal,  gravel 

113.2 

4.00 

.80 

4.264 

75-5 

Kander,  irregular  bed,  detritus.. 
Scheuss  Canal,  earth  and  some 

4.12 

9.18 

8.692 

44-7 

stones 

Solani  Canal,  rough  bed,  smooth 

21.3 

.... 

4-35 

1.85 

5-445 

60.8 

sides 

65.2 

5-3 

4-50 

.2gi 

2.82 

78.8 

River  Haine,  no  detritus 

River  Salzach 

50 

8 

4.92 

4.96 

• 1653 

.29 

2- 395 

3- 5i 

84.0 

92-3 

Zihl,  muddy  bed  and  irregular. . . 

5.02 

.46 

3.706 

77-1 

Elbe,  gravel  bed 

River  Arve 

Cavour  Canal 

Bear  River  Canal 

Linth  Canal,  earth 

411-3 

8.5 

5-i8 

5-50 

5.58 

5-63 

6.48 

6.72 

6.95 

7.232 

•37 

•450 

•357 

•18939 

•31 

•0933 

.150 

•37879 

3-74 

3.706 

2.6 

2.67 

4.152 

2.515 

3.01S 

4.70 

85-4 

74.6 
60.23 

81.77 

92.6 

Ohio  River 

Reuss  River,  sandy  bed 

Idaho  M.  and  I.  Canal 

1073 

8.0 

100.4 

93-2 

89.8 

Schanzengraben,  earth 

Missouri  at  St.  Charles 

7.81 

8.05 

8-35 

.09 
.117 
. 22 

1.706 

3.10 

64.6 

I0I.0 

Solani  Canal,  bed  quite  smooth.. 

184.2 

9-7 

3-98 

92.8 

Solani  Canal,  bed  rather  uneven 

174-9 

IO 

S 64 

.231 

3-98 

89.1 

Wesser . . 

371 

13.12 

9-44 

.2 

4.064 

93-2 

Tiber 

Seine 

243 

15 

9.46 

9.48 

.1306 
. I40 

3-413 

3-37 

97.1 

92.5 

Pannerden  Canal 

Danube,  sandy  bed 

551 

10.23 

n.88 

.224 

.04 

• 307 

.04 
. 1 

4.20 

2.25 

5-215 

2.369 

3-38 

3-959 

87.7 
102.3 

85-4 

98 

87.8 
84.4 

Rhine,  gravel  and  fine  detritus.  . 

Saone  

Aar,  sand  and  mud 

12. 1 1 
14.64 
14.9 

15-32 

Bayou,  Plaquemine 

268 

24 

•14372 

Bavou  La  Fcurche 

223 

27 

15-71 

.04468 

3.076 

116. 1 

Yssel  River 

321 

9 

5-96 

.1166 

2-773 

105.2 

Great  Nevka 

Seine 

Sacramento 

881 

21 

17.42 

17.87 

'9-93 

.01487 

•075 

.058 

2.049 

3-33 

2.879 

127-3 
91. 1 

83-71 

Irawadi,  at  Saiktho 

4820 

49.0 

22.97 

■03874 

3.091 

103.6 

Mississippi  at  New  Madrid 

5420 

24.06 

.124 

3.681 

67.4 

Mississippi  at  Fulton 

2463 

40.0 

30.4 

.01906 

2-37 

98.4 

Mississippi  above  Vicksburgh. . . . 

2507 

63 

31.16 

.02227 

3-523 

133-8 

Neva 

1218 

50 

35-42 

.01389 

3-23 

145.6 

Mississippi  at  Carrolton 

2369 

86 

60.7 

.0097 

3-38 

139-3 

Mississippi  at  Columbus 

2214 

88 

65.88 

.068 

6.958 

103.9 

3085 


FLOW  OF  WATER  IX  OF  EX  CHAXXELS. 


328a.  Classification  of  Channel  Contours. — The 

variation  in  the  coefficient  c,  as  shown  in  Table  74,  with 
variation  of  channel  surface,  suggests  a classification  of 
roughness  of  contours.  A convenient  classification  is  as 
follows : 

Lixed  Channels. 

B.  Smoothed  Cement. 

I).  Planed  Wood,  length  of  grain  with  current. 

G.  Smooth  Concrete. 

H.  Smooth  Brickwork. 

H.  Ilnplaned  Wood,  laid  across  the  current. 

I.  Smooth  Ashlar. 

I.  Ordinary  Brickwork. 

J.  Rough  Brickwork. 

K.  Smooth  Rubble  in  mortar. 

L.  Smooth  dry  Rubble. 

L.  Smooth  Rubble  sides,  regular  clean  soil  bed. 

M.  Ordinary  dry  Rubble. 

0.  Rough  Rubble. 

Channels  in  Earth. 

L.  Smooth,  clean  regular  Soil. 

M.  Smooth  sandy  Soil. 

N.  Smooth  Loam,  and  some  vegetation. 

N.  Clean,  smooth,  sandy  gravel. 

O.  Regular  Soil,  and  some  vegetation. 

O.  Gravel. 

P.  Gravel,  with  some  stones  or  detrius, 

Q.  Irregular  Gravel,  and  some  vegetation, 

Q.  Irregular  Gravel,  and  coarse  detrius.- 

R,  Very  rough  bed. 


FORMULAS  FOR  CHANNELS. 


308c 


TABLE  No.  75a. 
Classified  Coefficients  c,  for  Varying  r. 


For  about  three  feet  velocity. 


Hyd. 
Rad.  r 

A. 

B. 

c. 

D. 

E. 

F. 

G. 

H. 

1. 

•25 

100.0 

97.8 

94.0 

91 .8 

89.0 

86.7 

84.O 

8l.2 

74.2 

122.8 

II9.O 

I 12'.  O 

109.3 

IO7.O 

IO4.5 

100.0 

90.7 

88.3 

•75 

I36.O 

131.6 

I24.O 

121 . 2 

H8  4 

ll6.0 

1 10.7 

IO7.2 

98.0 

1 .oo 

I46.O 

I4r.4 

133-0 

130.0 

I27.O 

I24.O 

119.0 

115.0 

105.0 

1.25 

*54 -'5 

149.8 

I4O.4 

*37-4 

134  4 

131  .O 

125.7 

122.0 

1 1 1 .2 

1.50 

162.0 

156.5 

147.0 

M3-6 

140.7 

137  O 

122.0 

127.2 

116.3 

1 • 75 

168.2 

l62  7 

i53-o 

149.4 

146.2 

142.6 

136.8 

x32-3 

121 .0 

2.00 

174  0 

168.3 

158.2 

154.6 

151.0 

147.8 

MI-5 

136.7 

125.0 

2.25 

179  0 

!73-2 

163.0 

159.2 

15^.6 

152 . 2 

145.6 

140.7 

128.7 

2.50 

183  5 

178.0 

167.3 

163.4 

159.6 

156.2 

149-5 

144. s 

132.0 

2-75 

187.8 

182  3 

I7I  -3 

1670 

1635 

160.O 

x53  • 1 

148.0 

>35-1 

3.OO 

192.0 

186.2 

*75-o 

171 . 2 

167 .0 

163.4 

156.5 

I5I  -4 

138.2 

3-25 

196.0 

190.0 

178.5 

174  6 

170.6 

166.6 

’59-7 

154-3 

141  .O 

3-50 

199.7 

*91-5 

182.0 

178  O 

173.8 

170.0 

162.8 

*57-i 

143  7 

3-75 

203  2 

196.7 

185.1 

l8l  O 

176.8 

172.8 

'655 

159.8 

146.2 

4.00 

206.5 

200.0 

188.0 

183.8 

179-5 

175-6 

168.2 

162.4 

148.5 

4-5 

214.0 

205.5 

193.9 

189.3 

185.0 

l80.8 

J73-  3 

167.2 

153-u 

5*° 

218.5 

210.8 

193.9 

194.4 

190.0 

185.6 

178.0 

171.8 

157-1 

5-5 

223.7 

215.6 

203 . 7 

199. 1 

194  5 

190  I 

182.2 

176.0 

160.9 

6.0 

228.5 

220.0 

208.0 

203  5 

198.8 

194-3 

186.2 

170.0 

164.3 

6.5 

233-2 

224.4 

212.3 

207.5 

202  8 

198.3 

190.0 

183.7 

167.7 

7.0 

237-5 

228 . 4 

216.2 

2 f I . 4 

206.4 

202. 1 

193-5 

187.0 

170.7 

7-5 

241  5 

232.0 

220.0 

215.O 

210  0 

. 205.6 

196.8 

190.4 

173.6 

8.0 

245  ■ 5 

235  5 

223.6 

218.4 

213-5 

209.0 

200.0 

J93-4 

176.5 

9.0 

253-5 

245.0 

230.7 

225.5 

220.0 

215.0 

206.6 

199.0 

182.0 

19.0 

260.4 

251 . 6 

236-5 

231.2 

226.0 

220.5 

212.0 

204.5 

186.6 

A classification  of  tlie  surfaces  for  roughness  as  above 
leads  to  a classification  of  the  coefficients  c,  as  in  Table  75a, 
applicable  to  the  same  classes  of  contours,  in  the  formula 
for  velocity: 


m 


X Vri  = c Vri. 


328b.  Formulas  for  Channels. — The  classified  co- 
efficients, c = y — of  Table  75a,  illustrated  in  the  Di- 


m 


agram,  page  309,  for  medium  velocities,  may  be  used  in 
formulas  of  the  Chezy  form  and  its  transpositions,  viz.: — 

v = x V'^r  — X Vri  = = c VrT.  (10 b) 

Ol  m ml 


m 


^ Imv 2 lv" 
~ 2qr  ~ dr 


% — 


mv 
2 or 


dr 


and 


(10  c) 


ZQSd 


FLOW  OF  WATER  IX  OPEX  CHANNELS 


TABLE  No.  75a  .—(.Continued.) 
Classified  Coefficients  c,  for  Varying  r. 


Hyd. 
Rad.  r 

j. 

K. 

L. 

M. 

N. 

0. 

p. 

Q ■ 

R. 

.125 

61.5 

50.0 

43-o 

36.O 

30.0 

22.7 

19.0 

•25 

66.5 

60.5 

50.0 

44 

39-o 

•50 

79.0 

7i-5 

59  6 

52 

46.5 

38.7 

32.8 

25.O 

19.0 

•75 

87.3 

79.1 

66.0 

57-8 

5i-3 

43-° 

36.2 

28.3 

22.0 

1 .00 

94.0 

85.0 

71 .0 

62.0 

55-o 

46.0 

39-o 

3°-5 

24.O 

1.25 

99.4 

00.0 

75-4 

65.4 

58.0 

48.3 

41. 1 

32-4 

25-5 

1.50 

104.3 

95.2 

79.0 

68.5 

60.7 

50-4 

43* 1 

33-8 

26.7 

1 -75 

108.2 

97.8 

82 .0 

71. 1 

63.1 

52-3 

44-9 

35-i 

27.7 

2.00 

11 1 .8 

101 . 1 

84.7 

73-7 

65.3 

54-3 

46.4 

36.2 

28.6 

2.25 

115.1 

104.0 

87.0 

75.8 

67-3 

56.0 

47-7 

37-4 

29.4 

2.50 

118. 1 

106.8 

89.4 

78.0 

69.3 

57-6 

49.0 

384 

30.3 

2-75 

121 .0 

109.4 

91  4 

79.8 

70.9 

59-0 

50.2 

39-2 

31-0 

3.00 

123.8 

1 1 1 .8 

93-4 

81 .6 

72.4 

60.4 

513 

40.0 

31  -7 

3-25 

126.2 

114.0 

95-2 

83.4 

73-9 

61.6 

52.2 

41.0 

32.3 

3-5o 

128.6 

116.3 

97  • 1 

85.0 

75-3 

62.8 

53-2 

4i-7 

32.8 

3-75 

130.8 

118.3 

98.7 

86.5 

76.5 

63.9 

54-i 

42-5 

33-4 

4.00 

x33-° 

120.2 

100.4 

88.0 

77-7 

65.0 

55  0 

43-3 

34-o 

4.5o 

J37-o 

124.0 

103.3 

91. 1 

80.0 

67.0 

56.6 

44-5 

350 

5-° 

140.8 

127.3 

106.0 

93.0 

82.2 

68.8 

58.2 

44.8 

36.0 

5-5 

144.0 

130.3 

108.7 

95-o 

84.2 

7O.4 

59-7 

46.9 

36.7 

6.0 

147.0 

i33-o 

111 .0 

97.0 

86.0 

72.0 

61 .0 

47.8 

37.6 

6.5 

150  1 

135-7 

II3-4 

99.0 

87.7 

73  4 

62.2 

48.7 

38.3 

7.0 

152.9 

138.3 

115.5 

100.7 

89.4 

748 

63.4 

49.6 

39  0 

7-3 

J55-4 

140.7 

117.6 

102.5 

91.0 

76.1 

645 

50.4 

39.5 

8.0 

158.0 

143.0 

ll9-5 

104.2 

92.4 

77-4 

65-5 

51-2 

40.0 

9.0 

162.7 

147.0 

123.2 

107.8 

94.8 

79.8 

67.5 

53-o 

4i-5 

10. 0 

167 .0 

15*  .0 

126.3 

IIO. 7 

97-3 

82.0 

69.2 

54-3 

42.6 

12.0 

174-7 

158.3 

132.2 

ii6.o 

102  O 

85.6 

72-5 

56.7 

44  8 

14.0 

181 .4 

164.3 

*37-3 

120.3 

106.2 

89.0 

75-4 

59.0 

46.5 

16.0 

187.7 

170.0 

14^.0 

124-3 

OO 

92.0 

78.0 

61.0 

48.I 

18.0 

I93o 

T75-1 

146.2 

127.8 

1 13 .2 

94-8 

80.3 

62.8 

49-5 

20.0 

199  0 

180.0 

150.0 

i3i. 1 

116.3 

97-3 

82.5 

64.5 

509 

25.0 

2 1 1 . O 

190.5 

158.8 

138.5 

123.0 

102.8 

87.2 

68.2 

53-6 

30.0 

220.  6 

199.0 

166.2 

145.0 

128.8 

107.7 

9i-3 

71.4 

56.0 

35-° 

229.O 

207.0 

174.0 

151.0 

133.8 

112.0 

94.9 

74.3 

58.3 

40  0 

236.3 

214.0 

178.6 

156  0 

138.2 

115.8 

98.2 

76.9 

60.3 

50.0 

25O.O 

226.0 

188.9 

165.0 

146.0 

122.3 

103.7 

80.8 

63. 8 

60.0 

261.5 

236.5 

197-5 

172.4 

153.0 

127.8 

108  4 

84.7 

66.7 

70.0 

272.O 

245.6 

205 .0 

179.2 

159.0 

132.8 

112.7 

88.0 

69.2 

80.0 

282.O 

254-3 

212.2 

185.4 

164.5 

1375 

116.6 

01. 0 

71.8 

The  coefficients  c,  in  each  class,  increase  slightly  in  value 
as  velocities  increase  from  three  feet  per  second  and  de- 
crease more  rapidly  as  velocities  decrease  from  three  feet 
per  second. 

The  table  and  diagram  of  c present  attempts  to  harmon- 
ize such  data  of  flow  of  streams  as  are  now  available.  The 
records  indicate  that  methods'  of  measurement  of  flow 
were  varied  and  that  they  often  lacked  the  precision  neces- 
sary for  proper  analysis. 


for  Velocities  .about  3 feet  per  second. 


FORMULAS  OF  FLOW. 


309 


Exponential  formulas,  giving  approximate  velocities  in 
channels  of  the  different  classes  of  roughness  as  above 


classified  in 

§328a  are  as  follows 

• 

Class  A. 

v = 146.(r15i)-5. 

Class  J. 

V 

= 94.(rL5f)'5. 

E. 

v = 141.5(r1-5i)-5. 

K. 

V 

= 85.  (r1-5/)-3. 

C. 

v = 

L. 

V 

= 71.(r1”5f)-5. 

D. 

v — 130.  (r'-H'y5. 

M. 

V 

= 62.  (rL5/)-5. 

E. 

v = 127.  (r1-5?')-5. 

N. 

V 

= 55.  (r1-5/)-5. 

F. 

v = 124.  (r1-5^-5. 

0. 

V 

= 46.fr1 5i)-5. 

G. 

v = 119.  (r1-5^)-5. 

P. 

V 

= 39 

H. 

v = 115.  (r:5f)'5. 

Q. 

( 

V 

— 30 

I. 

v = 105.  (r'fi)-5. 

E. 

V 

= 24.  (r1-3/)-3. 

In  which  v = velocity  in  feet  per  second,  i = head  in 
feet  divided  by  length  in  feet,  and  r = hydraulic  radius 
equal  section  divide  by  contour. 

329.  Various  Formulas  of  Flow  Compared. — 

To  compare  the  simple  formula,  having  its  variable  m,  or 
c with  some  of  the  more  complex  formulas,  in  the  forms  in 
which  they  are  generally  quoted  in  text-books  and  cyclo 
pedias,  four  experiments  are  taken  from  Table  No.  74, 
having  their  hydraulic  mean  depths  and  sectional  areas  of 
mean,  minimum,  and  maximum  values,  and  their  velocities 
are  computed  by  it.  The  velocities  are  then  computed  by 
well-known  formulas  upon  the  same  data.  The  results  are 
given  in  the  following  Table  No.  76. 


310 


FLOW  OF  WATER  IN  OPEN  CHANNELS. 


TABLE  No.  7 6. 

Formulas  for  Flow  of  Water  in  Channels,  to  find  the  Velocity, 


Comparing  results  given  by  the  several  formulas. 


Authority. 

Formulas. 

a j 
2 d 

U N 
6 

Lautei 

Canal 

Id 

c n 

<“ 
— “ 

. as 

25  ^ 
£ 

Eq.  (9),  § 324 . 

2>  = \ -2?  . 

Coin- 
Put  ed 
veloc. 
in  ft. 
per 
sec. 
0.966 

Com- 
puted 
veloc. 
in  ft. 
Per 
sec. 

1-934 

Com- 
puted 
veloc. 
in  ft. 
per 
sec. 

Com- 
puted 
veloc . 
in  ft. 
Per 
sec. 

3- * * * §45 

1 m f 

Du  Buat 

88.51  (r*  — .03)  „ , X 

'■/.n  ~ /t  .03) 

— hyp.  log. 

1.929 

3.627 

2.411 

2.143 

Eytelwein  . . . 

3-i84 

2.442 

2.382 

1. 109 
1.962 

2.289 

-572 

2-545 

2-435 

2.479 
2 418 

D’A  ubuisson. 

3-i84 

Neville 

2.161 

3-^95 

2.778 

2.706 

100  Vr 

2.151 

3-338 

2.691 

2.627 

C C 

/ 1 

y T 

_ ( AS) 1 

3 438 

2.691 

2.627 

1 ic  S 

2.151 

3-438 

2.691 

2.627 

Darcy  and  { 
Bazin.  ) 

v-r\  IOO°Z‘  U 

1.047 

2.086 

2.166 

2.582 

( .08534?-  + -35  ) 

M.  Hagen 

1.237 

1-747 

2-350 

3.268 

Humphreys  / 

and  Abbott,  f 

' 

1-372 

2.078 

2.642 

4.582 

* Feeder  Chazilly.  Area,  11.3  sq.  ft.  Hydraulic  mean  depth,  1.04.  Inclination,  .000445. 
Ob  erved  velocity,  0.962  ft. 

t Lauter  Canal.  Area,  564  sq.  ft.  Hydraulic  mean  depth,  1.S2.  Inclination,  .000664. 
Observed  velocity,  2.106  ft. 

% Seine.  Area,  1978  sq.  ft.  Hydraulic  mean  depth,  5.70.  Inclination,  .000127.  Observed 
velocity,  2.094  ft. 

§ B.  La  Fourche.  Area,  3738  sq.  ft.  Hydraulic  mean  depth,  15.7.  Inclination,  .000044. 
Observed  velocity,  3.076  ft. 


VELOCITIES  OF  GIVEN  FILMS. 


311 


In  the  preceding  table,  the  symbols  in  the  formulas  have 
values  as  follows : 

r = hydraulic  mean  depth,  in  feet. 

i = inclination  of  surface  in  straight  channel,  in  feet. 

I — length,  in  feet. 

h"  = head,  or  fall  in  the  given  length,  in  feet. 

5 = sectional  area  of  stream,  in  square  feet. 

C = wetted  solid  perimeter,  in  feet. 

v = mean  velocity  of  stream,  in  feet  per  second. 

In  the  Humphreys  and  Abbott  formula,  the  symbols 
have  values  as  follows : 

a — sectional  area  of  stream,  in  square  feet. 

1 fiQ 

6 = a function  of  depth  = ' 

Vr  + 1.5 

p = wetted  perimeter. 

r = mean  hydraulic  depth. 

i = inclination  of  surface  of  stream,  corrected  for  bends. 

W = width  of  stream. 

v'  — value  of  first  term  in  the  expression  for  v. 

v = mean  velocity  of  stream. 

330.  Velocities  of  Given  Films. — Since  the  chief 
source  of  resistance  to  flow  arises  from  the  reactions  at  the 
perimeter  of  the  stream,  along  the  bottom  and  sides,  A,  B, 
B',  A',  Fig.  51,  and  in  a small  degree  along  the  surface 
A,  A',  in  contact  with  the  air,  it  is  evident  that  the  points 
of  minimum  velocity  will  be  along  the  solid  perimeter,  and 
the  point  of  maximum  velocity  will  be  that  least  influenced 
by  the  resultant  of  all  retarding  influences.  In  a channel 
of  symmetrical  section,  the  point  of  maximum  velocity 
should  be,  according  to  the  above  hypothesis,  on  a vertical 
line  passing  through  the  centre  of  the  section  and  a little 
below  the  water  surface,  provided  the  surface  was  unin. 


312 


FLOW  OF  WATER  IN  OPEN  CHANNELS. 


flueuced  by  wind.  The  velocity  measurements  of  Darcy 
and  Bazin*  with  an  improved  “Pitot”  Tube,  locate  the 
thread  of  maximum  velocity  in  a trapezoidal  channel,  at  a 
Fig.  51 ; a nearly  concentric  film  of  lesser  velocity  at  b,  and 
other  films,  decreasing  regularly  in  velocity,  at  c,  d,  e,  /, 
and  g. 

If  the  velocities,  at  the  depths  at  which  the  given  films 
cross  a vertical  centre  line,  are  plotted  as  ordinates  from  a 
vertical  line,  as  at  a,  b,  c,  etc.,  Fig.  52,  their  extremities  will 
lie  in  a parabolic  curve,  and  the  degree  of  curvature  will  be 
less  or  greater  as  the  velocity  is  less  or  greater,  and  as  the 
bottom  is  smoother  or  rougher,  for  the  given  section. 
Velocity  ordinates,  plotted  in  the  same  manner  for  any 
horizontal  section,  as  in  the  surface,  or  through  5,  a , b,  c , 
etc.,  Fig.  51,  will  also  have  then  extremities  from  shore 

Fig.  51.  Fig.  52. 


nearly  to  the  centre  in  parabolic  curves,  the  longest  ordi- 
nate being  near  the  centre  of  breadth  of  the  canal,  and  the 
two  side  parabolas  being  connected  by  a curve  more  or  less 
flat,  according  to  breadth  of  canal.  In  Fig.  51,  d indicates 
the  film  of  mean  velocity,  and  it  cuts  the  central  vertical  line 
at  nearly  three-fourths  the  depth  from  the  surface.  In 
deep  streams,  or  channels  in  earth,  it  is  usually  a little 
below  the  centre  of  depth. 

* Tome  XIX  des  Memoires  presentes  par  divers  Savants  a rinstitut  Impe. 
rial  de  France,  Planclie  4. 


SURFACE  VELOCITIES. 


313 


331.  Surface  Velocities.- -The  velocity  of  the  centre 
of  the  surface,  in  symmetrical  channels,  or  of  the  mid- 
channel in  unsymmetrical  sections,  is  that  most  readily 
obtainable  by  simple  experiment. 

For  such  velocity  observations  a given  length,  say  one 
hundred  feet  of  the  smoothest  and  most  symmetrical 
straight  channel  accessible  is  marked  off  by  stations  on 
both  banks,  and  a wire  stretched  across  at  each  end  at 
right  angles  to  the  axis  of  the  channel.  Thin  cylindrical 
floats  are  then  put  in  the  centre  of  the  stream  a short  dis- 
tance above  the  upper  wire,  by  an  assistant,  and  the  time 
of  their  passing  each  wire  accurately  noted. 

A transit  instrument  at  each  end  station  is  requisite  for 
very  close  observations.  A small  gong-bell,  on  a stand  or 
post  beside  the  transit,  is  to  be  struck  by  the  observer  the 
instant  the  centre  of  the  float  passes  the  cross-hair,  or  a 
signal  is  to  be  transmitted  by  an  electric  current,  and  the 
time,  noted  to  the  nearest  quarter-second  by  a skillful 
assistant,  is  to  be  recorded. 

i 

The  floats  are  sometimes  of  wax,  weighted  until  its 
specific  gravity  is  near  unity  ; sometimes  a short,  thick  vial, 
corked,  and  containing  a few  shot  or  pebbles ; and  some- 
times a thin  slice  of  wood  cut  from  a turned  cylinder,  which 
for  small  channels  may  be  two  inches  diameter.  For  large 
rivers,  the  float  may  be  a short  keg,  with  both  heads  in 
place,  and  weighted  with  gravel  stones.  The  float  is  to  be 
loaded  so  its  top  end  will  be  just  above  the  surface  of  the 
water.  In  broad  streams,  a small  flag  may  be  placed  in  the 
centre  of  the  float. 

If  a number  of  floats  are  started  simultaneously  at 
known  distances  on  each  side  of  the  axis  of  the  channel, 
they  should  have  each  a special  color-mark  or  conspicuous 
flag  number,  so  that  the  time  and  distance  from  axis,  at 


314 


FI.OW  OF  WATER  IN  OPEN  CHANNELS. 


each  station,  may  "be  correctly  noted  for  each  individual 
float. 

Du  Buat  made  experiments  with  small  rectangular  and 
trapezoidal  channels  of  plank,  141  feet  long  and  about 
18  inches  wide,  with  depths  from  .17  to  .895  feet,  and  veloc- 
ities from  .524  to  4.26  feet,  to  determine  the  ratio  of  the 
mean  velocity  v of  the  channel  section  to  its  central  surface 
velocity,  V.  From  the  mean  results  he  deduced  the  empir- 
ical formula  of  mean  velocity, 

v = (VT—  .15)2  + .02233.  (11) 

This  gives,  when  F is  taken  as  unity, 


v — .745  F. 

Prony  afterwards,  reviewing  the  same  experimental  re- 
sults, proposed  the  formula. 


V = 


v(Z±  Jl^] 

\ V + 10.345/ 


(12) 


Ximenes’  experiments  upon  the  River  Amo,  Raucort’s 
upon  the  Neva,  Funk’s  upon  the  W esser,  Defontaines  and 
Briinning’s  upon  the  Rhine,  on  larger  scales,  gave  mean 
velocities  in  a vertical  line  at  the  centre  equal  to  .915  F, 
which  being  the  maximum  velocity  in  its  horizontal  plane, 
indicates,  if  the  reduction  of  velocity  toward  the  shore  is 
considered,  an  approximate  mean  velocity, 

v = .915  (.915  F)  = .837  F.  (13) 

Mr.  Francis’  experiments  in  a smooth,  rectangular  chan- 
nel, with  section  about  10  feet  broad  and  8 feet  deep,  and 
velocity  of  4 feet  per  second,  indicates 

v = .911  F.  (14) 

In  the  Mississippi  River,  with  depths  exceeding  one 


RATIOS  OF  SURFACE  TO  MEAN  VELOCITIES. 


315 


hundred  feet,  Messrs.  Humphreys  and  Abbott  occasionally 
found  v greater  than  V. 

The  Ganges  Canal  experiments  at  Roorkee,  in  1875,  by 
Capt.  Cunningham,  R.  E.,  in  a rectangular  section  9 feet 
deep  and  85  feet  wide,  gave  the  mean  surface  velocity 
equal  to  .927  V. 

In  any  series  of  rectangular  channels  of  like  constant 
sectional  areas  or  of  like  constant  borders,  it  is  seen,  by 
simple  mathematical  demonstrations,  that  the  hydraulic 

mean  depth  — is  at  its  maximum  when  the  breadth 

equals  twice  the  depth.*  Since  the  velocity  of  flow  in  a 
series  of  rectangular  channels  is  nearly  proportional  to  the 
square  roots  of  their  hydraulic  mean  depths,  it  follows  that 
the  proportions  of  such  channels  most  favorable  for  high 
velocities  is  breadth  equal  twice  depth. 

These  proportions  of  breadth  to  depth  being  adopted 
again  for  another  series  of  rectangular  channels  of  varying 
section,  the  velocities  will  again  be  sensibly  proportional  to 
the  square  roots  of  their  hydraulic  mean  depths. 

The  ratio  of  v to  V should  be  at  its  maximum  when 
breadth  equals  twice  the  depth,  and  when  the  section  is  the 
maximum  of  the  given  series. 

332.  Ratios  of  Surface  to  Mean  Velocities. — Let 
d = depth  and  b = breadth  of  rectangular  channels,  then 
letting  depth  be  unity  for  a depth  of  8 feet  and  approxi- 
mately between  6 and  12  feet,  and  we  shall  have,  according 
to  the  various  recorded  experiments,  approximate  values 
of  the  mean  velocity  v of  flow  in  the  channel,  as  compared 
with  the  central  surface  velocity  V,  as  follows,  for  smooth 
channels : 


* The  influence  of  sectional  profile  upon  flow  is  elaborately  discussed  by 
Downing,  in  Elements  of  Practical  Hydraulics,  p.  204,  et  seq.  (London,  1875.) 


316 


FLOW  OF  WATER  IN  OPEN  CHANNELS. 


When 

b = 

2d 

then 

v = .920  V' 

tc 

b = 

‘6d 

U 

v — .910 V 

u 

b = 

4d 

U 

v = .896 V 

« 

b = 

5d 

a 

v = .882  V 

(( 

b = 

6d 

a 

v = .864  V - 

it 

b = 

7 d 

a 

v - .847  V 

it 

b - 

8d 

a 

v = .826 V 

ti 

b = 

9 d 

a 

v = .804  V 

u 

b = 

10<2 

a 

v = .780  V ^ 

The  values  of  v should  he  slightly  less  for  trapezoidal 
canals  of  equal  sections,  decreasing  as  the  side  slopes  are 
flattened.  The  values  of  v will  decrease  also  as  the  bottom 
and  sides  increase  in  roughness.  The  wind  may  enhance 
or  retard  the  surface  motion,  and  thus  affect  the  mean 
velocity. 

Since  inclination  of  water  surface,  section  of  stream, 
hydraulic  mean  depth,  and  roughness  of  bottom  and  side, 
all  affect  the  final  result  of  flow,  it  is  evident  that  experi- 
ence and  good  judgment  will  aid  materially  in  the  selection 
of  the  proper  ratio  of  v to  V.  A misapplication  of  formulae 
that  are  valuable  when  judiciously  used,  may  lead  to  gross 
errors;  as,  for  instance,  Prony’s  formula,  deduced  from 
experiments  with  Du  Buat’s  small  canal,  gave  result  fifteen 
per  cent,  too  small  when  tested  by  the  flow  in  the  Lowell 
flume,  10  feet  wide  and  8 feet  deep,  where  the  volume  was 
proved  by  tube  floats  and  weir  measurements  at  the  same 
time. 

333.  Hydrometer  Gaugings. — When  opportunity 
offers,  the  mean  velocity  for  the  whole  depth  should  be 
measured,  and  thus  some  of  the  uncertainties  accompany- 
ing surface  measures  be  eliminated.  Among  the  most 
reliable  hydrometers  that  have  been  used  for  this  purpose 


TUBE  GAUGE. 


317 


in  oanals  and  the  smaller  rivers  may  he  mentioned,  tin  tubes 
of  length  nearly  equal  to  the  depth  of  the  stream ; improved 
« Pitot  tubes  /”  and  “ Woltmann  tachometer sP 

334.  Tube  Gauge. — When  the  velocity  measurements 
are  to  he  taken  with  Francis’  tubes  or  Krayenlioff  poles, 
Fig  53,  a straight  section  of  the  stream  is  chosen,  with 
smooth  symmetrical  channel,  clear  of  weeds  and  obstruc- 
tions. A length  of  one  hundred  or  more  feet,  according  to 
circumstances,  is  marked  off  by  stations  at  each  end  on 
each  bank,  located  so  as  to  mark  lines  at  right  angles  to  the 
axis  of  the  stream.  A steel  measuring  chain,  or  wire  with 
marks  at  equal  intervals,  is  then  to  be  stretched  across  at 
each  end.  The  depths  are  then  to  be  taken  across  the  stream 
at  each  end,  and  at  the  centre  if  the  banks  are  warped,  at 
known  intervals  of  a few  feet,  accord- 
ing to  the  formation  of  the  banks  and 
bottom  of  the  stream,  so  that  the  sec- 
tional area  of  the  stream  shall  be 
accurately  known,  and  may  be  plot- 
ted. The  soundings  are  all  to  refer 
to  the  same  datum  previously  estab- 
lished,  and  referred  to  a permanent 

bench  mark  on  the  shore,  which  will  greatly  facilitate 
future  observations  or  verifications  at  the  same  point. 

The  requisite  number  of  tight  tin  tubes,  of  say  two 
inches  diameter,*  are  then  to  be  prepared,  one  for  the  axis 
of  the  stream,  and  others  for  short  successive  intervals  on 
each  side  of  the  axis,  all  to  be  duly  numbered  for  their 
respective  positions.  The  length  of  each  is  to  be  such  that 
it  will  float  just  clear  of  the  bottom,  and  extend  to  a little 
above  the  water  surface.  The  tube  is  to  be  loaded  at  one 

* Tubes  40  feet  long,  3 inches  diameter,  made  up  in  sections,  have  been 
used  by  the  United  States  Coast  Survey  Staff. 


Fig.  53. 


318 


FLOW  OF  WATER  IN  OPEN. CHANNELS. 


end  with  fine  shot  or  sand,  until  it  has  the  proper  sub 
mergence  in  a vertical  position,  .93  to  .95  depth. 

The  several  tubes  are  to  be  started  by  signal,  simultane- 
ously if  possible,  from  a short  distance  above  the  upper  end 
station,  so  that  they  may  cross  the  upper  station  as  nearly 
as  possible  at  the  same  instant.  Their  arrivals  at  the  lower 
stations  are  to  be  carefully  noted,  and  the  time  of  transit  of 
each  recorded. 

When  the  experiment  has  been  several  times  repeated, 
the  central  and  other  tubes  may  be  passed  down  singly,  if 
the  volume  of  the  stream  still  remains  constant,  to  verify  the 
first  observations.  In  the  last  observations,  transits  may 
conveniently  be  used  to  observe  the  passage  by  the  stations, 
as  suggested  above  for  observing  surface  floats. 

Suppose  the  stream  to  be  divided  transversely  into  seven 
sections,  as  in  Fig.  54,  then  tubes  1,  2, 3,  etc.,  may  be  started 


Fig.  54. 


in  the  centres  of  their  respective  sections.  The  degree  of 
accuracy  with  which  they  will  move  along  their  intended 
courses  will  depend  upon  the  symmetrical  regularity  of 
flow,  and  very  much  upon  the  regularity  of  the  side  banks, 
and  several  trials  may  be  necessary  to  get  satisfactory 
side  and  even  central  measurements,  since  a slight  obstruc- 
tion, or  a stray  boulder  upon  the  bottom,  may  distort  the 
fluid  threads  in  an  unaccountable  manner.  The  side  floats 
have  also  a tendency  away  from  shore. 

The  mean  area  of  each  of  the  sub-sections  being  known, 
and  the  mean  velocity  through  each  being  ascertained, 


GAUGE  FORMULAS. 


319 


their  product  gives  the  volume  flowing  through,  and  the 
sum  of  volumes  of  the  sub-section  gives  the  volume  for  the 
whole  section. 

When  streams  are  in  the  least  liable  to  fluctuations  front 
the  opening  or  closing  of  sluices  above,  or  the  opening  or 
closing  of  turbine  gates  when  the  stream  is  used  for  hy- 
draulic power,  a hook-gauge  (Fig.  48),  should  be  placed 
over  the  axis  of  the  stream  where  the  usual  vibration  of 
surface  is  least,  to  watch  for  such  fluctuations,  since  a vari- 
ation in  the  mean  level  of  the  water  surface  one-hundredth 
of  a foot  will  appreciably  affect  the  velocity  and  volume  of 
flow.  If  the  tubes  have  much  clearance  they  will  not  be 
influenced  by  the  films  of  slowest  velocity  next  the  bottom. 
A clearance  of  six  inches  in  a rectangular  flume  eight  feet 
deep,  may  give  an  excess  of  three  per  cent,  of  velocity. 
The  cross-section  depths,  in  canals  and  shallow  streams, 
may  be  taken  with  a graduated  sounding-rod  having  a flat 
disk  of  three  or  four  inches  diameter  at  its  foot,  and  in  deep 
streams  by  a measuring-chain  with  a sufficient  weight  upon 
its  foot  to  maintain  it  straight  and  vertical  in  the  current. 
A good  level  instrument  and  level  staff  are  requisite,  how- 
ever, for  accurate  work. 

In  broad  streams  the  transverse  stations  may  be  located 
trigonometrically  by  two  transits  placed  at  the  extremities 
of  a carefully  measured  base  line  upon  the  shore. 

335.  Gauge  Formulas. — The  volume  of  flow  through 
the  mean  transverse  section  (Fig.  54)  is  required. 

Let  s be  the  established  length , or  distance  between  the 
longitudinal  end  stations,  and  /,  t2l3 ...  . tn  the  times  occu- 
pied by  the  several  tubes  in  passing  along  tlieir  respective 
courses  between  end  stations ; then  the  mean  velocities  in 
the  respective  sub-sections  will  be 

s s s s 

r _ ®3  5 — rn  = Vn' 


320 


FLOW  OF  WATER  IN  OPEN  CHANNELS. 


Let  the  transverse  breadths  of  the  sub-sections  be,  al  az  . . . . On, 

“ “ mean  depths  “ “ “ “ dl  d2  d3  ...  . dn, 

“ “ mean  velocities  in  “ “ “ vx  va . . . . vn. 

“ “ “ volumes  of  flow  in  “ “ q^  q^  qz  ...  . qn. 

Then  the  whole  sectional  area  in  square  feet,  8,  of  the 
stream  is, 

S = al.dl  4-  a2.d2  + a-s.d^  + . ...  an.dn]  (16) 
and  the  whole  volume  in  cubic  feet,  Q , is 


Q = (a1.dl)vl  + (a2 . d2)  v2  + {a%.d.^v 3 + . . . {an . dr)  vn ; (17) 

and  the  mean  velocity  in  feet  per  second,  v,  of  the  whole 
section  is, 


(18) 


The  summary  of  field  notes,  beginning  at  a on  the  left 
shore,  is : 


Feet.  Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Breadths  of  sub-sections 
Mean  depths  of  “ 
Mean  velocities  in  the  l 
sub-sections j 

aL  16.45  a-i  20*00 
dl  4.85  9.74 

V,_  2.25  Z>2  3.80 

a 3 24.85 
d3  12.37 

v3  4.62 

aA  32.00 
d 4 15.68 

t/4  5.00 

as  29.50 
d 5 12.52 

v5  4-65 

aQ  26.80 

d.  9.71 

2'«  3-75 

a7  18.24 
di  4-79 

V7  2.00 

Cu.  ft.  | Cu.  ft. 

Cu.ft. 

Cu.ft. 

Cu.ft. 

Cu.ft. 

Cu.ft. 

Volume  in  the  sub-sec-  ) 
lions f 

179-5  g-i  740-2 
1 

? 3 1420.2 

qA  2508.8 

gsW-4 

1.  975-8 

It  174-7 

f=* 

The  sum  of  the  several  products  of  breadth  into  depth  is 
8 = 1800.675  square  feet. 

The  sum  of  the  several  volumes  is Q = 7716.73 

The  mean  velocity  for  the  whole  section  is  7.  — ' 

J S 1800.6 /o 

= v = 4.285  feet  per  second. 

If  the  tubes  have  several  inches  clearance  at  the  bot- 
tom, a slight  reduction,  say  two  and  a half  per  cent.,  from 
the  computed  velocity  and  volume  are  to  be  made,  to  com- 
pensate therefor. 

336.  Pitot  Tube  Gauge. — The  Pitot  tube  lias  been 
used  with  a tolerable  degree  of  success  in  many  experi- 
ments upon  a small  scale.  In  its  best  simple  form  it  has 


PITOT’S  TUBE. 


321 


Fig.  55. 


been  constructed  of  glass  tubing  swelled  into  a bulb  near 
one  end,  and  with  tube  of  smaller  diameter  below  the  bulb 
bent  at  a right  angle,  and  terminated  with  an  expanded 
trumpet-mouth,  as  in  Fig.  55. 

For  deep  measures  the  mouth  and  bulb  and  a con- 
venient part  of  the  tube  may  be  of  copper,  that  part  which 
is  to  project  above  the  surface 
of  the  water  being  of  glass,  and 
the  whole  instrument  may  be  at- 
tached to  a vertical  rod,  which 
rests  on  the  bottom,  so  as  to  be 
slid  up  and  down  on  the  rod  to 
the  heights  of  the  several  films 
whose  velocities  are  required. 

When  in  use,  the  bulb  and 
tube  are  to  be  held  vertically, 
and  the  small  trumpet-mouthed 
section  exposed  horizontally  to  the  current  so  as  to  receive 
its  maximum  force  into  the  mouth. 

The  object  of  the  expanded  bulb  and  contraction  below 
the  bulb  is  to  reduce  oscillation  of  the  water  within  the  tube 
to  a minimum. 

Theoretically  the  impulse  of  the  current,  acting  as  pres- 
sure on  the  water  within  the  tube,  should  raise  the  surface 

v2 

of  the  water  within,  a height,  7i  = above  the  normal 
surface. 

But  owing  to  reactions  from  several  parts  of  the  tube, 
the  entire  force  of  the  current  does  not  act  upon  the  column 
of  water  in  the  vertical  section  of  the  tube,  hence  the  eleva- 
tion of  the  water  in  the  tube  is  cji  and 


35 

pitot’s  tube. 


— cji  and  v — V2ycji. 


(19) 


322 


FLOW  OF  WATER  IN  OPEN  CHANNELS. 


The  coefficient  c0,  for  the  given  tube  and  the  different 
velocities,  must  be  determined  by  experiment  before  it  can 
be  used  for  practical  measures. 

The  stream  is  cross-sectioned,  as  before  described  for 
the  leading  station  when  long  tin  tubes  are  used,  and 
the  mean  velocity  is  ascertained  from  the  mean  velocity  of 
the  various  superposed  films  taken  in  a vertical  line  at  the 
centre  of  each  sub-section. 

The  computations  of  volume  are  made  in  a manner  sim- 
ilar to  those  when  tubes  are  used. 

Pitot  introduced  a plain  tube  bent  at  right  angles  as 
early  as  1730,  and  by  his  measurements  with  it  in  the  Seine 
and  other  streams,  overthrew  some  of  the  hypotheses  of  the 
older  hydraulicians. 

It  has  since  received  a variety  of  forms  and  entered  into 
a variety  of  combinations,  among  which  may  be  mentioned 
the  “ Darcy-Pitot  ” tube,  which,  after  an  instantaneous 
closing  of  a stop-cock,  can  be  lifted  up  for  an  observation, 
and  the  Darcy  double  tube,  but  there  is  still  difficulty  in 
reading  by  its  graduations  measures  of  small  velocities, with 
sufficient  accuracy,  and  the  capillarity  may  be  a source  of 
error  in  unskillful  hands.  . 

The  almost  exclusive  use  of  this  instrument  in  improved 
forms  by  Darcy  and  Bazin  in  their  valuable  series  of  ex- 
perimental observations,  has  given  to  it  prominent  rank 
among  hydrometers. 

337.  Woltmann’s  Tachometer. — The  most  success- 
ful of  all  the  simple  mechanical  hydrometers,  not  requiring 
the  assistance  of  an  electric  battery,  has  been  the  revolving 
mill  introduced  by  Woltmann  in  1790,  and  known  as 
“ WoltmanrC  s Tachometer ,”  or  mouZinet.  This  current 
meter  has  from  two  to  five  blades,  either  fiat  or  like  marine 
propeller  blades,  set  upon  a horizontal  shaft  as  shown  in 


WOLTMANN’S  TACHOMETER. 


323 


Fig.  56,  which  represents  the  entire  instrument  * in  its  actual 
magnitude,  for  small  canal  and  flume  measures. 

Upon  the  main  axle,  which  carries  the  propeller,  is  a 
worm-screw,  G.  A series  of  toothed  wheels  and  pinions, 
with  pointers  and  dials  similar  to  the  registering  apparatus 


Fig.  56. 


woltmann’s  tachometer. 


of  a water  or  gas  meter,  are  hung  in  a light  frame,  C,  imme- 
diately beneath  the  main  axle.  One  end  of  the  frame  is 
movable  upward  and  downward,  but  when  out  of  use  is 
held  down  by  a spring,  F. 

The  whole  instrument  is  secured  by  a set-screw  upon  an 
iron  rod,  D,  on  which  it  may  be  set  at  any  desired  height. 


* Another  form  with  two  blades  is  illustrated  in  Stevenson’s  Canal  and 
River  Engineering.  Edinburgh,  1872,  p.  101. 


324  FLOW  OF  WATER  IN  OPEN  CHANNELS. 

When  brought  into  practical  use,  the  instrument  is 
adjusted  upon  the  rod,*  so  that  when  the  staff  rests  upon 
the  bottom,  the  main  axle  will  be  at  the  height  of  the  lilm 
'O  be  first  measured.  It  is  then  placed  in  position  with  the 
propeller  toward  the  approaching  current  and  the  main  axle 
parallel  with  the  direction  of  the  current.  The  propeller 
will  soon  acquire  its  due  velocity  of  revolution  from  the 
moving  current,  when  the  movable  end  of  the  frame  carry- 
ing the  recording  train  is  lifted  by  the  wire  E,  and  the  first 
toothed  wheel  brought  into  mesh  with  the  worm-screw.  If 
the  train  does  not  stand  at  zero,  its  reading  is  to  be  taken 
before  the  instrument  is  brought  into  position.  The  times 
when  the  train  is  brought  into  mesh  with  the  worm-screw, 
and  when  disengaged,  are  both  to  be  accurately  noted  and 
recorded. 

Upon  the  slackening  of  the  wire  E , the  spring  F.  in- 
stantly throws  the  train  out  of  mesh,  and  it  is  held  fast  by 
the  stud  A,  which  engages  between  two  teeth  of  the  wheel. 
The  instrument  may  then  be  raised  and  the  revolutions  in 
the  observed  time  read  off.  In  waters  exceeding  a few  feet 
in  depth  there  are  usually  pulsations  of  about  one  minute, 
more  or  less,  intervals,  and  the  instrument  should  be  held 
in  position  until  several  of  these  have  passed. 

The  velocities  are  thus  measured  at  several  heights  on 
vertical  centre  lines  in  the  several  sub-sections,  and  the  com- 
putations for  mean  velocity  and  volume  completed  as  in  the 
above  described  case  when  long  tin  tubes  are  used. 

The  blades  of  the  propeller  are  usually  set  at  an  angle 
of  about  70°,  or  with  an  equivalent  pitch  if  warped  as  a pro- 
peller blade. 


* Several  moulinets  upon  the  same  staff,  at  known  heights  between  bottom 
and  surface,  expedite  the  work  and  tend  to  greater  accuracy. 


HYDROMETER  COEFFICIENTS. 


325 


338.  Hydrometer  Coefficients. — The  number  of  revo- 
lutions of  the  main  axle  is  nearly  proportional  to  the  velocity 
of  the  impinging  current ; but  there  is  some  frictional  resist- 
ance offered  by  the  mechanism,  hence  it  is  necessary  that 
the  coefficients  for  the  given  instrument  and  for  given  veloci- 
ties be  established  by  experiment,  and  tabled  for  convenient 
reference  before  it  is  put  to  practical  use.  These  coefficients, 
which  decrease  in  value  as  the  velocity  increases,  may  b > 
ascertained,  or  verified,  by  placing  the  instrument  sub 
merged  in  currents  of  known  velocity,  or  by  causing  it  tc 
move,  submerged,  through  still  water  at  known  velocities. 

An  apparatus  adapted  to  the  last  purpose  is  described 
by  L’  Abbe  Bossut,  and  illustrated  in  Plates  I and  II,  ii? 
“ Experts  * De  Bossut.” 

If  the  instrument  is  to  be  tested  in  a reservoir  of  still 
water,  by  moving  it  with  different  known  velocities  through 
a given  distance,  let  s be  that  distance,  t the  time  consumed 
in  passing  the  instrument  from  end  to  end  stations,  n the 
number  of  revolutions  of  the  main  axle  in  the  given  time  t, 
c0  the  coefficient  of  revolutions  for  the  given  velocity,  and  v 
the  given  velocity. 

Then  4 = ® ; and  — = cai  and  c0n  = s ; and  -4  = v. 
t n t 

Now  if  the  instrument  is  placed  in  a current,  and  n is 
the  observed  number  of  revolutions  in  the  given  time,  c0  may 
be  taken  from  the  table,  or  an  approximate  value  of  c0  as- 
sumed and  nearer  values  determined  by  the  formula 

^ = c0,  when  the  velocity  will  be,  v - — (20) 

* Nouvelles  Experiences  sur  la  Resistance  des  Fluids ; M.  l’Abbe  Bossut, 
Rapporteur.  Paris. 

Vide,  also,  Annales  des  Ponts  et  Cliaussees,  Nov.  et.  Dec.,  1847,  and  Journal 
of  Franklin  Institute,  May,  1869,  and  Beaufoy’s  Hydraulic  Experiments. 


325a  FLOW  OF  WATER  in  open  channels. 

When  an  electric  register  is  used,  one  minute  observa- 
tions, between  the  starting  and  stopping  of  the  recorder, 
gives  revolutions  per  minute  direct,  and  for  other  times 

their  ratio  r — j , in  which  tx  is  in  minutes.  From  this 
h 

ratio,  velocity  y — v of  flow  in  feet  per  second  is  desired, 
and  equals 

y — cx+m , (20a) 

in  which  x is  the  revolutions  per  minute  and  m the  small 
portion  of  velocity  balancing  friction  of  the  meter  mech- 
anism. 

A series  of  trial  tests  are  to  be  made  for  rating  each 
meter,  on  the  same  base  line,  in  still  water,  and  these  sev- 
eral values  are  found  from  the  experiments,  thus : 


TABLE  No.  76a. 

Current  Meter  Rating  Experiments. 


a 

9) 

B 

0 

Cu 

K 

Cd 

'0 

6 

2 

Rating  Base. 

Register  Reading. 

1 

y in  ft. 
200 

j 2115  1 
I 2161  | 

2 

“ 

22:6 

3 

2250 

4 

2300 

5 

2345 

6 

2397 

7 

2441 

8 

2493 

9 

2537 

10 

2589 

No.  of  Revolutions 
per  minute. 

Time. 

Coefficient. 

Observed 
Velocity  in  feet 
per  second. 

Ratio. 

= jt. 

sec. 
= t. 

min. 
= A- 

£ 

c°=  »• 

j 

y = i 

c0n 

= — = v 
1-7544 

n 

r ~ 77 

46 

114 

1.9000 

4 3478 

24.211 

45 

115 

1.9167 

4 • 4444 

1 -7391 

23.478 

44 

149 

2.4833 

4-5454 

I-3423 

x7-7r8 

50 

35 

•5833 

4.0000 

5-7143 

85 -710 

45 

no 

1-8333 

4.4444 

I .8l8l 

24-510 

52 

24 

.4000 

3.8461 

8-3333 

129.000 

44 

182 

3-°333 

4-5454 

I.O988 

14.502 

52 

27 

.4500 

3.8461 

7-4074 

”5-555 

44 

142 

2-3333 

4-5454 

I.4084 

18.  ,88 

52 

25 

.4166 

3.8461 

7-9998 

124.800 

i . 6328 


1.5863 
1. 1994 
5-74I5 


1.6585 

8.6845 

.9820 

7-7x95 

1.2766 

8.3384 


Having  values  as  above,  the  series  y may  be  plotted  to 
scale  as  abscissas  and  the  dependent  coefficients  c0  and  ratios 


CURRENT  METER  RATING  EXPERIMENTS. 


3255 


r as  ordinates,  and  more  complete  series  taken  from  the 
scale. 

If  the  experiments  are  conducted  with  proper  care  and 
precision,  and  the  meter  is  in  proper  condition,  the  extrem- 
ities of  the  ordinates  r will  be  found  to  lie  approximately 
in  a straight  line. 


Select  from  the  minimum  and  maximum  velocity  values, 
representative  values,  and  let  their  respective  symbols  be  y' 
and  y" ; also  let  their  respective  revolution  ratios  have 
symbols  x'  and  x".  Then,  for  the  equation  of  the  series  of 
ratings,  we  have 

= (20  i) 


From  experiments  Nos.  1 and  8 of  the  series  we  have 
values,  to  substitute  in  the  equation, 


y’  = 1.7544, 


y"  = 7.4074, 


x'  = 24.211, 


y'  - 7.4074  = 


x" 

7.4074  - 1.7544 
115.555  - 24.211 


= 115.555. 

(. x ' - 115.555). 


y — .06192?  + .255,  (20c) 

in  which  .0619  is  the  coefficient  for  the  meter  tested.  In 
the  practical  use  of  a meter,  x is  the  registered  revolutions 
per  minute , which  is  to  be  multiplied  by  the  coefficient  of 
the  given  meter  to  obtain  y,  the  velocity  in  feet  -per  second 
of  that  thread  of  the  current  in  which  the  meter  wheel  is 
revolving. 


326 


FLOW  OF  WATER  IN  OPEN  CHANNELS. 


339.  Electric  Moulinets. — The  ingenious  indicating 
current  meter*  invented  and  introduced  in  the  Lake  Survey 
by  D.  Farrand  Henry,  C.  E.,  has  greatly  increased  the  con- 
venience and  accuracy  of  measurements  in  broad  and  strong 
streams  and  tidal  estuaries,  since  with  the  aid  of  an  electric 
battery  and  current  the  revolution  recorder  may  be  retained 
on  shore,  float  or  vessel,  and  one  minute  observations  be 
repeated  in  alternate  minutes. 

The  general  features  of  this  meter  are  shown  in  the  plate 
fronting  this  chapter.  Another  excellent  form  of  meter, 
Fig.  56a,  was  designed  by  Mr.  A.  Fteley,  resident  engineer 
of  the  Boston  additional  water  supply.  The  writer  has  used 
the  “Price’'  meter,  Fig.  565,  with  satisfactory  results  in 
rapid  and  in  deep  currents,  and  also  in  head  and  tail  races  of 
water  powers,  and  found  it  to  embody  the  best  features  of 
substantial  registering  current  meters. 

340.  Earlier  Hydrometers. — Castelli’s  quadrant,  or 
hydrometric  pendulum,  Boileau’s  horizontal  gauge  glass, 
G-authey’s  and  Brunning’s  pressure  plates,  Brewster’s  long 
screw-meter,  and  Lapointe’s  beveled  gear-meter,  have  now 
all  been  superseded  by  the  more  perfect  modern  current 
meters. 

341.  Double  Floats. — Various  double-float  combina- 
tions, having  one  float  at  the  surface  and  a second  near  the 
bottom,  connected  with  the  first  by  a cord  or  fine  wire  rope, 
have  been  used  both  in  Europe  and  America.  The  liability 
of  erroneous  deductions  from  the  movements  of  such  com- 
binations has  been  ably  discussed  f by  Prof.  S.  TV  Rob- 
inson. 

342.  Mid-depth  Floats. — The  mid-depth  float  proves 


* This  meter  is  illustrated  in  the  Jour,  of  the  Franklin  Inst,.  May,  1869, 
and  Sept.  1871. 

f Vide  Van  Nostrand’s  Eclectic  Engineering  Magazine,  Aug.,  1875. 


Fig.  56 a. 


MID-DEPTH  FLOATS. 


327 


most  generally  satisfactory  of  all  float  apparatus,  excepting 
full-depth  tubes,  for  gauging  artificial  channels  and  the 
smaller  rivers. 

This  may  consist  of  a hollow  metal  globe  of  say  six 
inches  diameter,  with  a cork-stopper  or  pet-cock  at  its 
lower  vertical  pole,  which  permits  the  partial  filling  of  the 
globe  with  water  until  its  specific  gravity,  submerged,  is 
slightly  in  excess  of  unity.  This  globe  is  connected  by  a 
fine  flexible  wire  with  the  smallest  and  lightest  circular 
disk-float  upon  the  surface  that  can  retain  the  globe  in  its 
proper  mid-depth  position. 

It  is  desirable  that  the  float  be  controlled  as  fully  as 
possible  by  the  mid-depth  velocity,  where,  in  artificial 
channels  and  deep  streams,  the  film  of  most  constant 
velocity  is  found.  The  reactions  and  eddies  that  continually 
agitate  all  the  particles  that  flow  near  the  bottom  and  sides 
of  the  stream,  and  the  wflnd  pressure  and  motion  along  the 
surface,  make  the  motions  of  all  perimeter  (so  called)  films 
very  complex,  and  continually  cause  the  parabolic  velocity 
values  in  the  central  vertical  plane  to  change  between 
flatter  and  sharper  curves,  or  to  straighten  out  and  double 
up,  hinged,  as  it  were,  upon  a mid-depth  point ; hence  the 
bottom,  side,  and  surface  velocities  are  liable  to  great  irreg- 
ularities, and  these  irregularities  are  projected  to  some 
extent  through  the  whole  body  of  the  water.  These  effects 
may  be  readily  observed  in  a stream  carrying  fine  quartz 
sand,  upon  a sunshiny  day,  if  a position  is  taken  so  that 
the’  sunlight  is  reflected  from  the  sand-grains  to  the  eye.  If 
in  such  case  the  eye  and  body  is  moved  along  with  the  cur- 
rent, the  whole  mass  of  water  appears  in  violent  agitation 
and  the  particles  appear  to  move  upward,  downward,  back- 
ward, forward,  and  across,  with  writhing  motions,  illus- 
trating the  method  by  which  the  water  tosses  up  and  bears 


328 


FLOW  OF  WATER  IX  OPEN  CHANNELS. 


forward  its  load  of  sediment.  In  the  midst  of  this  agitation, 
the  film  having  a velocity  nearest  to  the  mean  resultant  of 
onward  progress  is  usually  over  the  mid-channel  of  a 
straight  course,  and  near  to,  or  a little  "below,  the  centre  of 
depth.  The  suspended  float  that  takes  this  mean  velocity 
is  more  certain  to  give  a reliable  velocity  measure  than  that 
controlled  by  any  other  point  of  the  stream  section. 

343.  Maximum  Velocity  Floats. — If  it  is  desired  to 
place  the  submerged  float  in  the  film  of  maximum  velocity 
in  artificial  channels,  then  this  may  be  sought  over  the 
mid-channel,  and  between  the  surface  and  one-third  the 
depth,  according  to  the  cross-section  of  the  stream  and 
velocity  of  flow.  In  a smooth  rectangular  section  with 
depth  equal  to  width,  or  with  depth  one-half  width,  it  will 
probably  be  near  one-third  the  depth,  and  higher  as  the 
depth  of  stream  is  proportionately  less,  until  depth  is  only 
one-fourth  breadth,  when  it  will  have  quite,  or  nearly, 
reached  the  surface. 

The  film  of  maximum  velocity  may  reacn  the  surface  in 
trapezoidal  canals  when  depth  of  stream  is  only  one-third 
mean  breadth.  It  is  at  one-fourth  depth  in  the  trapezoidal 
channel,  Fig.  51 , in  which  bottom  breadth  equals  twice  depth. 

In  shallow  streams,  the  maximum  velocity  is  at  or  near 
the  surface. 

344.  Relative  Velocities  and  Volumes  due  to 
Different  Depths. — When  the  mean  velocity  has  been 
reliably  determined  in  a channel,  or  small  stream,  at  some 
given  section,  and  for  some  particular  depth,  it  is  often 
desirable  to  construct  a table  of  velocities  and  volumes  of 
flow,  for  other  depths  in  the  same  section,  so  that,  if  a read- 
ing of  depth  is  taken  at  any  time  from  a gauge  established 
at  that  section,  the  velocity  and  volume  due  to  the  observed 
depth  at  that  time  may  be  read  off  from  the  table. 


RELATIVE  VELOCITIES  AND  VOLUMES. 


329 


The  inclination,  or  surface  slope,  i — , and  the  value 

1 7 

of  tiie  coefficient  of  friction,  m = may  he  observed 

within  the  ordinary  extremes  of  depth  at  the  time  of  the 
experimental  measurement,  if  opportunity  offers,  or  other- 
wise for  the  given  experimental  depth,  and  computed  for 
the  remaining  depths. 

Theory  indicates  that  the  variation  of  velocity,  with 
varying  depth,  is  nearly  as  the  variation  of  the  square  root 


of  the  hydraulic  mean  radius, 


and  the  variation  of 


volume  of  flow  is  nearly  as  the  variation  of  the  product  of 
sectional  area  into  the  square  root  of  hydraulic  mean  radius, 


= S 


These  terms  are  readily  obtained  for  the  several  depths, 
from  measurement  of  the  channel. 

To  compare  new  depths,  velocities,  and  volumes,  with 
the  depth,  velocity,  and  volume  accurately  measured  by 
experiment,  as  unity , 


let  tlie  experimental  depth  be  d , and  the  new  depth  be  dx  , 


“ « 

by.  mean  rad.  “ 

“ 

“ hy.  mean  rad.  “ 

ri. 

« u 

slope  “ 

ly  “ “ 

“ slope  !t 

h > 

tt  e< 

it 

coef.  of  friction  “ 

m,  “ “ 

“ coef.  of  friction  “ 

mi ; 

tt  tt 

tt 

sectional  area  “ 

S,  “ “ 

“ sectional  area  “ 

Sti 

it  « 

tt 

velocity  “ 

v,  “ “ 

“ velocity  “ 

; 

“ €€ 

tt 

volume  “ 

q,  “ “ 

“ volume  “ 

The  relative  values  of  new  depths,  velocities,  volumes, 
etc.,  will  be 


d’  v 5 


v : 


1 


h. 

V 


and  - 


330 


FLOW  OF  WATER  IN  OPEN  CHANNELS. 


q : Qi  ::  1 : — ; etc. 

q 

The  ratio  of  to  v is 


vy  _ . J2 gri\\ 

j rxixm  \ \ 

v 1 mi  1 ' I m ) 

( rim i>  ’ 

and 

( mml ) 

(21) 

* = i isi  = ^ 

(22) 

In  long  straight  channels  of  uniform  section,  ix  will  he 
less  than  i for  increased  depths,  and  greater  than  i for 
reduced  depths ; hut  ordinarily  (except  with  great  velocities) 
their  values  will  he  so  nearly  equal  to  each  other  that  they 
may  he  omitted  from  the  equation  without  serious  error, 
when  the  equation  of  velocity  will  become, 


The  variations  in  m cannot  he  neglected  in  relatively 
shallow  channels. 

For  illustration  of  the  equations,  let  Fig.  57  he  a smooth 


Fig.  57. 


trapezoidal  channel,  6 feet  hroad  at  the  bottom,  = e.  and 
with  side  slopes  inclined  thirty  degrees  from  the  horizon, 

— (p. 


FAIRMOUNT  PUMPING  MACHINERY,  PHILADELPHIA 


RELATIVE  VELOCITIES  AND  VOLUMES. 


331 


During  tlie  experimental  measurement,  let  the  depth  be 
4 feet ; the  slope,  one  foot  in  one  mile  = i — .000189  ; the 
experimental  velocity,  1.201  feet  per  second ; and  the  ex- 
perimental  volume,  62.128  cubic  feet  per  second. 

The  velocities  and  volumes  are  to  be  computed  when  the 
depths  are  2 feet  and  6 feet,  respectively. 

Let  d be  any  given  depth; 

e “ the  bottom  breadth,  = 6 feet ; 
b “ the  mean  breadth  ; 

“ the  slope  of  the  sides,  = 30° ; 

S the  sectional  area  ; 

C “ the  wetted  earth  perimeter. 

Then  we  have  for  the  given  values  of  d : 


Assumed  Values  of  d. 

2 Feet. 

4 Feet. 

6 Feet. 

II 

+ 

II 

12.93 

19.86 

26.79 

d2 

S = K de  . . = 

tan  1> 

18.93 

5T-73 

9^-35 

_ 2 d sec  0 

C — € -4” * — 

tan  (p 

14.00 

22.00 

30.OO 

s 

r~c ” 

I-3S 

2.30 

3.28 

i ... . — 

.0002 

.000189 

.OOO185 

m — 

.02396 

.0187 

.0146 

— 

.836 

1. 201 

I.606 

= 

M 

Cn 

bo 

N) 
C n 

62.128 

I57*95 

"With  increase  of  depth,  there  is  also  increase  of  velocity; 
hence  there  are  two  factors  to  increase  of  volume. 

Some  practical  considerations  relating  to  open  canals 
are  given  in  Chap.  XVII,  following. 


Fig.  58. 


DISTRIBUTING  RESERVOIR. 


SECTION  III. 


Practical  Construction  of  Water-works 


CHAPTER  XVI. 

RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 

345.  Ultimate  Economy  of  Skillful  Construction. 

— An  earthwork  embankment  appears  to  the  uninitiated 
the  most  simple  of  all  engineering  constructions,  the  one 
feature  that  demands  least  of  educated  judgment  and  expe- 
rience. Possibly  from  such  delusion  has,  in  part,  resulted 
the  fact,  which  is  patent  and  undeniable,  that  failures  of 
reservoir  embankments  have  exacted  more  terrible  and 
appalling  penalties  of  human  sacrifice,  and  sacrifice  of  cap- 
ital, than  the  weaknesses  of  all  other  hydraulic  works 
together. 

Each  generation  in  succession  has  had  its  notable  flood 
catastrophes,  when  its  broken  dams  have  poured  deluges 
into  the  valleys,  which  have  swept  away  houses  and  mills 
and  bridges  and  crops,  and  too  often  twenty,  fifty,  or  a 
hundred  human  beings  at  once. 

Such  devastations  are  scarcely  paralleled  by,  though 
more  easily  averted  by  forethought,  than  those  historical 
inundations  when  the  sea  has  broken  over  the  embanked 
shores  of  Holland  and  England,  and  when  great  rivers 


384 


RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 


have  poured  over  their  populous  leveed  plains,  yet  they 
seem  to  he  quickly  forgotten,  except  hy  the  immediate 
sufferers  who  survived  them. 

The  earliest  authenticated  historical  records  of  the  East- 
ern tropical  nations  describe  existing  storage  reservoirs  and 
embankments,  and  more  than  fifty  thousand  such  reser- 
voirs have  been  built  in  the  Indian  Madras  Presidency 
Districts  alone.  Arthur  Jacobs,  B.  A.,  says*  of  these 
Madras  embankments,  that  they  will  average  a half  mile  in 
length  each,  and  the  longest  has  a length  of  not  less  than 
thirty  miles. 

Two  thousand  years  of  practice  seems  to  have  developed 
but  a slight  advance  of  skill  in  the  construction  of  earth 
works,  while  their  apparent  simplicity  seems  to  have  dis- 
tracted modern  attention  from  then  minute  details,  and  to 
have  led  builders  to  the  practice  of  false  economy  in  some  in- 
stances, and  to  the  neglect  of  necessary  precautions  in  others. 

Among  the  recent  disastrous  failures  may  be  mentioned 
the  Bradfield  or  Dale  Dyke  embankment  of  the  Sheffield, 
England,  water- works,  in  1864  ; the  Danbury,  Conn.,  water- 
works embankment,  in  1866  ; the  Hartford,  Conn.,  water- 
works embankment,  in  1867 ; the  New  Bedford,  Mass., 
water- works  embankment,  in  1868 ; the  Mill  River,  or 
Williamsburglr,  Mass.,  embankment,  in  1875  ; and  Worces- 
ter, Mass.,  water-works  embankment,  in  1876.  More  than 
one  hundred  other  breakages  of  dams  are  upon  record  for 
New  England  alone  for  the  same  short  period. 

The  practical  utility  of  streams  is  dependent  largely 
upon  the  storage  of  then-  surplus  waters  in  the  seasons  of 
their  abundant  How,  that  they  may  be  used  when  droughts 
would  otherwise  reduce  their  volume. 


* Vide  Paper  read  before  the  Society  of  Engineers,  London. 


EMBANKMENT  FOUNDATIONS. 


335 


o 

Their  waters  aie  usually  stored  in  elevated  basins, 
whether  stored  for  power,  for  domestic  consumption,  for 
compensation,  or  to  regulate  floods  ; and  frequently  single 
embankments  toward  the  head-waters  of  streams  suspends 
millions  of  tons  of  water  above  the  villages  and  towns  of 
the  lower  valleys.  In  other  instances,  embanked  distrib- 
uting reservoirs  crown  high  summits  in  the  midst  of  popu- 
lous cities.  These  are  good  angels  of  health,  comfort,  and 
protection,  when  performing  their  appointed  duties,  but 
very  demons  of  destruction  when  their  waters  break  loose 
upon  the  hillsides. 

Every  consideration  demands  that  a storage  reservoir 
embankment  shall  be  as  durable  as  the  hills  upon  which  it 
rests.  To  this  end,  no  water  is  to  be  permitted  to  percolate 
and  gather  in  a rill  beneath  the  embankment ; its  core  must 
be  so  solid,  heavy  and  impervious  that  no  water  shall  push 
it  aside,  lift  it  up  or  flow  through  it,  or  follow  along  its  dis- 
charge pipes  or  waste  culvert ; its  core  must  be  protected 
from  abrasions  and  disintegrations ; and  its  waste  overfall 
must  be  ample  in  length  and  strength  to  pass  the  most 
extraordinary  flood  without  the  embankment  being  over- 
topped. 

346.  Embankment  Foundations. — The  foundation 
upon  which  the  structure  rests  is  the  first  vital  point  requir- 
ing attention,  and  may  contain  an  element  of  weakness  that 
shall  ultimately  lead  to  the  destruction  of  the  structure 
placed  upon  it. 

The  superposed  drift  strata  beneath  the  surface  layer  of 
muck  or  vegetable  soil  may  consist  of  various  combinations 
of  loam,  gravel,  sand,  quicksand,  clay,  shale  and  demoral- 
ized rock,  resting  upon  the  solid  impervious  rock,  or  above 
an  impervious  stratum  of  sufficient  thickness  to  resist  the 
penetration  of  water  under  pressure.  If  the  water  is  raised 


336 


RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 


fifty  feet  above  the  surface  and  there  are  thirty  feet  of  per- 
vious earth  in  the  bed  of  the  valley,  then  the  pressure  upon 
the  bed  stratum  will  be  five  thousand  pounds,  or  two  and 
one-half  tons  per  square  foot,  which  will  tend  to  force  the 
water  toward  an  outlet  in  the  valley  below.  That  much  of 
the  natural  earth  is  porous  is  well  demonstrated  by  the 
freedom  with  which  water  enters  on  the  plains  and  courses 
through  the  strata  to  the  springs  in  the  valleys,  even  with- 
out a head  of  water  to  force  its  entrance.  Such  porous 
strata  must  be  cut  off  or  sealed  over,  or  the  permanency  and 
efficiency  of  the  structure,  however  well  executed  above, 
cannot  be  assured. 

If  the  valley  across  which  the  embankment  is  thrown  is 
a valley  of  denudation,  or  if  the  embankment  stretches 
across  one  or  more  ridges  to  cover  several  minor  valleys 
with  a broad  lake,  the  waters  in  rising  may  cover  the 
outcropping  edges  of  coarse  porous  strata  that  shall  lead 
the  liowage  by  subterranean  paths  to  distant  springs  where 
water  had  not  flowed  before.  Hence  the  necessity  of  a 
thorough  examination  of  the  geological  substructure  of 
the  valley,  and  of  tests  by  trial  shafts,  supplemented  by 
deep  borings,  of  the  site  of  the  embankment  and  the  hill- 
sides upon  which  it  abuts.  The  test  borings  should  cover 
some  distance  above  and  below  the  site  of  the  embankment, 
lest  a mere  pocket  filled  with  impervious  soil  be  mistaken 
for  a thick  strata  supposed  to  underlie  the  whole  vicinity. 

The  trial  shafts  only,  permit  a proper  examination  of  the 
covered  rock,  which  may  be  so  shattered,  or  fissured.  aS  to 
be  able  to  conduct  away  a considerable  quantity  of  water, 
or  to  lead  water  from  the  adjoining  hills  to  form  springs 
under  the  foundations. 

Several  deep  reservoirs  constructed  within  a few  years 
past  have  demanded  excavations  for  cut-off  walls,  to  a 


SURFACE  SOILS. 


337 


depth  of  a hundred  feet  at  certain  points  along  their  lines, 
but  the  porosity  and  the  firmness  of  the  strata  in  such  cases 
are  points  demanding  the  exercise  of  the  most  mature  judg- 
ment, that  the  work  may  be  made  sure,  and  at  the  same 
time  labor  be  not  wasted  by  unnecessarily  deep  cutting. 

Thoroughness  in  the  preliminary  examination  of  the 
substrata  of  a proposed  site  may  frequently  result  in  the 
avoidance  of  a great  deal  of  vexatious  labor  and  enhanced 
cost  that  would  otherwise  follow  from  the  location  of  an 
embankment  over  a treacherous  sub-foundation. 

347.  Springs  under  Foundations. — If  the  excava- 
tion shall  cut  off  or  expose  a spring  that,  when  confined, 
will  produce  an  hydrostatic  pressure  liable  to  endanger  the 
outside  slope  of  the  embankment,  it  must  be  followed  back 
by  a drift  or  open  cutting  to  a point  from  whence  it  may 
be  safely  led  out  in  a small  pipe  below  the  site  of  the 
embankment. 

348.  Surface  Soils. — Dependence  cannot  be  placed 
upon  the  vegetable  soil  lying  upon  the  site  of  an  embank- 
ment to  hold  water  under  pressure,  for  it  is  always  porous 
in  a state  of  nature,  as  is  also  the  subsoil  to  the  depth  pene- 
trated by  frost.  The  vegetable  soil  should  be  cleared  from 
beneath  the  core  of  the  embankment,  and  the  subsoil  rolled 
and  compacted. 

The  vegetable  soil  will  be  valuable  for  covering  the  top 
and  outside  slope  of  the  embankment. 

If  good  hard-pan  underlies  the  surface  soil  to  a depth 
sufficient  to  make  a strong  foundation  for  the  embankment, 
then  its  surface  should  be  broken  up  to  the  depth  it  has 
been  made  porous  by  frost  expansion,  and  the  material 
rolled  down  anew  in  thin  layers  with  a grooved  roller  of 
not  less  than  two  tons  gross  weight,  or  of  one-half  ton  per 
lineal  foot. 


22 


338 


RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 


If  next  to  the  surface  soil  there  is  a layer  of  hard-pan 
within  the  basin  to  be  flowed,  and  this  hard-pan  covers  open 
and  porous  strata  that  extend  below  the  dam,  caution 
should  be  used  in  disturbing  the  hard-pan,  lest  the  water 
be  admitted  freely  to  the  porous  strata,  when  it  will  escape, 
perhaps  by  long  detour  around  the  dam. 

349.  Concrete  Cut-off  Walls.— If  the  trench  for  the 
cut-off  wall  is  deep  and  very  irregular,  it  is  well  to  level  up 
in  the  cuts  with  a water-proof  concrete  well  settled  in  place, 
and  this  may  prove  more  economical  than  to  cut  the  deep 
trench  of  sufficient  width  to  receive  a reliable  puddle  wall ; 
also,  the  greater  reliability  of  the  concrete  under  great  pres- 
sure should  not  be  overlooked. 

350.  Treacherous  Strata. — In  one  instance  the  writer 
had  occasion  to  construct  a low  embankment,  not  exceed- 
ing twenty  feet  height  at  the  centre,  across  an  abraded  cut 
through  a plain.  The  embankment  was  to  retain  a storage 
of  water  for  a city  water  supply,  and  the  enclosed  lake  was 
to  have  an  area  of  200  acres. 

The  test  pits  and  soundings  developed  the  fact  that  the 
abraded  valley  and  adjacent  plains  were  underlaid  with  a 
stratum  of  fine  sand  twelve  feet  in  thickness,  which,  when 
disturbed,  became  a quicksand,  and  if  water  was  admitted 
to  it,  would  flow  almost  as  freely  as  water. 

The  sand  lay  in  a compact  mass,  and  would  not  pass 
water  freely  until  disturbed.  Above  the  sand  was  a layer 
of  about  three  feet  of  fine  hard-pan,  and  above  this  about 
three  feet  of  good  meadow  soil  had  formed. 

For  this  case  the  decision  was,  not  to  uncover  the  quick- 
sand, but  to  seal  it  over  in  the  vicinity  of  the  embankment. 
The  foundation  of  the  embankment,  and  of  the  waste  over- 
fall  which  necessarily  came  in  the  centre  of  length  of  the 
embankment,  was  made  of  concrete  of  such  thickness  as  to 


EMBANKMENT  CORE  MATERIALS. 


339 


properly  distribute  the  weight  of  the  earthwork  and  over- 
fall  masonry.  Above  the  embankment,  after  a careful 
cleaning  of  the  soil  to  the  depth  penetrated  by  the  grass 
roots,  the  valley  was  covered  with  a layer  of  gravel  and 
clay  puddle  for  a distance  of  one  hundred  feet. 

Beneath  the  toe  of  the  inside  slope,  where  the  bottom 
puddle  joined  the  concrete  foundation,  a trench  was  cut 
across  the  valley  into  the  quicksand,  as  deep  as  could  be 
excavated  in  sections,  with  the  aid  of  the  light  pumping 
power  on  hand,  and  sheet  piling  placed  therein  and  driven 
through  the  quicksand,  and  then  the  trench  was  filled 
around  the  piling  with  puddle,  thus  forming  a puddle  and 
plank  curtain  under  the  inside  edge  of  the  embankment. 

Such  expedients  are  never  entirely  free  from  risks, 
especially  if  a faithful  and  competent  inspector  is  not  re- 
tained constantly  on  the  work  to  observe  that  orders  are 
obeyed  in  the  minutest  detail. 

In  the  case  in  question  many  thousands  of  dollars  were 
saved,  and  the  work  has  at  present  writing  successfully 
stood  the  test  of  seven  years  use,  during  which  time  the 
most  fearful  Hood  storm  recorded  in  the  present  century  has 
swept  over  the  section  of  Connecticut  where  the  storage  lake 
is  situated. 

351.  Embankment  Core  Materials.  — Barely  are 
good  materials  found  ready  mixed  and  close  at  hand  for 
the  construction  of  the  core  of  the  embankment.  It  is 
essential  that  this  portion  be  so  compounded  as  to  be  im- 
pervious. 

If  we  fill  a box  of  known  cubical  capacity,  say  one  cubic 
yard,  with  shingle  or  screened  coarse  gravel,  we  shall  then 
find  that  we  can  pour  into  the  full  box  with  the  gravel  a 
volume  of  water  equal  to  twenty-eight  or  thirty  per  Cent, 
of  the  capacity  of  the  box,  according  to  the  volume  of  voids ; 


340 


RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 


or  if  we  attempt  to  stop  water  with  the  same  thickness  (one 
yard)  of  gravel,  we  shall  find  that  water  will  flow  through 
it  very  freely.  Then  let  the  same  gravel  he  dumped  out 
upon  a platform  and  twenty-eight  per  cent,  nearly  of  fine 
gravel  he  mixed  with  it,  so  as  to  fill  the  voids  equally,  and 
the  whole  he  put  into  the  measuring-box.  We  now  find 
that  we  can  again  pour  in  water  equal  to  about  thirty  per 
cent,  of  the  cubical  measure  of  the  fine  gravel.  Then  let  fine 
sand,  equal  to  this  last  volume  of  water,  he  mixed  with  the 
coarse  and  fine  gravel,  and  the  whole  returned  to  the  meas- 
ure. We  now  find  that  we  can  pour  in  water,  though  not 
so  rapidly  as  before,  equal  to  thirty-three  per  cent,  approx- 
imately of  the  cubical  measure  of  the  sand,  and  we  resort 
to  fine  clay  equal  to  the  last  volume  of  the  water  to  again 
fill  the  voids.  The  voids  are  now  reduced  to  microscopic 
dimensions. 

If  we  could  in  practice  secure  this  strict  theoretical  pro- 
portion and  thorough  admixture  of  the  material,  we  should 
introduce  into  one  yard  volume  quantities  as  follows : Coarse 
gravel,  1 cubic  yard  ; fine  gravel,  0.28  cubic  yard ; sand, 
0.08  cubic  yard  ; and  clay,  0.03  cubic  yard,  or  a total  of 
the  separate  materials  of  1.39  cubic  yards. 

In  practice,  with  a reasonable  amount  of  labor  applied 
to  thoroughly  mix  the  materials  so  as  to  fill  the  voids,  we 
shall  use,  approximately,  the  following  proportion  of  ma- 
terials : 

Coarse  gravel 1.00  cubic  yard. 

Fine  grave] 0.35  “ “ 

Sand 0.15  “ “ 

Clay 0.20  “ 

Total 1.70  “ 

which,  when  mixed  loosely  or  spread  in  thin  layers,  will 
make  about  one  and  three-tenths  yards  bulk,  and  when 


WEIGHT  OF  EMBANKMENT  MATERIALS. 


341 


thoroughly  compacted  in  the  embankment,  will  make  about 
one  and  one-quarter  cubic  yards  bulk. 

The  voids  now  remaining  in  the  mass  may  each  be  a 
thousand  times  broader  than  a molecule  of  water,  yet  they 
are  sufficiently  minute,  so  that  molecular  attraction  exerts 
a strong  force  in  each  and  resists  flow  of  the  molecules, 
even  under  considerable  head  pressure  of  water. 

It  will  be  interesting  here  to  compare  the  weights  of  a 
solid  block  of  granite  with  its  disintegrated  products  of 
gravel  and  sand,  taking  for  illustration  a cubic  foot  volume. 


TABLE  No.  77. 
Weights  of  Embankment  Materials. 


Material. 

Av.  Weight. 

Specific  Gravity. 

Av.  Voids. 

Granite 

166 

lbs. 

2.662 

Coarse  Gravel 

120 

U 

I-925 

.28 

per 

cent. 

Gravel  

ii6 

U 

1. 86 1 

■30 

U 

U 

Sharp  Sand 

IIO 

u 

1-765 

•33 

u 

u 

Clay 

I25 

u 

2.000 

.12 

u 

u 

Water 

62.5 

u 

I. OOO 

If  the  shingle  is  omitted  and  common  gravel  is  the  bulk 
to  receive  the  finer  materials,  then  the  proportions  in  prac- 
tice may  be : 

Common  gravel 1.00  cubic  yard. 

Sand 0.36  “ 

Clay (L25  “ “ 

1.61 

which,  when  loosely  spread,  will  make  about  one  and  one- 
sixth  yards  bulk ; and  compacted,  some  less  than  one  and 
one-tenth  yards  bulk. 

Gravel  is  usually  found  with  portions  of  sand,  or  sand 
and  clay,  already  mixed  with  it,  though  rarely  with  a suf- 


342 


RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 


ficiency  of  fine  material  to  fill  the  voids.  The  lacking  ma- 
terial should  he  supplied  in  its  due  proportion,  whether  it 
be  fine  gravel  sand,  fine  sand,  or  clay.  The  voids  must  be 
filled,  at  all  events,  with  some  durable  fine  material,  to 
ensure  imperviousness. 

It  is  sometimes  found  expedient  to  substitute  for  a por- 
tion of  the  fine  sand  or  clay,  portions  of  loam  or  selected 
soil  from  old  ground,  and  on  rare  occasions  peat,  but 
neither  peat  nor  loam  should  be  introduced  in  bulk  into 
the  core  of  an  embankment. 

There  is  a general  prejudice  against  the  use  of  peat  or 
surface  soils  in  embankments,  and  the  objections  hold  good 
when  they  are  exposed  to  atmospheric  influences.  Mr. 
Wiggin  remarks,*  however,  that  a peat  sea-bank  which  was 
opened  after  being  built  for  seventeen  years,  exhibited  the 
material  as  fibrous  and  undecayed  as  when  first  deposited. 

Weight  is  a valuable  property  in  embankment  material, 
when  placed  upon  a firm  foundation,  since,  for  a given  bulk, 
the  heavier  material  is  able  to  resist  the  greater  pressure. 

Peat  and  loam  are  very  deficient  in  the  weight  property, 
and  therefore  need  the  support  of  heavier  materials.  Clay 
is  heavier  than  sand  or  fine  gravel ; shingle  is  heavier  than 
clay  ; but  the  compound  of  shingle,  gravel,  sand,  and  clay, 
above  described,  is  heavier  than  either  alone,  and  weighs 
when  compacted,  for  a given  volume,  nearly  as  much  as 
solid  granite. 

Cohesiveness  and  stability  are  valuable  properties  in 
embankment  materials,  but  sand  and  gravel  lack  perma- 
nent cohesiveness,  and  clay  alone,  though  quite  cohesive, 
is  liable  to  slips  and  dangerous  fissures,  if  unsupported ; 
but  a proper  combination  of  gravel,  sharp  sand,  and  clay, 


* Embanking  Lands  from  tbe  Sea,  p.  20.  London,  1852. 


PECULIAR  PRESSURES. 


343 


gives  all  the  valuable  properties  of  weight,  cohesiveness, 
stability,  and  imperviousness. 

352.  Peculiar  Pressures. — There  are  peculiar  pres- 
sure influences  in  an  earthwork  structure  that  are  not 
identical  with  the  theoretical  hydrostatic  pressures  upon  a 
tight  masonry,  or  fully  impervious  structure  of  the  same 
form.  The  hydrostatic  pressure  upon  an  impervious  face, 
whatever  its  inclination,  might  be  resolved  into  its  hori- 
zontal resultant  (§  111),  and  that  resultant  would  be  the 
theoretical  force  tending  to  push  the  structure  down  the 
valley,  and  would  be  equal  to  the  pressure  of  the  same 
depth  of  water  acting  upon  a vertical  face.  The  pressure 
would  be,  upon  a vertical  face,  jper  square  fool,  at  the  given 
depths,  as  follows : 


Depth,  in  feet | 5 

10 

15 

20 

25 

30 

35 

40 

45 

50 

60 

70 

80 

90 

100 

Pressure,  in  lbs '312. 1 

i 

624.3 

936-4 

1249 

1561 

1873 

2185 

2497 

2809 

3121 

3746 

4370 

4994 

5618 

6243 

The  effective  action  of  the  theoretical  horizontal  resultant 
is  neutralized  somewhat  upon  an  impervious  slope  by  the 
weight  of  water  upon  the  slope. 

But  all  embankments  are  pervious  to  some  extent.  If 
with  the  assistance  of  the  pressure,  the  water  penetrates  to 
the  centre  of  the  embankment,  it  presses  there  in  all  direc- 
tions, upward,  downward,  forward  and  backward,  and  at  a 
depth  of  fifty  feet  the  pressure  will  be  a ton  and  a half  per 
square  foot.  Such  pressure  tends  to  lift  the  embankment, 
and  to  soften  its  substance,  as  well  as  to  press  it  forward, 
and  if  in  course  of  time  the  water  penetrates  past  the  centre 
it  may  reach  a point  where  the  weight  or  the  imperviousness 
of  the  outside  slope  is  not  sufficient  to  resist  the  pressure, 
when  the  embankment  will  crack  open  and  be  speedily 
breached. 

That  portion  of  the  embankment  that  is  penetrated  by 


344 


RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 


the  water  lias  its  weight  neutralized  to  the  extent  of  the 
weight  of  the  water,  or  at  any  depth,  a total  equal  to  the 
water  pressure  at  that  depth ; thus,  at  fifty  feet  depth,  tliat 
portion  penetrated  is  reduced  in  its  total  weight  a total  of 
one  and  one-lialf  tons  per  square  foot. 

Hence  the  value  of  imperviousness  at  the  front  as  well 
as  in  the  centre  of  the  embankment,  so  that  the  maximum 
amount  of  its  weight  may  be  effective. 

If  water  penetrates  the  subsoil  beneath  the  embankment, 
as  is  frequently  the  case,  it  there  exerts  a lifting  pressure 
according  to  its  depth. 

353.  Earthwork  Slopes. — If  earth  embankments  of 
the  forms  usually  given  to  them,  and  their  subsoils  also, 
were  quite  impervious,  as  a wall  of  good  concrete  would  be, 
the  embankments  would  have  a large  surplus  of  weight, 
and  might  be  cut  down  vertically  at  the  centre  of  their 
breadth,  and  either  half  would  sustain  the  pressure  and 
impact  of  waves  with  safety,  but  the  vertical  wall  of  earth 
would  not  stand  against  the  erosive  actions  of  the  waves 
and  storms.  Surface  slopes  of  earthwork  are  controlling 
elements  in  their  design,  and  govern  their  transverse  profiles. 

Different  earths  have  different  degrees  of  permanent 
stability  or  of  f riction  of  their  particles  upon  each  other, 
that  enable  them  to  maintain  their  respective  natural  sur- 
face slopes,  or  angles  of  repose,  against  the  effects  of  gravity, 
ordinary  storms,  and  alternate  freezings  and  thawings,  until 
nature  binds  their  surfaces  together  with  the  roots  of  weeds, 
grasses  and  shrubs.  The  coefficient  of  friction  of  earth 
equals  the  tangent  of  its  angle  of  repose,  or  natural  slope. 
The  amount  or  value  of  the  slope  is  usually  described  by 
stating  the  ratio  of  the  horizontal  base  of  the  angle  to  its 
vertical  height,  which  is  the  reciprocal  of  the  tangent  of  the 
inclination. 


EARTHWORK  SLOPES. 


345 


The  following  data  relating  to  these  values  are  selected  * 
in  part  from  Rankine,  and  to  them  are  added  the  angles  at 
which  certain  earths  sustain  by  friction  other  materials  laid 
upon  their  inclined  surfaces. 


TABLE  No.  78. 


Angles  of  Repose,  and  Friction  of  Embankment  Materials. 


Material. 

Angle  of 
Repose. 

Coefficient  of 
Friction. 

Ratio 

of  Slope. 

Dry  sand,  fine 

o « 

oo 

04 

•532 

Hori. 

1.88 

to 

Vert . 

I 

“ “ coarse  . . 

3° 

•577 

i-73 

1 

Damp  clay  

45° 

1. 000 

I. OO 

U 

1 

Wet  clay 

ISo 

.268 

3-73 

u 

1 

Clayey  gravel  

45  o 

I. OOO 

1.00 

u 

I 

Shingle 

42 

.900 

I'll 

u 

I 

Gravel 

38° 

.781 

1.28 

u 

I 

Firm  loam 

36° 

.727 

1.38 

u 

I 

Vegetable  soil 

35° 

.700 

i-43 

u 

1 

Peat 

20 

•364 

2-75 

u 

I 

Masonry,  on  clayey  gravel. . 

3°° 

•577 

!-73 

u 

I 

“ “ dry  clay 

270 

•510 

1.96 

u 

I 

“ “ moist  clay.  .. 

18 

•325 

3.08 

a 

I 

Earth  on  moist  clay  ..... 

45° 

I. OOO 

1.00 

u 

I 

“ “ wet  clay  

I7° 

.306 

3.26 

u 

I 

Inclined  earth  surfaces  are  most  frequently  dressed  to 
the  slopes,  having  ratios  of  bases  to  verticals,  respectively 
1J  to  1 ; 2 to  1 ; 2|-  to  1 ; and  3 to  1 ; corresponding  respect- 
ively to  the  coefficients  of  friction  0.67,  0.50,  0.40,  and  0.33, 
and  to  the  angles  of  repose  33^°,  26^°,  21|°,  and  18J°, 
nearly. 

Gravel,  and  mixtures  of  clay  and  gravel,  will  stand 
ordinarily,  and  resist  ordinary  storms  at  an  angle  of  H to  1, 
but  the  angle  must  be  reduced  if  the  slope  is  exposed  to 
accumulations  of  storm  waters  or  to  wave  actions,  and  upon 


* Civil  Engineering,  p.  316.  London,  1812. 


346 


RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 


broad  lake  shores  the  waves  will  reduce  coarse  gravel,  if 
unprotected,  to  a slope  of  5 to  1,  and  liner  materials  to 
lesser  slopes.  Complete  saturation  of  clay,  loam,  and  vege- 
table soil,  destroys  the  considerable  cohesion  they  have 
when  merely  moistened,  and  they  become  mud,  and  assume 
slopes  nearly  horizontal ; hence  the  conditions  to  which  the 
above  table  refers  may  be  entirely  destroyed  and  the  angles 
be  much  flattened,  unless  the  slopes  are  properly  protected. 
On  the  other  hand,  the  table  does  not  refer  to  the  temporary 
stability  which  some  moist  earths  have  in  mass,  for  com- 
pact clay,  gravel,  and  even  coarse  sand  may,  when  their 
adhesion  is  at  its  maximum,  or  when  their  pores  are  par- 
tially and  nearly  filled  with  water,  be  trenched  through, 
and  the  sides  of  the  trench  stand  for  a time,  nearly  vertical, 
at  heights  of  from  6 to  15  feet.  In  such  cases,  loss  or 
increase  of  moisture  destroys  the  adhesion,  and  the  sides  of 
the  trench  soon  begin  to  crumble  or  cave,  unless  supported. 

354.  Reconnoissance  for  Site. — Let  us  assume,  for 
illustration,  that  a storage  reservoir  is  to  be  formed  in  an 
elevated  valley.  The  minimum  allowable  altitude  being 
fixed  upon,  and  designated  by  reference  to  a permanent 
bench  mark  in  the  outfall  of  the  valley,  the  valley  is  then 
explored  from  the  given  altitude  upward  for  the  most  favor- 
able site  for  the  storage  basin,  and  for  the  site  for  an 
embankment,  or  dam,  as  the  circumstances  may  require. 
W e may  expect  to  find  a good  site  for  the  storage  at  some 
point  where  a broad  meadow  is  flanked  upon  each  side  by 
abrupt  slopes,  and  where  those  slopes  draw  near  to  each 
other  at  the  outlet  of  the  meadow,  as  is  frequently  the  case. 
Having  found  a site  that  appears  favorable,  a preliminary 
reconnoissance  with  instruments  is  made  to  determine  if  the 
basin  has  the  required  amount  of  watershed  and  storage 
capacity,  previously  fixed  upon  (§  59).  and  to  determine 


DETAILED  SURVEYS. 


347 


approximately  the  height  the  embankment  or  masonry 
dam  must  have.  If  the  preliminary  reconnoissance  gives 
satisfactory  results,  then  the  site  where  the  embankment 
can  be  built  most  economically  and  substantially  is  care- 
fully sought,  and  test  pits  and  borings  put  down  at  the 
point  giving  most  promise  upon  the  surface.  It  is  impcri 
ant  to  know  at  the  outset  that  the  subsoil  is  firm  enough  it 
carry  the  weight  of  the  embankment  without  yielding,  and  if 
there  is  an  impervious  substratum  that  wi  11  retain  the  pond- 
ed water  under  pressure.  It  is  important  also  to  know  that 
suitable  materials  are  obtainable  in  the  immediate  vicinity. 

3 55.  Detailed  Surveys. — The  preliminary  surveys  all 
giving  satisfactory  indications  as  respects  extent  of  flowage, 
volume  of  storage,  depth  of  water,  inclination  and  material 
of  shore  slopes,  soils  of  flowed  basin,  and  the  detailed  sur- 
veys confirming  the  first  indications,  and  also  establishing 
that  the  drainage  area  and  rainfall  supplying  the  basin  is 
of  ample  extent  and  quantity  to  supply  the  required  amount 
of  water  (§  24)  of  suitable  quality  (§  100  et  seq.) ; then  let 
us  suppose  that  the  conditions  governing  the  retaining  em- 
bankment may  best  be  met  by  a construction  similar  to 
that  shown  in  Fig.  59,  based  upon  actual  practice. 

356.  Illustrative  Case. — Here  the  water  was  raised 
fifty  feet  above  the  thread  of  the  valley.  The  surface  of  the 
impervious  clay  stratum,  containing  a small  portion  of  fine 
gravel,  was  at  its  lowest  dip,  thirty  feet  below  the  surface 
of  the  valley,  and  was  overlaid  at  this  point,  in  the  following 
order  of  superposition,  with  stratas  of  sandy  clay,  coarse 
sand,  quicksand,  sandy  marl,  gravel  and  sand,  gravelly  loam, 
and  vegetable  surface  soil,  each  of  thickness  as  figured. 

Gravel  and  sand  and  loam  were  obtainable  readily  in 
the  immediate  vicinity,  but  clay  was  not  so  readily  pro- 
cured, and  must  therefore  needs  be  economized. 


348 


RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 


Fig.  59. 


STORAGE  RESERVOIR  EMBANKMENT. 

357 . Cut-off  Wall. — A broad  trench  was  cut,  after  the 
clearing  of  the  surface  soil,  dowu  to  the  sandy  marl,  and 
then  a narrow  trench  cut  down  to  eighteen  inches  depth  in 
the  thick  clay  strata,  finishing  four  feet  wide  at  the  bottom. 

A wall  of  concrete,  four  feet  thick,  composed  of  machine- 
broken  stone,  four  parts ; coarse  sand,  one  part ; fine  sand, 
one  part ; and  good  hydraulic  cement,  one  part,  was  built 
up  to  eighteen  inches  above  the  top  of  the  marl  stratum. 

The  concrete  was  mixed  with  great  care,  and  the  materials 
rammed  into  the  interstices  of  the  bank,  to  insure  imper- 
viousness in  the  wall,  and  to  prevent  water  being  forced 
down  its  side  and  under  its  bottom.  Puddle,  of  one  part 
mixed  coarse  and  tine  sharp  gravel,  one  part  fine  sand,  and 
one  part  good  clay  then  filled  the  broad  trench  up  to  the 
surface  of  the  embankment  foundation. 

358.  Embankment  Core. — The  core  of  the  embank- 
ment was  composed  of  carefully  mixed  coarse  and  fine 
gravel,  sand,  and  clay,  in  the  proportions  given  above 


EMBANKMENT  CORE. 


349 


(p.  340),  requiring  for  one  cubic  yard  of  core  in  place,  ap- 
proximately : 

Coarse  gravel 74  cubic  yard. 

Fine  “ 26  “ “ 

Sand 11  “ “ 

Clay 15  «<  « 

1.26  “ 

When  measured  by  cart-loads,  these  quantities  became 
eight  loads*  of  mixed  gravels,  one  load  of  sand,  and  two 
loads  of  clay,  the  cubic  measure  of  each  load  of  clay  being 
slightly  less  than  that  of  the  dry  materials.  The  gravel 
was  spread  in  layers  of  two  inches  thickness,  loose,  the  clay 
evenly  spread  upon  the  gravel  and  lumps  broken,  and  the 
sand  spread  upon  the  clay.  When  the  triple  layer  was 
spread,  a harrow  was  passed  over  it  until  it  was  thoroughly 
mixed,  and  then  it  was  thoroughly  rolled  with  a two-ton 
grooved  roller,  made  up  in  sections,  the  layer  having  been 
first  moistened  to  just  that  consistency  that  would  cause  it 
to  knead  like  dough  under  the  roller,  and  become  a com- 
pact solid  mass. 

Such  a core  packs  down  as  solid,  resists  the  penetration 
or  abrasion  of  water,  nearly  as  well,  and  is  nearly  as  diffi- 
cult to  cut  through  as  ordinary  concrete,  while  rats  and  eels 
are  unable  to  enter  and  tunnel  it. 

The  proportions  adopted  for  the  core  were — a thickness 
of  five  feet  at  the  top  at  a level  three  feet  above  high-water 
mark,  and  approximate  slopes  of  1 to  1 on  each  side. 

For  the  maximum  height  of  fifty-four  feet  this  gave  a 
breadth  of  113  feet  base. 

This  core  was  abundantly  able  to  resist  the  percolation 
of  the  water  through  itself,  and  to  resist  the  greatest  pres- 

* Seven  loads  of  coarse  and  three  loads  of  fine  gravel  make,  when  mixed, 
about  eight  loads  bulk. 


850 


RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 


sure  of  the  water,  and  had  these  been  the  only  matters  to 
provide  for,  the  embankment  core  would  have  been  the 
complete  embankment. 

359.  Frost  Covering. — Frost  would  gradually  pene- 
trate deeper  and  deeper  into  that  part  of  the  work  above 
water  and  into  the  outside  slope,  and  by  expansions  make 
it  porous  and  loose  to  a depth,  at  its  given  latitude,  of  from 
four  to  five  feet.  A frost  covering  was  therefore  placed 
upon  it,  and  carried  to  a height  on  the  inside  of  five  feet 
above  high-water  line,  and  of  just  sufficient  thickness  at 
high-water  line  to  protect  it  from  frost. 

The  frost-covering  was  composed  of  such  materials  as 
could  be  readily  obtained  in  the  vicinity  of  the  embank- 
ment. It  was  built  up  at  the  same  time,  in  thin  layers,  with 
the  core,  and  the  whole  was  moistened  and  rolled  alike, 
making  the  whole  so  compact  as  to  allow  no  apparent 
“ after  settlement.’’'1  The  wave  slope  was  built  eighteen 
inches  full,  and  then  dressed  back  to  insure  solidity  be- 
neath the  pavement. 

The  core  of  an  embankment  should  be  built  up  at  least 
to  the  highest  flood  level,  which  is  dependent  upion  length 
of  overfall  as  well  as  height  of  its  crest,  and  the  frost-cover- 
ing should  be  built  of  good  materials  to  at  least  three  feet 
above  maximum  flood  level. 

300.  Slope  Paving. — The  exterior  slope,  when  soiled, 
was  dressed  to  an  inclination  of  11  to  1 ; the  interior  slope 
was  made  2 to  1 from  one  foot  above  high  water  down  to  a 
level,  three  feet  below  proposed  minimum  low  water,  where 
there  was  a berm  five  feet  wide,  and  the  remainder  of  the 
slope  to  the  bottom  was  made  11  to  1.  The  lower  interior 
slope  was  paved  with  large  cobbles  driven  tightly,  the  berm 
with  a double  layer  of  flat  quarried  stone,  and  the  upper 
slope,  which  was  to  be  exposed  to  wave  action,  was  covered 


PUDDLE  WALL. 


351 


with  one  foot  thickness  of  machine-broken  stone,  like  “ road 
metal”  and  then  paved  with  split  granite  paving-blocks  of 
dimensions  as  follows : Thickness,  10  to  14  inches  ; widthss 
12,  14,  or  16  inches  ; and  lengths,  24  to  48  inches. 

A granite  ledge,  in  sheets  favorable  for  the  splitting  of 
the  above  blocks,  was  near  at  hand,  and  supplied  the  most 
economical  slope  paving,  when  labor  of  placing  and  future 
maintenance  was  considered.  From  one  foot  above  high 
water  to  the  underside  of  the  coping,  the  paving  had  a slope 
of  1 to  1,  and  the  face  of  the  coping  was  vertical. 

361.  Puddle  Wall. — The  policy  might  be  considered 
questionable  of  using  clay  in  so  large  a section  of  the 
embankment,  when  the  haulage  of  the  clay  was  greater 
than  of  any  of  the  other  materials,  and  when  the  clay  might 
be  confined  to  the  lesser  section  of  the  usual  form  of  puddle 
wall.  These  methods  of  disposing  the  clay  were  compared 
in  a preliminary  calculation,  both  upon  the  given  basis,  and 
that  of  a puddle  wall  of  minimum  allowable  dimensions, 
viz.,  five  feet  thick  at  the  top  and  increasing  in  thickness 
on  each  side  one  foot  in  eight  of  height,  which  gave  a maxi- 
mum thickness  of  18.6  feet  at  base  with  54  feet  height.  (See 
dotted  lines  in  Fig.  59.) 

The  estimate  of  loose  materials  for  each  cubic  yard  of 
complete  core  was — coarse  gravel,  .74  cu.  yard  ; fine  gravel, 
.26  cu.  yd.  ; sand,  .07  cu.  yd.  ; and  clay,  .15  cu.  yd.  ; and 
for  puddle  wall  of  equal  parts  of  gravel  and  clay — gravel 
.59  cu.  yd.,  and  clay  .59  cu.  yd. 

This  calculation  gave  the  excess  of  clay  in  the  maximum 
depth  of  embankment,  less  than  4 cubic  yards  per  lineal 
foot  of  embankment,  and  the  excess  at  the  mean  depth  of 
thirty  feet,  about  three-fourths  yard  per  lineal  foot  of 
embankment. 

The  difference  in  estimated  first  cost  was  slightly  against 


352 


RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 


the  mixed  core,  hut  in  that  particular  case  this  was  consid- 
ered to  be  decidedly  overbalanced  by  more  certainly  in- 
sured stability,  more  probable  freedom  from  slips  and 
cracks  in  a vital  part  of  the  work,  and  by  the  additional 
safety  with  which  the  waste  and  draught  pipes  could  be 
passed  through  the  core. 

The  value  of  puddle  in  competent  hands  has,  however, 
been  demonstrated  in  many  noble  embankments.  It  is 
usually  placed  in  the  centre  of  the  embankment,  as  in 
Fig.  61,  and  occasionally  near  the  slope  paving,  as  in 
Fig.  62,  from  a design  by  Moses  Lane,  C.  E. 

362.  Rubble  Priming  Wall.  — The  drift  formation 
presents  a great  variety  of  materials  ; but  not  always  such 
as  are  desired  for  a storage  embankment,  in  the  immediate 
vicinity  of  its  site.  The  selection  of  proper  materials  often 
demands  the  best  judgment  and  continued  attention  of  the 
engineer.  Clay,  which  is  often  considered  indispensable  in 
an  embankment,  may  not  be  found  within  many  miles. 

Fig.  60  (p.  84)  gives  a section  of  an  embankment  con- 
structed where  the  best  materials  were  a sandy  gravel  and 
a moderate  amount  of  loam,  but  abundance  of  gneiss  rock 
and  boulders  were  obtainable  close  at  hand. 

Here  a priming  wall  of  thin  split  stone  was  carried  up 
in  the  heart  of  the  embankment  from  the  bed-rock,  which 
was  reached  by  trenching.  Each  stone  was  first  dashed 
clean  with  water,  and  then  carefully  floated  to  place  in  good 
cement  mortar,  and  pains  taken  to  fill  the  end  and  side 
joints,  and  exceeding  care  was  taken  not  to  move  or  in  any 
way  disturb  a stone  about  which  the  mortar  had  begun  to 
set.  No  stones  were  allowed  to  be  broken,  spalted,  or 
hammered  upon  the  wall,  neither  were  swing  chains  drawn 
out  through  the  bed  mortar.  The  construction  of  a water- 
tight wall  of  rubble-stone  is  a work  of  skill  that  can  be 


APPLICATION  OF  FINE  SAND. 


353 


performed,  but  the  ordinary  layer  of  foundation  masonry 
in  cement  mortar  seems  no  more  to  comprehend  it  than 
would  a fiddler  at  a country  dance  the  enchanting  strains 
of  a Vieuxtemps  or  Paganini. 

Grouting  such  rubble-stone  walls,  according  to  the  usual 
method,  will  not  accomplish  the  desired  result,  and  is 
destructive  of  the  most  valuable  properties  of  the  cement. 

363.  A Light  Embankment. — In  this  embankment 
(Fig.  60),  selected  loam  and  gravel  were  mixed  m due  pro- 
portions on  the  upper  side  of  the  priming  wall,  so  as  to 
insure,  as  nearly  as  possible,  imperviousness  in  the  earth- 
work. The  entire  embankment  was  built  up  iu  layers, 
spread  to  not  exceeding  four  or  five  inches  thickness,  and 
moistened  and  rolled  with  a heavy  grooved  roller. 

The  cross-section  of  this  work  is  much  lighter  than  that 
advised  by  several  standard  authorities,  both  slopes  being 
1|  to  1 , but  great  bulk  was  modified  by  the  application  of 
excellent  and  faithful  workmanship.  This  embankment 
retains  a storage  lake  of  sixty-six  acres  and  thirty  feet 
maximum  depth.  It  was  completed  in  1868,  and  has 
proved  a perfect  success  in  all  respects.  This  work  fills  the 
offices  of  both  an  impounding  and  distributing  reservoir,  in 
a gravitation  water  supply  to  a New  England  city. 

364.  Distribution  Reservoirs. — Distributing  reser- 
voirs are  frequently  located  over  porous  sub-soils  and 
require  puddling  over  their  entire  bottoms  and  beneath 
considerable  portions  of  their  embankments,  and  puddle 
walls  are  usually  carried  up  in  the  centres  of  their  embank- 
ments or  near  their  inner  slopes. 

The  same  general  principles  are  applicable  to  distrib- 
uting as  to  storage  reservoir  embankments. 

365.  Application  of  Fine  Sand. — Fig.  58  ( p.  333 ) illus- 
trates a case  where  the  bottom'was  puddled  with  clay,  but  a 


354 


RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 


sufficiency  of  clay  to  puddle  tlie  embankments  was  not  ob- 
tainable. The  embankment  is  here  constructed  of  gravel, 
coarse  sand,  very  fine  sand,  and  a moderate  amount  of 
loam.  The  materials  were  selected  and  mixed  so  as  to 
secure  imperviousness  to  the  greatest  possible  extent,  and 
were  put  together  in  the  most  compact  manner  possible,  and 
have  proved  successful.  This  has  demonstrated  to  the  sat- 
isfaction of  the  writer  that  very  fine  sand  may  replace  to  a 
considerable  extent  the  clay  that  is  usually  demanded,  and 
his  experience  includes  several  examples,  among  which,  on 
a single  work,  is  more  than  three-fourths  of  a mile  of  suc- 
cessful embankment  entirely  destitute  of  clay,  but  sand 
was  used  with  the  gravel,  of  all  grades,  from  microscopic 
grains  to  coarse  mortar  sand,  and  a sufficiency  of  loam  was 
used  to  give  the  required  adhesion.  The  outside  slopes 
were  heavily  soiled  and  grassed  as  soon  as  possible. 


Fig.  61. 


366.  Masonry-faced  Embankment. — When  there 
is  a necessity  for  economizing  space,  one  or  both  sides  of  an 
embankment  may  be  faced  with  masonry. 

An  example  of  such  construction  is  selected  from  the 
practice  of  a successful  engineer  in  one  of  the  Atlantic 


EMBANKMENT  SLUICES  AND  PIPES. 


355 


States,  and  is  shown  in  Fig.  61.  A method  of  introducing 
clay  puddle  into  a central  wall  in  the  embankment,  beneath 
the  embankment,  and  on  the  reservoir  bottom,  is  also  here 
shown.  The  puddle  of  the  reservoir  bottom  is  usually 
covered  with  a layer  of  sand. 

367.  Concrete  Paving. — The  lower  section  of  the 
slope  paving  of  the  distributing  reservoir,  Fig.  58,  was  built 
up  of  concrete,  composed  of  broken  stone  4 parts ; coarse 
sand  1 part ; fine  sand  1 part ; and  hydraulic  cement  1 part. 
The  cement  and  sand  were  measured  and  mixed  dry,  tlieD 
moistened,  and  then  the  stone  added  and  the  whole  thor- 
oughly worked  together.  The  concrete  was  then  deposited 
and  rammed  in  place,  building  up  from  the  base  to  the  top, 
in  sections  of  about  forty  feet  length.  A very  small  quan- 
tity of  water  sufficed  to  give  the  concrete  the  proper  con- 
sistency, and  if  more  was  added  the  concrete  inclined  to 
quake  under  the  rammer,  which  was  an  indication  of  too 
much  water. 

The  general  thickness  of  the  concrete  sheet  is  ten  inches, 
and  there  is  in  addition  four  ribs  upon  the  back  side  to  give 
it  bond  with  the  embankment,  and  to  give  it  stiffness,  and 
also  to  check  the  liability  of  the  sheet  being  lifted  or  cracked 
by  back  pressure  from  water  in  the  embankment,  when  the 
water  in  the  reservoir  may  be  suddenly  drawn  down. 

The  upper  part  of  the  slope  that  is  exposed  to  frost  is 
of  granite  blocks  laid  upon  broken  stone.  The  layer  of 
broken  stone  at  the  wave  line  is  fifteen  inches  thick,  which 
is  none  too  great  a thickness  to  prevent  the  waves  from 
sucking  out  earth  and  allowing  the  paving  to  settle. 

368.  Embankment  Sluices  and  Pipes. — Aiched 
sluices  have  been  in  many  cases  built  through  the  founda- 
tion of  the  embankment  and  the  discharge  pipes  laid  therein, 
and  then  a masonry  stop-wall  built  around  the  pipes  near 


356 


RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 


the  upper  end  of  the  sluice.  By  this  plan  the  pipes  are 
open  for  inspection  from  the  outside  of  the  embankment  up 
to  the  stop  wall.  If  the  sluice  is  not  circular  or  elliptical, 
its  lioor  should  be  counter-arched,  and  its  sides  made  strong, 
to  resist  the  great  pressure  of  the  water  that  may  saturate 
the  earth  foundation. 


Fig.  60. 


Such  a sluice  is  sometimes  built  in  a tunnel  through  the 
hillside  at  one  end  of  the  embankment.  The  latter  plan, 
when  the  upper  end  of  the  tunnel  is  through  rock,  is  the 
safer  of  the  two,  otherwise  there  is  no  place  where  it  can  be 
more  safely  founded,  constructed,  and  puddled  around, 
than  when  it  is  built  upon  the  uncovered  foundation  of  the 
embankment,  either  at  the  lowest  point  in,  or  upon,  one 
side  of  the  valley,  since  every  facility  is  then  offered  for 
thorough  work,  which  cannot  so  easily  be  attained  in  an 
earth  tunnel  obstructed  by  timber  supports. 

A circular  or  rectangular  well  rising  above  the  watej 
surface,  is  usually  built  over  the  upper  end  of  the  sluice, 
and  contains  the  valves  of  the  discharge  pipes,  and  inlet 
sluices  at  different  heights,  admitting  water  to  the  pipes 
from  different  points  below  the  surface  of  the  reservoir. 

When  the  sluice  is  used  for  a waste-sluice,  also,  the 
stop -wall  is  omitted,  and  the  sluice  well  rises  only  to  the 
weir  crest  level,  or  has  openings  at  that  level  and  an  addi- 
tional opening  at  a lower  level  controlled  by  a valve. 


GATE  CHAMBERS. 


357 


Sometimes  heavy  cast-iron  pipes,  for  both  delivery  and 
waste  purposes,  are  laid  in  the  earthwork  instead  of  in 
sluices,  in  which  case  the  puddle  should  be  rammed  around 
them  with  thoroughness.  In  this  latter  case  they  should  be 
tested,  in  place,  under  water  pressure  before  being  covered. 
A suitable  hand  force-pump  may  be  used  to  give  tl 
requisite  pressure  if  not  otherwise  obtainable.  Bell  am 
socket  pipes  with  driven  lead  joints  are  used  in  such 
cases,  and  projecting  flanges  are  cast  around  the  pipes  at 
intervals. 

The  method  of  laying  and  protecting  discharge  pipes,  as 
shown  in  Fig.  60  (p.  84),  has  been  adopted  by  the  writer  in  sev- 
eral instances  with  very  satisfactory  results.  A foundation  of 
masonry  is  built  up  from  a firm  earth  stratum  to  receive  the 
pipes,  and  then  when  the  pipes  have  been  laid  and  tested, 
they  are  covered  with  masonry  or  concrete.  In  such  case 
the  sides  of  the  masonry  are  not  faced,  and  pointed,  or  plas- 
tered, but  the  stones  are  purposely  left  projecting  and 
recessed,  and  the  covering  stones  are  of  unequal  heights, 
making  irregular  surfaces.  This  method  is  more  economi- 
cal in  construction,  and  attains  its  object  more  successfully 
than  the  faced  break-walls  sometimes  projected  from  the 
sides  of  gate-chambers  and  sluices. 

The  puddle  or  core  material  is  rammed  against  the  ma- 
sonry in  all  cases,  so  as  to  fill  all  interstices  solid.  This 
portion  of  the  work  demands  the  utmost  thoroughness  and 
faithfulness ; and  with  such,  the  structure  will  be  so  far 
reliable,  and  otherwise  may  be  uncertain. 

369.  Grate  Chambers.— When  an  impounding  reser- 
voir is  deep,  requiring  a high  embankment,  it  is  advisable 
to  place  the  effluent  chamber  upon  one  side  of  the  valley 
toward  the  end  of  the  embankment,  with  the  effluent  pipes 
for  ordinary  use  only  as  low  as  may  be  necessary  to  draw 


358 


RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 


the  lake  down  to  the  assumed  low  water  level,  as  in  Fig.  63, 
showing  the  inside  slope  of  an  embankment. 

A waste-pipe  for  drawing  off  the  lowest  water  is,  in  such 
case,  extended  from  the  front  of  the  effluent  chamber,  side- 
ways down  the  slope  and  side  of  the  valley  to  the  bed  of 
its  old  channel,  and  is  fitted  with  all  details  necessary  for  it 


Fig.  63. 


to  perform  the  office  of  a siphon  when  there  shall  be  occa- 
sion to  draw  the  reservoir  lower  than  the  level  of  the  gate 
chamber  floor.  By  such  arrangement  the  pipes  may  pass 
through  the  embankment,  or  through  a sluice  or  tunnel  in 
the  side  of  a hill  at  a level  twenty  or  twenty-five  feet  above 
the  bed  of  the  valley. 

When  a valve-chamber  is  built  up  from  the  inner  toe  of 
the  embankment,  so  that  the  water  surrounds  it  at  a higher 
level,  provision  must  be  made  for  the  ice-thrust,  lest  it  crowd 
back  toward  the  embankment  the  upper  portion  sufficiently 
to  make  a crack  in  the  wall ; and  precaution  must  also  be 
taken  to  prevent  the  ice  lifting  bodily  the  whole  top  of  the 


GATE  CHAMBERS. 


359 


chamber  when  the  water  rises  in  winter,  as  it  usually  does 
in  large  storage  reservoirs. 

The  writer  has  usually  connected  the  gate-house  with 
the  embankment  by  a solid  pier,  when  there  would  other- 
wise be  opportunity  for  the  ice  to  yield  behind  the  chamber 
by  slipping  up  the  paving,  as  it  expanded,  and  thus  en- 
danger the  gate-chamber  masonry. 

There  are  iulets  through  the  front  of  the  effluent  chamber 
shown  iu  Fig.  63,  at  different  depths,  permitting  the  water 
to  be  drawn  at  different  levels. 

These,  when  the  volume  of  water  to  be  delivered  is  small, 
may  be  pieces  of  flanged  cast-iron  pipe  built  into  the 
masonry,  with  stop-valves  bolted  thereon,  but  usually  are 
rectangular  openings  with  cast-iron  sluice  - valves  and 
frames  (Fig.  64)  secured  at  their  inside  ends.  The  seat  and 
bearing  of  the  valves  are  faced  with  a bronze  composition, 
which  is  planed  and  scraped  so  as  to  make  water-tight 
joints.  The  screw-stem  of  the  valve  is  also  of  composition, 
or  aluminum  or  manganese  bronze. 

If  such  a valve  exceeds  2-3"  x 2-9"  in  area,  or  is 
under  a pressure  of  more  than  twenty  feet  head,  some  form 
of  geared  motion  is  usually  necessary  to  enable  a single 
man  to  start  it  with  ease. 

It  is  usually  advisable  to  increase  the  number  of  valves 
rather  than  to  make  any  one  so  large  as  to  be  unwieldy  in 
the  hands  of  a single  attendant,  even  at  the  expense  of  some 
frictional  head. 

The  stem  of  the  small  valves  usually  passes  up  through 
a pedestal  resting  on  the  floor  of  the  chamber,  and  through 
a nut  in  the  centre  of  a hand- wheel  that  revolves  upon  the 
pedestal. 

The  outside  edge  of  each  valve-frame  should  be  so  formed 
that  a temporary  wood  stop-gate  might  be  easily  fitted 


360 


RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 


Fig.  64. 


against  it  by  a diver,  in  case  accident  required  the  removal 
of  the  valve  for  repairs.  The  chamber  might  then  be  readily 
emptied  and  the  valve  removed,  without  drawing  down  the 
lake. 

Upon  the  back  of  the  valve  (Fig.  64)  are  lugs  faced  with 
bronze,  and  upon  the  frame  corresponding  lugs,  both  being 
arranged  as  inclined  planes,  and  their  office  is  to  confine  the 
valve  snug  to  its  seat  when  closed. 

If  the  valve  is  secured  to  the  side  of  the  opening  opposite 
to  that  which  the  current  approaches,  or  to  the  pressure,  its 
bolts  must  enter  deep  into  or  pass 
through  the  masonry. 

A slight  flare  is  usually  given  to  the 
sluice-jambs,  from  the  sluice-frame  out- 
ward. 

.370.  Sluice-Valve  Areas. — When 
the  head  is  to  be  rigidly  economized, 
the  submerged  sluice-valve  area  must 
be  sufficient  to  pass  the  required  vol- 
ume of  water  at  a velocity  not  exceeding 
about  five  lineal  feet  per  second ; when 
the  loss  of  head  due  to  passage  of  the 
valve  will  not  exceed  about  one-half 
foot. 

If  Q is  the  maximum  volume,  in  cu. 
ft.  per  second  ; S,  the  area  of  the  sluice 
in  square  feet ; v,  the  assumed  maxi- 
mum velocity ; then 

Q = cSv,  (1) 

in  which  c is  a coefficient  of  contraction, 
that  may  be  taken,  for  a mean,  as  equal 
to  .70  for  ordinary  chamber- sluices. 


IRON  SLUICE— VALVE. 


STOP-VALVE  INDICATOR. 


361 


From  this  equation  of  Q , we  derive  that  of  area, 

Q 


s 


cv 


(2) 


Let  Q = 70  cubic  feet  per  second ; v = 5 lineal  feet 

Q 

per  second  ; then  we  have  = 20  square  feet  area,  and  we 

CD 

may  make  the  valve  opening,  say  4’  x 5'. 

If  there  are  a number  of  valves,  whose  respective  areas 
are  sh  s2,  s3 ... . sn,  then 

£ 

cv 


Sl  + #2  4*  ^3 


(3) 


or  advisedly  we  should  give  a slight  excess  to  the  sum  of 
areas  and  make  + s2  + s*  • • • • + sn>  — • 

CD 

371.  Stop- Valve  Indicator — When  a stop-valve  is 

used,  instead  of  a sluice-valve  whose  screw  rises  through 
the  hand-wheel,  it  is  usually  desir- 
able to  have  some  kind  of  an  indi-  Fig.  65. 

cator  to  show  how  nearly  the  stop- 
valve  is  to  full  open. 

Fig.  65  illustrates  such  an  indi- 
cator attached  to  the  hand -wheel 
standard,  as  manufactured  by  the 
Ludlow  Valve  Co.,  at  Troy,  1ST.  Y. 

A worm-screw  upon  the  valve-stem 
revolves  the  indicator- wheel  at  the 
side  of  the  standard,  and  indicates 
the  various  lifts  of  the  valve  between 
shut  and  full  open. 

372.  Power  Required  to  Open 
a Valve. — The  theoretical  computa- 
tion of  the  power  required  to  start  a 


362 


RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 


closed  valve,  wlien  it  is  pressed  to  its  seat  by  a head  of  watei 
upon  one  side  and  subject  only  to  atmospheric  pressure  on 
the  other  side,  is  attended  with  some  uncertainties  ; neverthe- 
less this  computation,  subject  to  such  coefficients  as  experi- 
ence suggests,  is  a valuable  aid  when  proportioning  the  parts 
of  new  designs. 

Take  the  case  of  the  metal  sluice-valve,  Fig.  64,  raised 
by  a screw,  with  its  nut  placed  between  collars  in  the  top 
of  a pedestal,  and  revolved  by  a hand-wheel,  and  let  the 
centre  of  water  pressure  upon  the  valve  be  at  a depth  of 
30  feet.  Let  the  size  of  valve-opening  be  2'-6"  x 2'-9",  the 
pitch  of  the  screw  .75  inch,  and  the  diameter  of  the  hand- 
wheel  30  inches. 

The  weight  has  to  slide  along  the  spiral  inclined  plane 
of  the  screw,  but  its  actual  advance  is  in  a vertical  line,  the 
pitch  distance,  for  each  revolution  of  the  screw. 

The  power  is  applied  to  the  hand-wheel,  which  is  equiva- 
lent to  a lever  of  length  equal  to  its  radius,  moving  through 


The  distance  d , moved  through  by  the  power  in  each 
revolution,  is  the  hypothenuse  be,  Fig.  66,  of  an  angle 
whose  base,  ab,  equals  the  circumference  of  its  circle,  and 
whose  perpendicular,  ac,  equals  the  pitch  of  the  screw  = 
^circumference2  + pitch2  = d. 

Let  w be  the  weight  in  lbs.;  p the  pitch,  in  inches  ; d the 
distance  moved  by  the  power  per  revolution,  in  inches,  and 
P,  the  power,  in  foot-ponnds.. 

According  to  a theory  of  mechanics,  the 


1 


Fig.  66. 


a horizontal  distance  equal 
to  the  circumference  of  its 
circle  (=  radius  x 6.283) 
and  a vertical  distance 
equal  to  the  pitch  of  the 
screw. 


POWER  REQUIRED  TO  OPEN  A VALVE. 


363 


Vel,  of  Power  : Vel.  of  Weight  ::  Weight  : Power;  or, 
d : p : : w : P. 


The  weight , in  this  case,  includes  the  actual  weight  of 
the  iron  valve  and  its  stem  ; its  friction  upon  its  seat  due  to 
the  pressure  of  water  upou  it ; the  friction  of  the  screw  upon 
its  nut,  and  the  friction  of  the  nut  upon  its  collar.  These 
we  compute  as  follows  : 


Weight  of  valve,  assumed 
Friction  of  valve  (15469  lbs.  pres,  x coef.  20) 
Friction  of  screw  (300  + 3094)  x coef.  20 
Friction  of  nut  (300  + 3094)  x coef.  15 
Total  equivalent  weight,  w 


= 300  lbs. 

= 3094  “ 
= 679  “ 

= _501  “ 

: 4574  “ 


Distance  of  power,  d = ) circum.2  x pitch2 fa  = 94.25  inches. 

Pitch  = .75  “ 


In  the  form  of  equation, 


p _ vyp  _ 4574  x .75 
^ 9425 


36.4  libs. 


(4) 


Theoretically,  this  power  applied  at  the  circumference 
of  the  hand- wheel  would  he  just  upou  the  point  of  inducing 
motion,  or  if  this  power  was  in  uniform  motion  around  the 
screw,  it  would  just  maintain  motion  of  the  weight.  The 
theory  here  admits  that  the  screw  and  nut  are  cut  truly  to 
them  iucline,  and  that  there  is  no  binding  between  them  due 
to  mechanical  imperfection. 

When  two  metal  faces  remain  pressed  together  an  ap- 
preciable length  of  time,  the  projections  of  each  enter  into 
the  opposite  recesses  of  the  other,  to  a certain  extent.  These 
projections  of  the  moving  weight  must  be  lifted  out  of  lock, 
and  the  inertia  of  the  weight  must  be  overcome  before  it 
can  proceed.  Metal  valves  usually  drop  against  an  inclined 
wedge  at  their  back  that  presses  them  to  their  seat,  and 
there  is  also  a fibre  lock  with  this  wedge,  or  “stick,”  as  it 


364 


RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 


is  commonly  called,  according  to  the  force  with  which  the 
valve  is  screwed  home. 

Hence,  the  power  required  to  start  a valve  is  often  double 
or  treble,  or  even  quadruple  that  that  would  theoretically 
be  required  to  maintain  it  in  motion  the  instant  after  start- 
ing. The  equation  for  starting  the  valve  in  such  case  may 
become, 

= P.  (5) 

The  computed  distance  which  the  power  moves  per  revo- 
lution (94.25  inches)  equals  7.854  feet,  and  the  computed 
power  36.4  lbs.  If  twenty  revolutions  of  the  hand- wheel  are 
made  per  minute,  then  the  power  exerted  is  theoretically 
7.854  ft.  x 20  rev.  x 36.4  lb.  = 5717.7  foot-pounds  per  minute. 
This  is  a little  more  than  one-sixth  of  a theoretical  horse- 
power. 

If,  for  the  hand-wheel,  which  revolves  the  nut,  there  is 
substituted  a spur-gear  of  equal  pitch  diameter,  and  into 
this  meshes  a pinion  of  one-third  this  diameter,  and  the 
same  hand-wheel  is  placed  upon  the  axle  of  the  pinion,  then 
the  new  power  required  will  be  reduced  proportionally,  as 
the  square  of  diameter  of  the  pinion  is  reduced  from  the 
square  of  diameter  of  the  spur,  or  in  this  case,  one-ninth. 

373.  Adjustable  Effluent  Pipe. — An  adjustable 
effluent  pipe,  capable  of  revolving  in  a vertical  plane,  and 
connected  directly  to  the  main  supply  pipe,*  is  shown  in 
Fig.  60  (p.  84). 

This  adjustable  pipe  is  constructed  of  heavy  sheet  cop- 
per, and  is  sixteen  inches  in  diameter.  Upon  its  end  is  a 


* This  ingenious  form  of  flexible  joint  was  suggested  to  the  writer  by  Hon. 
Alba  F.  Smith,  one  of  our  most  able  American  mechanical  engineers.  Mr. 
Smith  designed  this  joint  many  years  ago,  and  used  it  at  watering  stations 
upon  the  Hudson  River,  and  other  railroads  under  his  charge. 


364 


FISH  SCREENS. 


‘m 

perforated  bulb,  through  which  the  water  enters  the  pipe. 
The  movable  section  of  the  pipe  is  counter-weighted  within 
the  chamber,  so  the  bulb  can  be  set  at  any  desired  depth 
in  the  water,  or  raised  out  of  water  to  the  platform  upon  the 
chamber,  for  cleaning,  expeditiously  and  easily  by  a single 
attendant.  This  arrangement  has  operated  most  satisfac- 
torily during  the  eight  years  since  its  completion,  and  de- 
livers the  water  supply  for  about  18,000  inhabitants. 

Equivalent  devices  have  been  adopted  in  several  in- 
stances in  Europe  and  in  India,  and  they  are  especially 
applicable  to  cases  where  the  impounding  reservoirs  are 
also  the  distributing  reservoirs,  without  the  intervention  of 
filtering  basins,  and  to  cases  where  the  surface  fluctuates 
frequently,  rapidly,  or  to  a considerable  extent. 

When  a sudden  or  considerable  decrease  of  the  tem- 
perature of  the  air  chills  the  quiet  reservoir  water  surface, 
and  thus  induces  a vertical  motion  in,  or  shifting  of  position 
of  the  whole  mass  of  water,  the  bulb  may  be  made  to  fol- 
low the  most  wholesome  stratum. 

If  the  impounded  water  is  to  be  led  to  filter-beds  or  to 
one  or  more  distributing  reservoirs,  then  the  discharge- 
pipes  lead  directly  from  the  effluent  chamber. 

374.  Fish  Screens. — In  the  chamber,  Fig.  67,  is  shown 
a set  of  fish-screens,  arranged  in  panels  so  as  to  slide  out 
readily  for  cleaning.  The  finer  ones  of  the  double  set  are 
of  No.  15  copper  wire,  six  meshes  to  the  inch,  and  the 
coarser  ones  of  No.  12  copper  wire,  woven  as  closely  as 
possible. 

Figs.  67  and  68  show  a plan  of  and  a vertical  section 
through  an  influent  chamber  of  a distributing  reservoir. 

The  pipes  d d deliver  water  from  the  impounding  reser- 
voir, or  may  be  force  mains,  leading  from  pumping  engines 
to  the  chamber  A.  The  main  chamber  is  divided  in  two 


366  RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 

Fig.  67. 


parts,  for  convenience  in  management  when  there  are  sev- 
eral delivery  pipes.  There  are  sluices  k k,  controlled  hy 
valves,  through  which  the  water  may  be  admitted  to  the 
reservoir  C.  There  is  also  a weir,  i,  over  which  water  may 
be  passed,  instead  of  through  the  sluices. 


Fig.  68. 


/0  5 0 10  20  30  &0 

L-l  J -U  -LI  I 1 ! 1 ! J i I ! 1 

SECTION  THROUGH  INFLUENT  CHAMBER. 


Grooves  are  prepared  in  each  section  of  the  main  cliam 
ber  for  a double  set  of  screens.  ss. 


GATE-CHAMBER  FOUNDATIONS. 


367 


B is  a waste  chamber,  and  e a waste  pipe,  and  w a waste 
overflow  weir. 

A frost  curtain,  m,  is  placed  in  front  of  the  inflow  weir, 
to  prevent  the  water  surface  in  the  chamber  from  freezing, 
if  the  pumps  are  not  in  operation  during  winter  nights. 

There  are  drain  pipes,  p,  leading  from  the  sections  of 
the  main  chamber  to  the  waste  well. 

In  the  dividing  partition  is  a sluice,  with  valve  so  that 
the  whole  chamber  may  be  connected  as  occasion  requires. 

A distributing  reservoir  effluent  chamber  might  be  simi- 
lar to  the  above,  omitting  the  waste  chamber,  weirs,  and 
frost  curtain  ; the  direction  of  the  current  would  in  this  case 
be  reversed,  of  course. 

In  the  effluent  chamber  of  the  reservoir  shown  in  Fig.  58, 
a check- valve  is  placed  in  the  effluent  pipe,  so  that  when 
the  pumps  are  forcing  water  into  the  distribution  pipes 
around  the  reservoir,  with  direct  pressure,  the  water  will 
not  return  into  the  reservoir  by  the  supply  main. 

375.  Grate- Chamber  Foundations. — Gate-chambers 
built  into  the  inner  slope  of  an  earthwork  embankment  will 
introduce  an  element  of  weakness  at  that  point,  unless 
intelligent  care  is  exercised  to  prevent  it. 

Any  after  settlement  along  the  sides  of  the  foundation 
or  walls  of  the  chamber  separates  the  earth  from  the 
masonry,  leaving  a void  or  loose  materials  along  the  side 
of  the  masonry,  which  permits  the  water  of  the  reservoir  to 
percolate  along  the  side  to  the  back  of  the  chamber,  under 
the  full  head  pressure. 

The  stratum  of  earth  on  which  the  foundation  rests 
should  be  not  only  impervious,  but  so  firm,  or  made  so 
firm,  that  no  settlement  of  the  foundation  can  take  place. 
If  the  chamber  is  high  and  heavy,  the  footing  courses 
should  be  extended  on  each  side  so  as  to  distribute  the 


368 


RESERVOIR  EMBANKMENTS  AND  CHAMBERS. 


weight  on  an  area  of  earth  larger  than  the  section  of  the 
chamber. 

The  foundation  of  the  chamber  is  to  be  water-tight,  and 
capable  of  resisting  successfully  the  upward  pressure  upon 
its  bottom  due  to  the  head  of  water  in  the  reservoir,  when 
the  chamber  is  empty. 

376.  Foundation  Concrete. — The  use  of  deton,  or 
hydraulic  concrete,  is  often  advisable  for  the  bed-course  of 
a valve-chamber  foundation,  to  aid  in  distributing  the 
weight  of  the  structure  and  in  securing  a water-tight  floor. 
The  composition  of  the  concrete  is  to  be  proportioned  for 
these  especial  objects.  Concrete  for  a revetment,  demands 
weight  as  a special  element ; for  a lintel,  tensile  strength ; 
for  an  arch,  compressile  strength ; but  for  the  submerged 
foundation  of  a gate-chamber,  imperviousness , which  will 
ensure  sufficient  strength. 

The  volume  of  cement  should  equal  one  and  one-third 
times  the  volume  of  voids  in  the  sand.  The  volume  of  mor- 
tar should  equal  one  and  one-third  times  the  volume  of 
voids  in  the  coarse  gravel  or  broken  stone.  The  cement 
and  sand  should  be  first  thoroughly  mixed,  then  tempered 
with  the  proper  quantity  of  water  equally  worked  in,  and 
then  the  mortar  should  be  thoroughly  mixed  with  the 
coarse  gravel  or  broken  stone,  which  should  be  clean,  and 
evenly  moistened  or  sprinkled  before  the  mortar  is  intro- 
duced. None  of  the  inferior  cement  so  often  appearing  in 
the  market  should  be  admitted  in  this  class  of  work.  Good 
hydraulic  lime  may  in  some  cases  be  substituted  for  a 
small  portion  of  the  cement,  say  one-third. 

The  concrete  should  be  rammed  in  place,  but  never  by 
a process  that  will  disturb  or  move  concrete  previously 
rammed  and  partially  set.  A very  moderate  amount  of 
water  in  the  concrete  suffices  when  it  is  to  be  rammed. 


CHAMBER  WALLS. 


369 


317.  Chamber  Walls.  — Fine -cut  beds  and  builds, 
hammered  end  joints,  and  coursed  work,  in  chamber  ma- 
sonry, make  expensive  structures,  but  even  such  work  is 
hardly  made  water-tight  by  a poor  or  careless  mechanic. 
A great  deal  of  skill  and  care  must  be  brought  into  requi- 
sition to  make  a rubble  wall  water-tight. 

Imperviousness  is  here,  again,  a special  object  sought. 
That  a wall  may  be  impervious,  its  mortar  must  be  imper- 
vious ; its  voids  must  be  compactly  tilled,  every  one ; its 
stones  must  be  cleaned  of  dust,  moistened,  laid  with  close 
joints,  and  well  bedded  and  bonded ; and  no  stone  must 
be  shaken  or  disturbed  in  the  least  after  the  mortar  has 
begun  to  set  around  it. 

Stone  must  not  be  broken  or  hammered  upon  the  laid 
wall,  or  other  stones  will  be  loosened.  Stones  should  be  so 
lewised  or  swung  that  the  bed  or  joint  mortar  shall  not  be 
disturbed  when  the  stone  is  floated  into  place. 

The  plan  occasionally  adopted  of  grouting  several  courses 
at  the  same  time  with  thin  liquid  grout,  might  answer  in  a 
cellar  wall  when  the  object  was  to  prevent  rats  from  peram- 
bulating through  its  centre,  but  it  is  unreliable  in  a cham- 
ber or  tank-wall  intended  to  resist  percolation  under  pres- 
sure. Skillful  workmanship,  in  hydraulic  masonry,  is 
cheaper  than  expensive  stock. 

24 


CHAPTER  XYIL 


OPEN  CANALS. 

378.  Canal  Banks. — The  stored  waters  of  an  impound- 
ing reservoir  are  sometimes  conveyed  in  an  open  canal 
toward  the  distributing  reservoir,  or  the  city  where  they  are 
to  be  consumed,  or  for  the  purposes  of  irrigation.  The 
theory  of  flow  in  such  cases  has  been  already  discussed 
(Chap.  XV). 

The  subsoils  over  which  the  canal  leads  require  careful 
examination,  and  if  they  are  at  any  point  so  open  and 
porous  as  to  conduct  away  water  from  the  bed  of  the  canal, 
the  bed  and  sides  must  be  lined  with  a layer  of  puddle 
protected  from  frost,  as  in  Fig.  69,  showing  a section  of  a 
puddled  channel  in  a side-hill  cut. 


Fig.  69. 


The  retaining  channel  bank  on  the  down-hill  side  is  con- 
structed upon  the  same  principles  as  a reservoir  embank- 
ment (§  351),  the  chief  objects  being  to  secure  solidity, 
imperviousness,  and  permanence. 


INCLINATIONS  AND  VELOCITIES. 


371 


A longitudinal  drain  along  the  upper  slope  of  side-liill 
sections  will  prevent  the  washing  of  soil  into  the  canal. 
The  water  slopes  will  require  revetments  or  paving  from 
three  feet  below  low-water  to  two  feet  above  high-water 
line,  and  paving  or  rubbling  down  the  entire  slope  at  them 
concave  curves. 

Substantial  revetments  or  pavings  of  sound  stone  are  the 
most  economical  in  the  end. 

Eevetments,  built  up  of  bundles  of  fascines  laid  with 
ends  to  the  water  and  each  layer  in  height  falling  back 
with  the  slope  line,  have  been  used  to  some  extent  on  the 
banks  of  canals  of  transport,  and  on  dykes.* 

If  the  slopes  are  rip-rapped,  or  pitched  with  loose  stone, 
the  slopes  must  be  sufficiently  flat,  so  the  waves  and  the 
frost  will  not  work  the  stones  down  into  the  water,  and  de- 
mand constant  repairs. 

The  retaining  canal  banks  of  the  head  races  of  water- 


perviousness,  prevent  vermin  from  burrowing  through  the 
bank,  and  lasts  a long  time  in  compact  earth. 

379.  Inclinations  and  Velocities  in  Practice. — 
The  unrevetted  trapezoidal  canals  in  earthwork,  for  water- 

* Vide  illustration  of  Foss  Dyke  in  Stevenson’s  Canal  and  Kiver  Engineer- 
ing, p.  18,  Edinburgh,  1872 ; and  Mississippi  River  Dyke  at  Sawyer’s  Bend. 
Report  Chief  of  U.  S.  Engineers,  June  30,  1873. 


SHEET-PILED  CHANNEL  BANK. 


Fig.  70. 


powers  have  sometimes 
a longitudinal  row  of 
jointed-edged  sheet-piles 
through  their  centre.  The 
selected  mixed  earth  is 
compactly  settled  on  both 
sides  of  this  piling,  as 
shown  in  Fig.  70.  Such 
piling  tends  to  insure  im- 


372 


OPEN  CANALS. 


supplies,  irrigation,  and  for  hydraulic  power,  except  in 
water -powers  of  great  magnitude,  have  sectional  areas, 
respectively,  between  500  and  50  square  feet  limits,  and 
hydraulic  mean  radii  between  7 and  2.5. 

In  such  canals  the  surface  velocities  range  between 
5 feet  and  2 feet  per  second,  and  the  inclinations  of  surface 
between  .75  feet  (=  .000104)  and  3.5  feet  (=  .000663)  per 
mile. 

Practice  indicates  that  the  favorite  surface  velocity  of 
flow,  in  such  straight  canals,  is  about  2.5  feet  per  second, 
in  canals  of  about  five  feet  depth,  being  less  in  shallower 
canals,  and  increased  to  3.5  feet  per  second  in  canals  of 
nine  feet  depth. 

Only  very  firm  earths,  if  unprotected  by  paving  or  nib- 
ble, will  bear  greater  velocities  without  such  considerable 
erosions  as  to  demand  frequent  repairs. 

Burnell  states*  that  the  inclinations  given  to  the  re- 
cently constructed  irrigation  canals  in  Piedmont  and  Lom- 
bardy, varies  from  (=  .000625)  to  (=  .000278) ; 
but  that  inclinations  frequently  given  to  main  conductors 
in  the  mountainous  districts  of  the  Alps,  Tyrol,  Savoy, 
Daupliine  and  Pyrenees,  is  (=  .002). 

In  the  numerous  shallow  irrigation  canals  in  Spain, 
Italy,  and  northen  India,  a mean  velocity  approximating 
three  feet  per  second  is  necessary  to  prevent  a luxuriant 
growth  of  weeds  on  the  bottoms  and  side  slopes  of  canals 
in  earth.  This  often  necessitates  paving  at  the  curves. 
Mean  velocities  as  great  as  twelve  feet  per  second  are 
usually  the  maximums  allowable  in  brick  or  mortared 
rubble  lined  canals. 


* Rudiments  of  Hydraulic  Engineering,  p.  127.  London,  1858. 


CANAL  GATES. 


373 


381.  Table  of  Data  of  Lined  Canals. — Tlie  di- 
mensions and  coefficients  of  a few  well-known  canals  are 
given  in  Table  No.  79,  as  illustrative  of  the  general  practice 
in  various  parts  of  the  world,  relating  especially  to  water- 
supply  and  irrigation. 

TABLE  No.  79. 

Coefficients  of  Flow  of  Lined  Channels  (at  medium 
velocities). 


Locality  and  Lining. 

Surf. 

Width. 

Depth 

of 

Water. 

r 

z\  in  ft. 
per  1000 
ft. 

V 

feet 
per  sec. 

m 

c 

Montpelier  Aq  , concrete 

I . oo 

6.500 

0.250 

0.300 

0.716 

.00942 

89.44 

Mill  Race,  sandstone  masonry.. 

i .08 

.308 

1.400 

1.378 

.0146044 

66. 10 

Gouten,  dry  rubble 

6.oo 

.500 

.320 

42.350 

9.446 

•0099379 

80  50 

5-9° 

Mill  Race,  dry  rubble 

.700 

•345 

3- 100 

1.250 

•0555596 

38.20 

Test  Channel,  neat  cement 

2.87 

• 590 

.365 

1.500 

3.020 

.003877 

128.90 

“ “ cement  mortar . . . 

2.92 

.610 

•379 

1.500 

2.870 

.005622 

120.50 

Chazilly,  smooth  ashlar  

4.04 

.500 

.410 

8 . 100 

5-73° 

.006395 

100.70 

Tail  Race,  dry  rubble 

.690 

.419 

2.500 

1.643 

.0198225 

50.80 

Aqueduct,  dry  rubble 

.810 

.486 

4.500 

2.432 

.0238166 

52.00 

Mill  Race 

2.02 

1. 310 

•576 

3. 100 

1.932 

.0308357 

45.70 

Pont  Pyla  Aq.,  cement  mortar. 

1.83 

1.833 

.611 

1.660 

2.950 

.007510 

92.63 

Grobois  Canal,  hammered  stone 

10.30 

1 .200 

.860 

14.600 

4.190 

.0457956 

37.50 

It  “ “ “ 

3-9 

1 .600 

.880 

12 . 100 

7-580 

.01 19209 

73-50 

Metz  Aq.,  cement  mortar 

3-x7 

2. 167 

.915 

1 .000 

2.783 

.007610 

92.00 

Mill  Race,  cement  mortar 

2.040 

•977 

.500 

2.523 

.006222 

114 . 10 

Dhuys  Aq.,  cement  mortar.  .. 

.984 

. 100 

1.148 

.004818 

115-30 

Roquencourt  Aq.,  cement  mor- 

tar  

3-92 

2-583 

1.115 

.300 

1.661 

.007800 

90.86 

Pont  du  Gard,  cement  mortar.. 

4.00 

3-333 

1.250 

.400 

2.000 

.008050 

89.44 

Cochituate  Aq.,  bricks  

5.00 

6-333 

1. 417 

•050 

1 .000 

.004570 

TI4- 53 

Vanne  Aq.,  circular,  concrete  . 

5-63 

5-ooo 

1 .482 

. ICO 

1.436 

.004629 

117.92 

Roquefavour  Aq. .smooth  bricks 

7.40 

2.500 

1 504 

3.720 

10.260 

.003423 

188 . 14 

Grobois  Canal,  smooth  ashlar.. 

6.50 

3- 120 

1 .60 

•347 

2.470 

.005861 

104.83 

Aq  de  Crau,  smooth  ashlar  . . . 

8.50 

3. coo 

1-774 

.840 

5-550 

.003116 

143.76 

Washington  Aq.,  circular,  brick 

9.00 

3 463 

1.874 

.150 

1.893 

. 005050 

112.93 

Sudbury  Conduit,  brick 

3.768 

2. nr 

.158 

2.805 

.002720 

153.60 

Croton  old  Aq.,  brick  

7-4I7 

6.083 

2-345 

.210 

2.218 

.006445 

100.04 

Sudbury  conduit,  brick 

9.000 

5.300 

2-459 

.200 

3.029 

.003450 

136.63 

Brooklyn  Aq.,  brick 

10.00 

5.000 

2.524 

. 100 

1.588 

.006450 

99.92 

Lock  Katrine  Aq,,  brick 

8.00 

6.850 

2.525 

.158 

1-7*3 

.008760 

84.76 

Croton  New  Aq.,  brick  ... 

9.200 

4.006 

•133 

3-°99 

.003566 

I34- r4 

Solani  Aq.,  brick  floor,  masonry 

sides  -. 

85.00 

5.600 

5.000 

.240 

3-430 

.006569 

99.00 

Turlock,  rock-cut.  ...  

5.900 

1 .500 

7.500 

.0101333 

79.72 

382.  Canal  Gates. — Fig.  71  is  a half  elevation  of  the 
gates  in  the  Manchester,  N.  H.,  water- works  canal. 

The  water  rises  and  falls  with  the  lake.  The  canal  is 
sixteen  hundred  feet  long,  and  has  similar  gates  at  its 


374 


OPEN  CANALS. 


entrance  and  at  the  head  of  the  turbine  penstock.  The 
-entrance  gates  are  provided  with  a set  of  iron  racks  to  inter* 
cept  floating  matters  that  might  approach  from  the  lake, 
and  the  penstock  gates  are  provided  with  a set  of  fine  mesh 
copper-wire  fish-screens. 

There  are  four  gates  in  each  set,  each  3 feet  wide  and 
5 feet  high.  On  the  top  of  each  gate  is  secured  a cast-iron 


Fig.  71. 


tube  containing  a nut  at  its  top.  Over  each  tube  is  fastened, 
to  a lintel,  a composition  screw,  working  in  its  nut,  which 
raises  or  lowers  its  gate. 

Two  gates  in  each  set  have  their  screws  provided  with 
gears  and  pinions.  The  pinions,  or  screws,  are  turned  bj  a 
ratchet  wrench,  so  the  operator  may  turn  them  either  w ay, 
to  raise  or  lower  the  gate,  by  walking  around  the  screw , or 
by  a forward  and  backward  motion  of  the  arms. 

The  floor  covering  the  gate-chamber  is  of  tar-concrete 
resting  upon  brick  arches. 


MINERS’  CANALS. 


875 


When  large  sluices  are  necessary,  a system  of  worm 
gearing  is  usually  applied  for  hoisting  and  lowering  the 
gates.  These  gears  may  be  operated  by  hand-power,  or 
may  be  driven  by  the  belts  or  gears  upon  a counter-shaft, 
which  is  driven  by  a turbine  or  an  engine. 

Canals  leading  from  ponds  subject  to  floods  or  sudden 
rise  above  normal  level,  are  to  be  provided  with  waste- weirs 
near  their  head  gates,  and  with  waste-gates,  so  their  banks 
will  not  be  overtopped  or  their  waters  rise  above  the  pre- 
determined height. 

' Stop-gates  are  placed  at  intervals  in  long  water-supply 
and  irrigation  canals,  with  waste-gates  immediately  above 
them  for  drawiug  off  their  waters,  to  permit  repairs,  or  for 
flushing,  if  the  waters  deposit  sediment. 

Culverts  are  sometimes  required  to  pass  the  drainage  of 
the  upper  adjoining  lands  beneath  the  canal,  and  these  may 
be  classed  among  the  treacherous  details  that  require  ex* 
ceeding  care  in  their  construction  to  guard  against  settle- 
ments, and  leakage  of  the  canal  about  them. 

383.  Miners’  Canals. — The  sharp  necessities  of  the 
gold-mining  regions  of  California  and  Nevada  have  led  to 
some  of  the  most  brilliant  hydraulic  achievements  of  the 
present  generation.  The  miners  intercept  the  torrents  of 
the  Sierras  where  occasion  demands,  and  contour  them  in 
open  canals,  along  the  rugged  slopes,  hang  them  in  flumes 
along  the  steep  rock  faces,  syphon  them  across  deep  can- 
yons, and  tunnel  them  through  great  ridges,  in  bold  defi- 
ance of  natural  obstacles,  though  constant  always  to  laws 
of  gravity  and  equilibrium. 

The  force  of  water  is  an  indispensable  auxiliary  in  sur- 
face mining,  and  capital  hesitates  not  at  thirty,  fifty,  or  a 
hundred  miles  distance,  or  almost  impassable  routes,  when 
the  torrent’s  power  can  be  brought  into  requisition.  A 


376 


OPEN  CANALS. 


hundred  ditches , as  the  miners  term  them,  now  skirt,  the 
mountains,  where  hut  a few  years  ago  there  was  no  evi- 
dence that  the  civilization  or  energy  of  man  had  ever  been 
present. 

The  Big  Canyon  Ditch,  near  North  Bloomfield,  Nevada, 
for  instance,  is  forty  miles  long  and  delivers  54,000,000 
gallons  of  water  per  day.  The  sectional  area  of  the  stream 
is  about  33  square  feet,  and  the  inclination  16  feet  to  the 
mile.  Its  flumes  are  6 feet  wide  with  grade  of  one-half 
inch  in  twelve  feet,  or  about  18  feet  to  the  mile.  The  con- 
tour line  of  the  canal  is  from  200  to  270  feet  above  the 
diggings,  to  which  its  waters  are  led  down  in  wrought- 
iron  pipes. 

With  a terrible  power,  fascinating  to  observe,  its  jets 
dasli  into  the  high  banks  of  gravel,  rapidly  under-cutting 
their  bases,  and  razing  them  in  huge  slides  that  flow  down 
the  sluice-boxes  with  the  stream. 

Thus,  in  a single  mine,  30.000  cubic  yards  of  gravel  melt 
away  in  a single  day,  under  the  mighty  hydraulic  influence 
that  has  been  gathered  in  the  torrent  and  canaled  along  the 
eternal  hills. 

The  Eureka  Ditch,  in  El  Dorado  County,  is  forty  miles 
long,  and  there  are  many  others  of  great  length,  whose 
magnitude  and  mechanical  effect  entitle  them  to  considera- 
tion, as  valuable  hydraulic  works,  and  monuments  of 
hardy  enterprise. 

The  Eureka  embankment  is  seventy  feet  in  height,  flows 
two  hundred  and  ninety-six  acres,  and  is  located  six  thou- 
sand five  hundred  and  sixty  feet  above  the  lev&l  of  the  sea. 
We  quote  from  Mr.  P.  J.  Flynn,  C.  E.,  some  data  relating 
to  Irrigation  Canals,  as  follows : 


IRRIGATION  CANALS, 


376a 


TAB  L E No.  79  a. 


Dimensions  of  Irrigation  Canals. 


Name  and  Locality. 


AMERICAN  CANALS. 

Eagle  Rock  & Willow  Creek,  Idaho.. 

Calloway,  Cal 

Fort  Morgan,  Col 

Seventy-six,  Cal 

San  Joaquin  & King’s  River 

Idaho  Canal  Co.’s  Idaho 

North  Poudre,  Col 

Grand  River,  Col 

Phyllis,  Idaho 

Empire,  Col 

Citizens,  Col 

Del  Norte,  Col 

Central  District,  Cal 

High  Line,  Col 

Arizona,  Ari 

Larimer,  Col 

Merced,  Cal 

Turlock,  Cal 

Idaho  Min.  & Ir.  Co.,  Ida 

NOTED  FOREIGN  CANALS. 

Main  Delta,  Egypt 

Agra,  India 

Upper  Ganges,  India 

Cavour,  Italy 


Length  in  Miles. 

Bottom  Width, 
in  Feet. 

Depth,  in  Feet. 

Slope. 

Discharge  in  cu. 
ft.  per  sec. 

1 

5° 

3° 

3 

i in  880 

3 2 

80 

3-5 

1 “ 6600 

700 

28 

3° 

3-5 

1 “ 33°° 

340 

100 

4 

1 “ 352° 

.... 

39 

55 

4 

1 “ 5280 

.... 

43 

40 

4 

1 “ 352i 

.... 

3° 

20 

4 

1 “ 2640 

45° 

35 

5 

1 “ 2880 

54 

1 2 

5 

1 “ 2640 

250 

32 

60 

5-5 

1400 

45 

40 

5-5 

r “ 1760 

1000 

5° 

65 

5-5 

1 “ 660 

2400 

60 

60 

6 

1 “ 10000 

720 

70 

40 

7 

1 “ 3000 

1 184 

4i 

36 

7-5 

1 “ 2640 

1000 

45 

3° 

7-5 

720 

8 

70 

IO 

1 “ 5280 

3400 

80 

20 

IO 

1 “ 666 

1500 

75 

45 

IO 

1 “ 2640 

2585 

174 

10 

1 “ 12000 

3943 

137 

70 

10 

1 “ 10560 

I IOO 

456 

170 

10 

1 “ 4224 

6000 

53 

I3 1 

I I 

1 “ 2000 

325° 

Fig.  140. 


r 


CHAPTER  XVIII. 

WASTE-WEIRS. 

384.  The  Office  ancl  Influence  of  a Waste-Weir. 

— An  ample  waste-weir  is  the  safety-valve  of  a reservoir 
embankment. 

The  outside  slope  of  an  earth  embankment  is  its  weakest 
part,  and  if  a flood  overtops  the  embankment  and  reaches 
the  outer  slope,  it  will  be  cut  away  like  a bank  of  snow 
before  a jet  of  steam. 

The  overfall  should  be  maintained  always  open  and 
ready  for  use,  independent  of  all  waste  sluices  that  are 
closed  by  valves  to  be  opened  mechanically,  for  a furious 
storm  may  rage  at  midnight,  or  a waterspout  burst  in  the 
valley  when  the  gate-keeper  is  asleep. 

Data  relating  to  the  maximum  flood  flow  is  to  be  dili- 
gently sought  for  in  the  valley,  and  the  freshet  marks 
along  the  watercourse  to  be  studied.  The  overfall  is  to  be 
proportioned,  in  both  dimensions  and  strength,  for  the 
extraordinary  freshets,  which  double  the  volume  of  ordi- 
nary floods,  and  if  there  are  existing  or  there  is  a proba- 
bility of  other  reservoirs  being  built  in  the  valley  above,  it 
may  be  wise  to  anticipate  the  event  of  their  bursting,  espe- 
cially if  an  existing  reservoir  dam  is  of  doubtful  stability. 

A short  overfall  may  increase  or  affect  the  damage  by 
flood  flowage  to  an  important  extent,  and  makes  necessary 
the  building  of  the  embankment  to  a considerable  height 
above  its  crest  level ; while,  on  the  other  hand,  a long  over- 
fall,  if  exposed  to  the  direct  action  of  the  wind,  may  permit 


378 


WASTE- WEIRS. 


too  great  a volume  of  water  to  be  rolled  over  its  crest  in 
waves  just  at  the  commencement  of  a drought,  when  it  is 
important  to  save,  to  the  uttermost  gallon.  Such  wave 
action,  under  strong  winds,  might  draw  down  a small  reser- 
voir several  inches,  or  even  a foot  below  its  crest,  unless 
such  contingency  is  anticipated  and  guarded  against. 
Strong  winds  blowing  down  a lake  often  heap  up  its  waters 
materially  at  the  outlet,  and  increase  the  volume  of  waste 
flowing  over  its  weir  or  outfall. 

An  injudicious  use  of  flash-boards  upon  waste- weirs  has 
in  many  instances  led  to  disastrous  results.  In  all  cases,  a 
maximum  flood  height  of  water  should  be  determined  upon, 
and  then  the  weir  dimensions  be  so  proportioned  that  no 
contingency  possible  to  provide  for  shall  raise  the  water 
above  the  predetermined  height.  The  length  of  the  overfall 
and  volume  of  maximum  flood-flow  govern  the  distance 
the  highest  crest-level  must  be  placed  below  the  maximum 
flood-level.  Flash-boards  may  in  certain  cases,  and  in  cer- 
tain seasons,  be  serviceable  in  governing  the  level  of  water 
below  or  just  at  the  crest  line , especially  when  there  are  low 
lands,  or  lands  awash , as  they  are  termed,  bordering  upon 
the  reservoir,  with  their  surfaces  not  exceeding  three  feet 
above  the  crest  line. 

Several  English  writers  mention  that  a general  rale  for 
length  of  waste-weir,  accepted  in  English  practice,  is  to 
make  the  waste- weir  three  feet  long  for  every  100  acres  of 
watershed.  This  rule  will  apply  for  watersheds  not  exceed- 
ing three  square  miles  area,  but  for  larger  areas  gives  an 
inconvenient  length. 

385.  Discharges  over  Waste- Weirs. — Having  de- 
termined, or  assumed  from  the  best  data  available,  the 
maximum  flood-flow  which  the  overfall  may  have  to  dis- 
charge, if  a very  heavy  storm  takes  place  when  the  reservoir 


DISCHARGES  OVER  WASTE-WEIRS. 


379 


is  full,  the  overfall  is  then  to  be  proportioned  upon  the 
basis  of  this  flow. 

For  the  calculation  of  discharge,  the  overfall  may  be 
considered  to  be  a species  of  measuring- weir  (§  303),  and 
subject  to  certain  weir  formulas. 

If  there  are  flash-boards,  with  square  edges,  forming  the 
crest,  then,  for  depths  of  from  nine  inches  to  three  feet,  Mr. 
Francis’  formula  may  be  applied  with  approximate  results, 
aud  we  have  the  discharge  : 


Q = 3.33  (l  - 0.1  nil)  H*,  (1) 

in  which  Q is  the  volume  of  discharge,  in  cubic  feet  per 
second ; II,  the  depth  of  water  upon  the  crest,  measured  to 
the  lake  surface  level ; l,  the  clear  length  of  overfall ; and 
n the  number  of  end  contractions.  (Vide  § 313,  p.  289.) 

We  have  seen  (§  309)  that  the  velocities  of  the  parti- 
cles flowing  over  the  crest  are  proportionate  to  the  ordinates 
of  a parabola,  and  that  the  mean  velocity  is  equal  to  two- 
thirds  the  velocity  of  the  lowest  particles  ; hence  we  have 
the  mean  velocity,  v,  of  flow  over  the  crest, 


® — | V 2gH  — 5.35  V H.  (2) 

Multiplying  the  depth  of  water  II  upon  the  weir,  into 
the  length  l of  the  weir,  and  into  the  mean  velocity  »,  we 
have  the  volume  of  discharge,  when  there  are  no  interme- 
diate flash-board  posts : 


Q = mill  x |V2f///=  5.35mlH*,  (3) 

in  which  m is  a coefficient  of  contraction  (§  312),  with 
mean  value  about  .622  for  sharp-edged  thin  crests. 

By  transposition,  we  have  : 


II- 


Q 


(4) 


\ml  V2  g 

If  the  overfall  has  a wide  crest  similar  to  that  usually 
given  to  masonry  dams,  Fig.  47,  then  we  may  apply  more 


380  WASTE-WEIRS. 

accurately  the  formula  suggested  by  Mr.  Francis  for  such 
cases,  viz. : 

Q = 3.012W'®.  (5) 

If  we  desire  to  know  the  depth  of  discharge  for  a given 
volume  and  weir  length,  then,  by  a transposition  of  this 
last  formula,  we  have : 


Table  80  gives  values,  C (=  fra  \/2 g)  and  volumes,  q , 
for  sharp  weirs  of  the  Francis  type,  Hat  weirs  of  about 
six  feet  width  on  top,  standard  stone  crests  of  dams,  Fig. 
47,  and  broad  rounded  masonry  crests,  as  deduced  from 
experiments  by  Francis,  Fteley  and  Stearns,  Bazin  and 
Rafter. 


TABLE  No.  80. 

Waste-Weir  Volumes,  per  Linear  Foot  of  Weir. 

(Q  = C?H§.) 


Depth 
on  Weir. 

Sharp. 

Flat  Top. 

Standard. 

Rounded. 

H. 

C. 

Q- 

c. 

Q- 

c. 

Q- 

c. 

Q- 

0.5 

1.0 

feet 

3-346 

3-328 

1.1830 

3.3280 

2.525 

2.527 

0.8928 

2.5270 

3.007 

3.031 

M 

b b 

LO  Qs 
* LO 

O W 

3.328 

3.3280 

i-5 

3-317 

6.0937 

2.529 

4.6461 

3-054 

5-6105 

3.406 

6.2572 

2.0 

3.310 

9.3621 

2.535 

7-1701 

3-073 

8.6917 

3.45S 

9. 7S06 

2.5 

3.306 

13.0861 

2.547 

10.0679 

3.091 

12.2181 

3-493 

13.8071 

3-0 

3.306 

17-1785 

2.563 

13.3177 

3. 108 

16. 149S 

3.520 

18.2906 

3-5 

3.308 

2 1 . 6604 

2.583 

16.9132 

3.124 

20.4556 

3-540 

23.1796 

4.0 

3-3II 

26.4880 

2.607 

20.8560 

3.140 

25. 1200 

3-557 

28.4560 

4-5 

3.3I5 

31.6448 

2.632 

25.1250 

3-156 

30. 1269 

3-572 

34.0980 

5.0 

3.321 

37.1299 

2.660 

29-7397 

3.170 

35-4416 

3-  5S4 

40.0702 

5-5 

3-327 

42.9138 

2.687 

34.6586 

3. 182 

41.0433 

3-594 

46.3576 

6.o 

3-332 

48.9702 

2.713 

39.8728 

3-194 

46.9419 

3.600 

52.9088 

6.5 

3.338 

55.3167 

2.736 

45.3405 

3.204 

53.0960 

3.606 

59-7579 

7.0 

3-343 

61.9132 

2.759 

51.0975 

3.211 

59.46S7 

3.611 

66.  S76S 

7-5 

3-349 

68.7871 

2.  780 

57.  IOOI 

3.216 

66.0554 

3.610 

74. 14S0 

8.o 

3-355 

75.9150 

2.801 

63.3793 

3.224 

72.9507 

3.609 

81.6623 

REQUIRED  LENGTH  OF  WASTE - WEIRS. 


381 


386.  Required  Length  of  Waste-Weirs. — The  fol- 
lowing table,  prepared  to  facilitate  preliminary  calculations, 
gives  estimated  flood  volumes  of  waste  from  small  impound- 
ing reservoirs,  in  ordinary  Atlantic  slope  basins,  for  water- 
sheds of  given  areas  ; also  the  length  of  waste- weir  required, 
and  approximate  depth  of  water  on  the  crest  of  the  given 
length  : 

TABLE  No.  8 1. 

Lengths  and  Discharges  of  Waste-Weirs  and  Dams. 


Area  of 
Watersheds. 

Required  length 
of  overfall  for 
given  watershed. 

Approx,  depth  of 
water  on  overfall 
of  given  length. 

Approx,  disch’ge 
per  lin,ft,of  given 
overfall  for  given 
depth. 

Flood  volume 
from  whole  area. 

Q = 200  (M)£. 

Square  Miles . 

Feet. 

Feet. 

Cubic  Feet. 

Cu.  ft.  per  second. 

I 

23.01 

2.0 

8.692 

200.00 

2 

28.49 

2.5 

12.214 

348.22 

3 

39-43 

2.5 

12.214 

481.64 

4 

37-55 

3-o 

16.144 

606.29 

6 

51-94 

3.0 

16.144 

838.52 

8 

65-39 

3-0 

16.144 

1,055.61 

10 

61.73 

3-5 

20.442 

1,261.92 

15 

85.38 

3-5 

20.442 

L745-43 

20 

87-55 

4.0 

25.096 

2,197.  12 

25 

104. 66 

4-0 

25.096 

2,626.53 

30 

I2I.OQ 

4.0 

25.096 

3,038.97 

40 

127.18 

4-5 

30.079 

3,825.41 

50 

129.23 

5-0 

35-386 

4,573-05 

75 

154-35 

5-5 

40.979 

6,325.20 

100 

169.83 

6.0 

46.883 

7,962. 14 

200 

261.25 

6.5 

53-063 

13,862.9 

300 

332.03 

7.0 

59-543 

19,174.6 

400 

364.04 

7-5 

66.302 

24,136.7 

500 

393-57 

8.0 

73-3I3 

28,854.0 

600 

417.31 

8.5 

80.00 

33,384-9 

800 

481.40 

9.0 

87.30 

42,024.4 

1000 

491.08 

10.0 

102.3 

50,237.7 

1500 

679-25 

10.0 

102.3 

69,486.9 

2000 

855-02 

10.0 

102.3 

87,469. 

3000 

1182.64 

10. 0 

102.3 

120,984. 

4000 

1488.68 

10.0 

102.3 

152,292. 

5000 

I779-63 

10.0 

102.3 

182,056. 

381  a 


LENGTH  OF  WASTE- WEIRS. 


The  length,  L,  of  an  overfall  of  a dam  is,  for  a given 
depth,  H,  thereon,  proportioned  to  the  total  flood,  or 
approximately  to  the  modified  area,  in  square  miles, 
(M)%  hence  when  c is  the  coefficient  in  the  flood  formula, 
and  C is  the  coefficient  in  the  depth  formula  (Table  80), 


L = 
H = 


c.M* 

(6a) 

e.ib 

rc.M*  if 

L C.L  J 

m 

also  when  an  existing  dam  of  length,  L,  with  maximum 
depth  of  overflow,  H,  has  proved  safe  and  is  considered  a 
basis  for  the  length,  Z,  of  a new  dam  up  or  down  stream 
on  the  same  or  a similar  watershed,  then  if  M is  the 
symbol  of  square  miles  of  the  first  and  m of  the  second 
watershed, 


7 _ H*  Lra* 

1 ~ wm 


(6c) 


or  when  watershed  characteristics  differ  and  the  flood 
coefficient  is  c (Table  81a), 


H*L(c.m*) 

Zd(c.M^) 


(6«h 


An  extreme  coefficient  in  the  formula  Q = cMy  would  b< 
for  the  outlet  of  a square  mile  of  paved  city  area,  dis 
charging  the  equivalent  of  the  total  of  0.5  inch  of  rain  in 
an  hour,  when  c would  equal  32*2.67. 

Table  Sla  shows  coefficients  ranging  above  200  for 
mountainous  watersheds  and  ranging  less  than  200  for 
undulating  watersheds  having  more  or  less  storage  areas, 
and  ranging  less  than  50  on  large  prairie  areas  of  the 
Middle  West. 


FLOOD  COEFFICIENTS. 


3816 


TABLE  No.  81a 
Data  of  Flood  Flows  of  Streams. 
Q = c (M)« 


Streams. 

Sq.  miles  oi 
Watershed. 

M. 

Cu.  feet  per 
second  per 
square  mile. 
Q-M. 

Flood  Vol. 
in  cubic  feet 
per  second. 

S- 

Coefficient 

c 

Chemung,  at  Elmira,  N.Y 

2,055 

67.10 

137,890 

297.14 

Potomac,  at  Chain  Bridge,  Md.. 

‘xi,i6i 

42.49 

474,231 

274.05 

Croton,  at  Croton  Dam,  N.  Y.. . . 

339 

74.87 

25,380 

240.08 

Raritan,  at  Bound  Brook,  N.  J. . . 

879 

59.16 

52,002 

229.  52 

Delaware,  at  Stockton,  N.  } 

6,790 

37.50 

254,630 

218.98 

Stony  Brook,  at  Roxbury,  Mass.. 

13 

121.00 

L573 

202.  II 

Ramapo,  at  Pompton,  N.  J 

159 

66.10 

9,745 

182.29 

Shetucket,  at  Norwich,  Conn.... 

1,200 

41.29 

49,548 

170.48 

Pawtuxet,  R.  I 

I90 

56.85 

10,801 

162.36 

Nashua,  South  Branch 

122. 

56.21 

6,858 

146.92 

Tohicon,  Point  Pleasant,  Pa 

102 

54-30 

5,539 

136.94 

Merrimac,  at  Manchester 

2,838 

26.36 

74,800 

I29.27 

“ Lowell 

4,085 

21.42 

87,480 

112.97 

“ Lawrence 

4,599 

20.87 

96,000 

112.74 

Genesee,  at  Mount  Morris.. 

1,060 

32.00 

33,941 

128.97 

Neshaminy,  PaT.  . ., 

139 

41.40 

5,755 

1 1 1. 08 

Connecticut,  at  Holyoke 

8,006 

I7.I5 

137,295 

103.50 

Sudburv,  at  Framingham 

75 

43.00 

3,234 

102.26 

Perkiomen,  at  Frederick,  Pa 

152 

34-9° 

5,305 

95.32 

Rockawav,  at  Dover 

52 

43-10 

2,241 

94-99 

Desplaines,  at  Chicago 

630 

21.40 

13,482 

77.68 

St.  Louis,  at  Fond  du  Lac,  Minn. 

3,ro6 

5-47 

16,990 

27.32 

Mississippi,  at  Minneapolis. ..... 

19,736 

3-04 

59,997 

21.97 

Missouri,  at  Great  Falls,  Mont.  . . 

22,000 

2-35 

51,700 

17.36 

The  Potomac  and  Delaware  watersheds  have  large  percentages  of  nioun 
tainous  areas.  The  Merrimac  has  some  mountain  watershed,  but  large 
lake  storage. 

The  Sudbury  has  about  six  per  cent,  of  its  watershed  of  reservoir  area. 
The  St.  Louis  river  watershed  has  much  swamp  area. 

The  Mississippi  river  has  large  storage  of  its  head  waters. 


382 


WASTE- WEIRS. 


A phenomenally  heavy  storm  moves  usually  along  a 
narrow  belt  and  affects  only  a part  of  the  large  watershed 
which  it  crosses,  but  may  have  great  flood  effect  on  a 
branch  stream. 

Large  streams  having  upper  watershed  surfaces  hilly 
and  steep  have  usually  broad  bottom  lands  along  their 
mid  and  lower  lengths  where  the  floods  are  spread  out. 
The  effect  of  this  unit  flow  on  small  and  large  watersheds 
is  illustrated  in  column  3 of  Table  9,  page  67.  The  max- 
imum flood  and  depth  on  the  overfall  varies  with  the 
periodic  rainfall,  the  inclination  and  porosity  of  the  soil, 
the  sum  of  swamp  or  reservoir  surfaces  on  the  watershed 
and,  in  northern  climates,  with  varying  spring  temper- 
atures and  meltings  of  ice  and  snow. 

387.  Forms  of  Waste-Weirs. — Fig.  72  illustrates  a 
waste-weir  placed  in  the  centre  of  length  of  an  earthwork 
embankment,  retaining  a storage  lake  of  twenty-four  hun 
dred  acres,  and  the  drainage  of  forty  square  miles  of  water- 
shed. 

Fig.  72. 


The  down-stream  face  of  the  weir  is  constructed  in  a 
series  of  steps  of  decreasing  height  and  increasing  projec- 
tion, from  the  crest  downward,  so  that  the  edges  of  the  steps 
nearly  touch  an  inverted  parabolic  curve. 


ISOLATED  WEIRS. 


383 


The  apron  receiving  the  fall  of  waste  .water  from  the 
crest  of  the  weir  is  of  rubble  masonry,  and  contains  two 
upright  courses  intended  to  check  any  scorn’  from  the 
undertoe”  during  freshets,  and  also  to  lock  the  founda- 
tion courses  that  receive  the  heaviest  shocks  of  the  falling 
water. 

The  projection  of  the  steps  was  arranged  to  break  up 
die  force  of  the  falling  water  as  much  as  possible. 

The  fall  from  crest  to  apron  is  twenty-five  feet,  and  the 
flood  depth  upon  the  weir  twenty  inches  ; yet  the  force  of 
the  falling  water  is  so  thoroughly  destroyed  that  it  has  not 
been  sufficient  to  remove,  in  three  years  service,  the  coarser 
stones  of  some  gravel  carted  upon  the  apron  during  con- 
struction of  the  upper  courses  of  the  weir. 

There  is  a 3 by  5 feet  waste-sluice  through  the  weir  at 
one  end,  discharging  upon  the  apron.  In  front  of  the  sluice 
the  apron  consists  of  two  eighteen-inch  courses  of  jointed 
granite  upon  a rubble  foundation,  doweled  and  clamped 
together  in  a thorough  manner. 

A carriage-bridge  spans  the  weir,  and  rests  upon  the 
wing  walls  and  three  intermediate  piers  built  upon  the  weir. 

388.  Isolated  Weirs. — Where  the  topography  of  the 
valley  admits  of  the  waste-weir  being  separated  from  the 
embankment,  it  should  be  so  placed  at  a distance,  and  it 
is  often  conveniently  made  to  discharge  into  a side  valley 
where  the  flowage  nearly,  or  quite,  reaches  a depression  in 
the  dividing  ridge. 

But  it  is  not  always  admissible  to  so  divert  the  water,  as 
riparian  rights  may  be  affected,  or  flood  damages  be  created 
on  the  side  stream. 

When  possible,  it  is  advisable  to  locate  the  waste-weii 
upon  a ledge  at  one  end  of  the  embankment,  so  that  the 
fall  from  the  crest  will  not  exceed  three  or  four  feet. 


384 


WASTE -WEIRS. 


There  should  be  a fall  of  at  least  three  feet  from  the  crest, 
as  in  such  case  a less  length  of  weir  will  be  required  than  if 
it  slopes  gently  away  as  a channel. 


Fig.  73 


389.  Timber  Weirs. — In  those  localities  where  sound 
and  durable  building-stones  are  scarce,  and  timber  is  plenty 
and  cheap,  the  waste-weir  may  be  substantially  constructed 
of  timber  in  crib  form.  Fig.  73  represents  such  a weir 
placed  upon  a gravel  foundation.  The  fall  is  twenty  feet, 
and  the  face  of  the  weir  is  divided  into  three  benches  so  as 
to  neutralize  the  force  of  the  fall  that  in  freshets,  if  vertical, 
would  tend  to  excavate  a hole  in  the  gravel  in  front  of  the 
dam  at  least  two-thirds  as  deep  below  the  lower  water  sur- 
face as  the  height  of  the  fall. 

The  timbers  are  faced  upon  two  sides  to  twelve  inches 
thickness  and  entirely  divested  of  bark.  The  bed-sills  are 


TIMBER  WEIRS 


385 


Bunk  in  trenches  in  the  firm  earth,  and  two  rows  of  jointed 
sheet-piling  are  sunk,  as  shown,  to  a depth  that  will  prevent 
the  possibility  of  water  working  under  them.  Upon  the 
bed-sills  longitudinal  timbers  are  laid  five  feet  apart,  then 
cross  timbers  as  shown,  and  so  alternately  to  the  top.  As 
each  tier  is  put  upon  another  it  is  thorougldy  fastened  to 
the  lower  tier  by  trenails  or  f-inch  round  iron  bolts.  The 
bolts  should  pass  entirely  through  two  timbers  depth  and 
one-half  the  depth  of  the  next  tier,  requiring  for  twelve-inch 
timbers  30-incli  bolts. 

As  each  tier  is  laid  it  should  be  filled  with  stone  ballast 
and  sufficient  coarse  and  fine  gravel  puddled  in  to  make  the 
work  solid,  leaving  no  interstices  by  the  side  of  or  under 
timbers.  The  gravel  should  be  rammed  under  the  timbers 
so  as  to  give  them  all  a solid  bearing. 

A tier  of  plank  is  placed  under  each  bench  capping,  and 
a tier  of  close-laid  timbers  is  placed  under  the  crest  capping. 
The  bench  and  crest  cappings  are  of  timbers  jointed  upon 
their  sides  and  laid  close.  The  upper  and  lower  faces  are 
planked  tight  with  jointed  plank. 

A weir  thus  solidly  and  tightly  constructed  will  prove 
nearly  as  durable  as  the  best  masonry  structures.  The 
capping  and  face  plankings  will  be  the  only  parts  requiring 
renewal,  and  these  only  at  intervals  of  a number  of  years 
if  they  are  at  first  of  proper  thickness. 

Similar  forms  of  crib-work  have  been  used  with  com- 
plete success  on  rock  bottoms,  on  impetuous  mountain 
streams,  where  they  were  subject  to  the  shocks  of  ice  at  the 
breaking  up  of  winter,  and  to  great  runs  of  logs  in  the 
spring.  In  such  cases  the  bed-sills  are  bolted  to  the  rocks. 

Similar  crib  foundations  may  be  used  to  carry  masonry 
weirs  upon  gravel  bottoms,  but  the  crib-work  should  in 
such  case  be  placed  so  low  as  to  be  always  submerged. 

25 


386 


WASTE-WEIRS. 


Fig.  73  was  designed  for  a case  where  the  watershed  is 
of  about  one  hundred  square  miles  area.  Its  crest-length  is 
two  hundred  feet,  and  six  feet  is  the  estimated  maximum 
flood-depth  upon  its  crest. 

390.  Ice-tlirust  upon  Storage  Reservoir  Weirs.— 

Those  weirs  that  are  located  in  Northern  climates  upon 
storage  ponds,  such  as  are  drawn  down  in  summer  and  do 
not  rise  to  the  crest-level  until  past  mid-winter,  should  be 
backed  with  gravel  to  the  level  of  the  backs  of  their  caps, 
and  the  gravel  should  be  substantially  paved,  as  in  Fig.  72. 
Otherwise  the  expansion  of  the  thick  ice  against  the  verti- 
cal backs  of  the  weirs  may  act  with  such  powerful  thrust  as 
to  displace  or  seriously  injure  its  upper  portion. 

391.  Breadth  of  Weir-Caps. — The  cap-stones  of  weirs 
in  running  streams  should  incline  downward  toward  the 
pond  side  at  least  two  inches  for  each  foot  of  breadth,  so 
that  the  floating  ice  and  logs  will  not  strike  against  their 
back  ends  when  the  water  is  flowing  rapidly. 

There  is  a lack  of  uniformity,  in  practice,  in  breadths  of 
tops  of  waste-weirs,  and  the  unsatisfactory  working  of  the 
quarry  from  which  the  caps  are  supplied  often  controls 
this  dimension  so  far  as  to  reduce  it  to  an  unsubstantial 
measure. 

The  breadth  of  cap  required  depends  somewhat  on  the 
pond  behind  the  weir.  If  the  pond  is  relatively  broad  and 
deep,  water  and  whatever  floating  debris  it  carries,  will 
approach  the  weir  with  a relatively  low  velocity.  If  the 
pond  is  small  and  the  stream  torrential,  with  liability  of 
great  depth  upon  the  weir,  then  the  cap-stones  must  have 
length  and  weight  to  resist  the  force  of  the  current  and  im- 
pact of  the  floating  bodies.  Overfalls  upon  logging  streams 
rising  in  the  lumber  regions,  require  particularly  heavy 
caps,  and  the  force  of  the  logs  or  ice  upon  the  caps  will 


TRIAL  SECTIONS  FOR  WEIRS  AND  DAMS. 


a 


THICKNESS  OF  WASTE-WEIRS  AND  DAMS. 


387 


usually  be  greater  when  the  depth  upon  the  weir  is  from 
one  and  one-half  to  two  feet,  than  when  deeper. 

392.  Thickness  of  Waste-Weirs  and  Dams. — Low 
masonry  over  fall  weirs,  founded  on  hard  rock,  have  usually 
a batter  of  about  two  inches  per  foot  on  the  down-stream 
face  and  then  such  batter  on  the  up-stream  face  as,  with 
the  assumed  top  breadth,  is  necessary  to  fulfil  the  ele- 
ments of  stability  for  the  given  case. 

Weirs,  exceeding  ten  feet  in  height  to  thirty  feet  in 
height,  are  often  stepped  on  the  down-stream  front,  as  in 
the  dam  illustrated  in  the  plate  facing  page  391. 

High  weirs  are  usually  curved  on  the  face,  so  as  to  lead 
the  overflowing  water  to  the  river  bed  below  without  im- 
pact. Only  the  hardest  bed  rock  can  resist  the  cutting- 
force  of  a large  volume  of  water  falling  free  from  more 
than  ten  or  twelve  feet  height,  and  if  timber  aprons  are 
used  to  protect  sand  rocks,  they  are  rapidly  cut  away  by 
floating  ice  or  logs  falling  vertically  more  than  ten  feet 
from  a weir  overfall. 

The  theory  of  water  pressures  applied  to  weirs  and 
dams,  and  the  theory  of  the  stabilities  of  the  masonries  of 
weirs,  dams,  partitions,  and  retaining  walls  are  treated  in 
the  next  chaper.  {Vide  §396  to  §407,  pp.  391  to  404,  et  seq.) 

An  advisable  method  of  finding  the  best  section  of  a 
high  weir,  for  which  no  equivalent  precedent  is  known,  is 
to  sketch  an  approximate  trial  section  and  test  it  by  the 
moments  of  water  pressure  and  weight  resistance  of 
masonry  and  for  stability  on  its  base,  and  then  correct  the 
section  until  the  best  outline  is  developed  to  meet  all  the 
conditions  of  the  given  case. 

High  weirs  are  usually  vertical  on  the  up-stream  face, 
from  the  crest  down  to  the  depth  at  which  the  safe  limit  of 
pressure  ou  the  masonry  from  its  own  weight,  near  its  face, 


387a 


WASTE-WEIRS. 


is  reached,  approximately  130  ft.  depth  from  crest  in 
granite,  100  ft.  in  strong  stratified  rock,  and  70  ft.  in 
hard  burned  bricks,  and  below  these  levels  should  Jiave 
batters,  of  one  in  one-fifth  the  above  respective  heights, 
say  1 in  26,  1 in  20,  and  1 in  14,  respectively. 

The  minimum  thickness  at  the  crest  is  usually  governed 
by  the  forces  of  the  moving  ice,  logs,  or  debris,  that  may 
impact  against  or  pass  over  the  weir  with  the  current. 

Assuming  that  the  upper  side  of  the  dam  is  vertical  and 
the  crest  thickness  constant,  then  thicknesses  at  given 
depths  may  be  found  for  plotting  a trial  section  by  the  fol- 
lowing equations  : 


Let  b be  the  assumed  breadth  at  crest  and  t the  thick- 
ness at  any  given  depth,  d , below  the  crest  level,  then 

For  total  depth  not  exceeding  ) d1'5 

50  ft.  and  top  breadth  = 8 ft.  ' * + 10 


For  total  depth  not  exceeding  j du45 

70  ft.  and  top  breadth  = 10  ft.  i * 10 


(7  a) 


For  total  depth  not  exceeding  | duil 

110  ft.  and  top  breadth  = 12  ft.  i J + 10 

For  total  depth  not  exceeding  ) ^ ^ du™ 

160  ft.  and  top  breadth  = 15  ft.  f + 10 


For  total  depth  not  exceeding ) _ dU3SS  ^ , 

220  ft.  and  top  breadth  = 16  ft.  ^ 10 

The  values  of  equations  7,  7a,  7b,  7c,  and  7 d are  shown 
in  the  following  table  : 


PROFILES  OF  WEIRS  AND  DAMS. 


3875 


TABLE  No.  82. 

Data  for  Thicknesses  and  Profiles  of  Masonry  Dams. 


d = height 
from  top 
of  Dam. 

When 
d=  4'  to  50' 
b = 8' 

t = b+- 

10 

When 

d — 50'  to  70' 
b = 10' 

d1'*  5 

t = b + - 

10 

When 

d = 70'  to  11c/ 
b = 12' 

*1.*! 

t = b + 

10 

When 

d =■  11  o'  to  160' 
b = 15' 

*1.37. 

i = b + 

10 

When 

d = i6o/  to  2207 
b — 16' 

d 1,355 

t=6+- 

10 

d 

t 

t 

t 

t 

t 

0 

8.000 

10.000 

12.000 

15.OOO 

16.000 

4 

8.800 

10. 746 

12.706 

15-674 

16.655 

6 

9.470 

11.344 

13-251 

16.175 

17-133 

8 

10.263 

12.039 

13-876 

16.748 

17.674 

10 

11.162 

12.818 

14-570 

17-377 

18.265 

12 

12.167 

13.671 

15-324 

18.054 

18.899 

15 

13.810 

15-074 

16.553 

19.152 

I9-923 

20 

16.944 

17.700 

18.830 

21. 169 

21.793 

25 

20.  500 

20.641 

21.356 

23.199 

23.838 

3° 

24.430 

23.862 

24.099 

25-777 

26.034 

35 

28.706 

27-334 

27.036 

28.324 

28.365 

40 

33-298 

31-037 

30.151 

31.011 

30.818 

45 

38.187 

34-955 

33-430 

33-828 

33-382 

50 

43-355 

39-°74 

36.862 

36.766 

36.048 

55 

43-383 

40.432 

39.816 

38.813 

6o 

47.871 

44.151 

42.972 

41.668  , 

65 

52-533 

47.992 

46.229 

44.608 

70 

57.358 

51-956 

49.582 

47-63I 

75 

56.039 

53.026 

50.730 

80 

60.234 

56.557 

53-904 

85 

64-538 

60.173 

57-H9 

go 

68.948 

63.869 

60.464 

95 

73.460 

67.630 

63.842 

IOO 

78.069 

71.492 

67.286 

no 

87.225 

79-793 

73-225 

120 

88.209 

80.837 

130 

97-133 

88.406 

140 

106.359 

96.388 

150 

115.872 

104.797 

160 

125.658 

113-043 

170 

121.687 

180 

130.527 

i go 

I39-558 

200 

148.770 

210 

158.157 

220 

167.742 

388 


WASTE-WEIRS. 


The  weir  profiles  based  on  equations  7 to  Id , and  on 
Table  No.  82,  are  illustrated  in  Fig.  1 of  the  accompanying 
plate  of  “Trial  Sections  for  Weirs.” 

The  plate  illustrates  how  readily  the  face  curve  may  be 
modified  to  meet  any  given  conditions  by  a slight  change 
in  the  exponent  of  d in  the  equation. 

Fig.  1,  in  the  plate,  illustrates  conditions  of  stability 
when  the  maximum  depth  of  water  flowing  over  the  crest 
is  nine  feet. 

If  similar  equations  are  used  for  reservoir  retaining 
walls  then  the  crest  will  be  six  to  twelve  feet  above  water 
surface,  and  the  relatively  increased  weights  of  masonry 
will  permit  reductions  in  the  exponent  of  d in  the  equation. 

392 n.  Crest  Curves  of  Overfall  Weirs. — The  crest 
of  the  weir  should  have  a reverse  curve  of  such  nature  that 
the  overflowing  water  will  not  lose  contact  with  the 
masonry  at  any  point,  and  this  curve  may  be  slightly  more 
full  than  the  parabolic  curve  which  the  film  of  water  at 
two-thirds  depth  on  the  crest  tends  to  take.  The  ordinates 
and  abscissae  of  this  parabola  are  found  by  the  equations — 


V.  = V2g  (f h) 

(8) 

and 

H=  .5gt\ 

(9) 

in  which  V.  equals  velocity  of  film,  in  feet  per  second  : li 
equals  depth  a c,  Fig.  2.  from  surface  of  water  to  crest ; 
H equals  depth  b e,  Fig.  2,  below  two-thirds  depth  on 
crest,  and  t equals  time  in  seconds  required  for  a particle 
of  the  jet  to  fall  the  height  II. 

392 b.  Foot  Curves  of  Overfall  Weirs. — The  foot 
of  the  face  curve,  after  the  correction  and  adaptation  to 
the  movements  of  the  various  strains  and  reactions,  should, 
by  a supplementary  curve  of  approximately  one  hundred 


HEIGHTS  OF  WAVES. 


389 


feet  radius,  be  changed  so  that  when  it  reaches  the  river 
bed,  the  bed  will  be  tangent  to  the  face  curve,  as  shown  by 
the  supplementary  line  in  Fig.  1. 

393.  Force  of  the  Overflowing-  Water. — When 
the  face  curve  has  been  resolved  into  an  ogee  or  into  steps, 
as  is  advisable  for  high  overfall  weirs  resting  on  tertiary 
rocks,  then  the  masonry  of  the  lower  curve  and  the  caps 
of  the  steps  must  be  very  heavy  and  substantially  placed 
to  withstand  for  a long  term  of  years  the  shocks  of  the  ice, 
logs,  and  debris  passing  swiftly  down  over  them,  and  the 
masonry  must  be  especially  firm  where  the  lower  supple- 
mentary curve  leaves  the  regular  face  curve. 

The  face  stones  should  be  set  on  edge  radially  as  re- 
spects the  curves,  and  at  the  foot  should  be  countersunk 
flush  into  the  bed  rock. 

The  desired  object  is,  to  pass  the  water  from  the  ele- 
vated pond,  above  the  weir,  to  the  lower  level  below  the 
weir  with  the  least  possible  erosion  of  the  curved  face  of 
the  weir  and  river  bed,  and  with  the  least  possible  shock 
upon  the  river  bed. 

394.  Heights  of  Waves. — Stevenson  gives,  in  his 
treatise  on  Harbors,  the  following  formula  for  computing 
the  height  of  waves  coming  from  a given  exposure,  or 
“ fetch  ” of  clear  deep  water : 

H = 1.5  VJ)  + (2.5  - J/D),  (10) 

in  which  H is  the  height  of  waves  in  feet,  and  D is  the  length 
of  exposure  or  fetch  in  miles. 

The  numerical  values  of  height  of  wmve,  according  to 
this  formula,  for  given  exposures,  are  as  follows  : 


TABLE  No.  83. 

Heights  of  Reservoir  and  Lake  Waves. 


Exposure,  in  miles ' .25 

.50  ! .75 

1 1-5  2 *3  5 

IO. 

Height  of  wave,  in  feet. . I2. 543 

2.756  2.868 

3 3-031  3-332  3-782)4.437 

5-466 

CHAPTER  XIX. 

PARTITIONS,  AND  RETAINING  WALLS. 

395.  Design. — The  hydraulic  engineer  finds  necessary 
exercise  for  his  skill  on  every  hand  to  adapt  a variety  of 
constructions  in  masonry  to  their  several  ends,  in  methods 
at  once  substantial  and  economical. 

Designs  are  required  for  reservoir’  partitions  and  gate 
chambers  that  are  to  sustain  pressures  of  water  upon  both 
sides,  and  either  side  alone ; revetments  for  reservoirs, 
canals,  and  lake  and  river  fronts  that  are  to  sustain  pres- 
sures of  water  and  earth  upon  opposite  sides,  and  earth 
alone  upon  one  side;  coal-shed  walls  that  are  to  sustain 
tire  pressure  of  coal,  whose  horizontal  thrust  nearly  equals 
that  of  a liquid  of  equal  specific  gravity  ; conduit  and  filter 
gallery  walls,  that  are  to  sustain  pressures  of  earth  and 
water  and  thrusts  of  loaded  arches ; basement  walls  and 
bridge  abutments  that  are  to  sustain  thrusts  of  earth  and 
carry  weight ; wing  walls  of  triangular  elevations  and  vary- 
ing heights,  that  are  to  sustain  varying  thrusts  ; and  waste- 
weirs,  that  are  to  sustain  pressures  of  water  higher  than 
their  summits  and  moving  with  velocity. 

Rule  of  thumb  practice  in  such  structures  has  led  to 
many  failures,  when  the  amounts  and  directions  of  thrusts 
were  not  understood  ; and  such  failures  have,  on  the  other 
hand,  led  to  the  piling  up  of  superfluous  quantities  of 
masonry,  often  in  those  parts  of  section  where  it  did  not 
increase  the  stability  of  position,  but  did  endanger  the 
stability  of  the  foundations. 


dam  ON  NATCHAUG  RIVER,  WILLIMANTIC,  CONN.  To  fogo j>.  301, 

CThc  arrow  gives  position  of  the  resultant  when  there  is  six  feet  depth  of  flood  op  the  overfall,) 


THEORY  OF  WATER  PRESSURE. 


391 


Good  design  only,  unites  economy  with,  stability  in 
masonry  subjected  to  lateral  thrusts. 

396.  Theory  of  Water  Pressure  upon  a Vertical 
Surface. — The  theory  of  pressure  of  water  upon  a plane 
surface,  and  of  the  stability  of  a vertical  rectangular  retain- 
ing wall,  is  quite  simple,  and  is  easily  exemplified  by 
graphic  illustration,  and  by  simple  algebraic  equations. 

Let  BD,  Fig.  74,  be  a vertical  plane,  receiving  the 
pressure  of  water. 

The  pressure,  y>,  at  any  depth  is  proportional  to  that 
depth  into  the  density  of  the  fluid. 

Let  wx  be  the  weight  of  one  cubic  foot  of  water  = 
62.5  lbs. ; then  the  pressure  upon  any  square  foot  of  the 
vertical  plane,  whose  depth  of  centre  of  gravity  is  represent- 
ed by  d,  is  p — dwx. 

Let  the  depth  of  the  water  B,D  be  12  feet  = h.  Plot  in 
horizontal  lines  from  BZD , at  several  given  depths,  the 
magnitudes  of  the  pressures  at  those  depths  =dwx,  as  at  ssx ; 
then  the  extremities  of  those  lines  will  lie  in  a straight  line 
pa  ssing  through  B2,  and  cutting  the  horizontal  line  CDJ\  in 
/,  I)f  being  equal  to  the  magnitude  of  the  pressure  at  I). 

The  total  pressure  upon  the  plane  B2B,  and  its  horizon- 
tal effects  at  all  depths  are  graphically  represented  by  the 
area  and  ordinates  of  the  figure  B >f  D. 

In  theoretical  statics,  the  effect  of  a pressure  upon  a 
solid  body  is  treated  as  a force  acting  through  the  centre  of 
gravity  of  the  body. 

Consider  the  pressure  of  BzfD  to  be  gathered  into  its 
resultant , passing  through  its  centre  of  gravity,*  g.  The 


* To  find  tlie  centre  of  gravity  of  a triangle  draw  a broken  line  from 

D,  bisecting  the  opposite  side  in  s, , and  from/,  bisecting  the  opposite  side  in 
s : the  centre  of  gravity  will  then  lie  in  the  intersection  of  those  lines.  Or 
draw  a line  from  any  angle  B.,,  bisecting  the  opposite  side,  and  the  centre  of 


392  PARTITIONS,  AND  RETAINING  WALLS. 

Fig.  74 


horizontal  resultant  through  g will  meet  B2D  in  i\T,  at  two- 
tliirds  the  depth  BZD. 

Let  BOB  be  a section  of  wall  one  foot  long.  Let  B:I) 


gravity  will  lie  in  this  line,  at  one-third  the  height  from  the  side  bisected. 
The  centre  of  gravity  is  at  two-thirds  the  vertical  depth  B2D  = ih  from  Bs. 


WATER  PRESSURE  UPON  AN  INCLINED  SURFACE.  393 


<=  h = 12  ft.  The  centre  of  gravity  of  the  submerged  wall 

surface  B,D  is  at  one-half  its  height,  = • The  total 

& 

pressure  of  water  P upon  the  wall-surface  B2I>  equals  the 
product  of  the  surface  area,  B2D  = Au  into  the  weight  of 
one  cubic  foot  of  water,  wu  into  one-half  the  height,  = 

„ . 7i  TO 

P=  Am-j  = vh~2  (1) 

= (12  x 1)  x 62.5  x ~ 

£ 

= 4500  pounds  = 2.25  tons. 

Draw  this  total  pressure  to  scale,  in  the  resultant  gN, 
meeting  B ,D  in  N. 

The  force  tending  to  push  the  wall  along  horizontally 
is  yN,  assumed  to  act  at  either  N or  x. 

If  the  wall  is  a weir  and  water  is  overflowing,  then  let 
the  depth  of  overflow  be  7q.  The  value  of  P,  will  then  be 


P = 


(h  + 

w>— 2— 


wl 


(la) 


397.  Water  Pressure  upon  an  Inclined  Surface. 

— Tlie  maximum  resultant  of  pressure  of  water  upon  the 
inclined  plane  JO  has  a direction  perpendicular  to  the 
plane,  and  meets  the  plane  in  Pl5  at  two-thirds  the  vertical 
depth  of  the  water. 

The  entire  weight  of  the  triangular  body  of  water  CiJ  is 
supported  by  the  masonry  surface  JO.  Its  vertical  pressure 
resultant  upon  JO  passes  through  its  centre  of  gravity  in  g_. 
and  meets  JO  in  P2,  at  two-thirds  the  vertical  depth  iC  or 
JO.  Its  horizontal  pressure  resultant  also  meets  JO  in  Px. 

Let  x1  be  the  symbol  of  its  horizontal  resultant. 

“ e “ “ “ vertical  “ 

“ y “ “ “ maximum  “ 


394 


PARTITIONS,  AND  RETAINING  WALLS. 


The  horizontal  effect  of  the  pressure,  xx,  may  he  com- 
puted as  acting  upon  the  plane  of  its  vertical  projection  or 
trace,  iC,  and  will  equal, 

Xx  = ~ = ^--wx,  (2) 

= 2.25  tons,  when  7z  = 12  ft. 


Draw  xx  — 2.25  tons  to  scale  in  xxPx . Let  fall  a perpen- 
dicular upon  JC , meeting  it  in  Px ; then  will  the  angle 
yP xxx  equal  the  angle  JCi  — 0,  and  yPjwill  equal  * 


y — x,-  sec 


• sec  angle  xxPxy 


= 2.704  tons ; 


(3) 


and  ePx  will  equal 

e — xX‘  tan  0 = j wx  j-  • tan  angle  xxPxy  (4) 
= 1.5  tons. 


The  horizontal  force  tends  to  displace  the  wall  horizon- 
tally. The  vertical  downward  force  tends  to  hold  the  wall 
in  place,  by  friction  due  to  its  equivalent  weight. 

If  water  penetrates  under  the  base  of  the  wall,  it  will 
there  exert  an  upward  pressure  upon  the  base,  opposed  to 
the  downward  pressure  upon  JC,  and  to  the  weight  of  the 
wall,  with  maximum  theoretical  effect  equal  to  area  CD 
into  depth  of  its  centre  of  gravity  into  the  weight  of  one 
cubical  foot  of  water. 

Let  zx  be  the  symbol  of  the  maximum  upward  pressure, 
and  let  cx  be  the  ratio  of  the  effective  upward  pressure  in 
any  case  to  the  maximum. 

Draw  cxzx  in  the  vertical  line  through  the  centre  of  gravity 
of  the  masonry,  in  Gzx. 

When  computing  the  resultant  weight  of  the  masonry, 


* Vide  trigonometrical  diagram  and  table  in  tlie  Appendix. 


FRICTIONAL  STABILITY  OF  MASONRY. 


395 


opposed  to  the  horizontal  water  pressure,  deduct  from  the 
weight  of  wall  the  excess  of  upward,  cxz,  over  downward 
pressure,  e,  = cxzY—  e. 

398.  Frictional  Stability  of  Masonry.— The  weight , 
W,  in  pounds,  of  the  wall  (of  one  foot  length)  equals  its 
sectional  area  DCB  = A,  in  square  feet,  into  the  weight*  of 
one  cubical  foot  w of  its  material : W = Aw.  (5) 

The  downward  resultant  of  weight  is 

Wr  — (Aw)  + e — (C{Z\).  (6) 

The  upward  pressure  of  the  water  upon  the  base  will  rare- 
ly exceed  50  per  cent,  of  the  theoretical  maximum,  even 
though  the  wall  is  founded  upon  a coarse  porous  gravel,  or 
upon  rip-rap,  without  a like  upward  relief  of  backfilling. 

The  frictional  stability , S,  of  the  wall,  equals  its  result- 
ant weight  into  its  coefficient,  c,  of  friction, 

S = l W + e — (CiZi)\  x c.  (7) 

Foundations  of  masonry  upon  earth  are  usually  placed 
in  a trench,  by  which  means  the  frictional  stability  upon 
the  foundation  is  aided  by  the  resistance  of  the  earth  side 
of  the  trench,  and  the  coefficient  thus  made  at  least  equal  to 
unity.  In  such  case  the  measure  of  resistance  to  horizontal 
displacement  is  the  friction  of  some  horizontal  or  inclined 
joint. 

The  value  of  the  adhesion  of  the  mortar  in  bed-joints  is 
usually  neglected  in  computations  of  horizontal  stability, 
and  sufficient  frictional  stability  should  in  all  cases  be  given 
by  weight,  so  that  the  resistance  of  the  mortar  may  be 
neglected  in  the  theoretical  investigation. 

If,  however,  the  mortar  is  worthless,  or  its  adhesion  is 


* Submerged  umnortared  masonry  and  porous  back-filling  are  reduced  in 
effective  weight  an  amount  equal  to  the  weight  of  the  water  actually  displaced. 


396 


PARTITIONS  AND  RETAINING  WALLS 


destroyed  "by  frost  or  careless  workmanship,  or  otherwise, 
then  the  mortar  "becomes  equivalent  to  a layer  of  sand  as  a 
lubricant,  and  the  coefficient  of  friction  may  thus  be  reduced 
very  low. 

399.  Coefficients  of  Masonry  Friction.  —The  fol- 
lowing table  of  coefficients  of  masonry  frictions  will  be  found 
useful.*  They  are  selected  from  several  authorities,  and 
have  been  generally  accepted  as  mean  values. 

TABLE  No.  84. 

Coefficients  of  Masonry  Frictions  (Dry). 


• 

0~F. 

Angle 

OF 

Repose, 

Point  dressed  granite 

(medium) 

on  dry  clay 

• 5i 

O / 

27.0 

((  ii  ii 

it 

“ moist  clay 

•33 

18.15 

ii  ii  it 

“ gravel . 

.58 

30 

a a a 

it 

“ like  granite 

.70 

35 

u a a 

“ 

“ common  brickwork 

■63 

32.2 

a a a 

“ 

“ smooth  concrete 

.62 

31.4S 

Fine  cut  granite 

“ like  granite 

•58 

30 

Very  fine  cut  granite 

ii  ii  it 

“ “ “ 

.61 

30.30 

“ pressed  Beton  Coignet. . . 

.61 

30.30 

Dressed  hard  limestone  (medium) 

“ like  limestone 

•38 

20.48 

“ “ “ 

“ 

“ brickwork 

.60 

3i 

Beton  blocks 

(pressed) 

“ like  Beton  blocks 

.66 

33-15 

Polished  marble 

“ common  bricks 

• 44 

23-45 

“ “ 

“ fine  cut  granite 

.6l 

30.30 

Common  bricks 

“ common  bricks 

.64 

32. 3S 

a a 

“ dressed  hard  limestone.. . 

,60 

31 

When  S and  x{  are  equal  to  each  other,  the  wall  is  just 
upon  the  point  of  motion,  and  S must  be  increased ; that 
is,  more  weight  must  be  given  to  the  wall  to  ensure  frictional 
stability. 

Let  the  water  be  withdrawn  from  the  side  BD.  Fig.  74, 
and  let  the  upward  pressure  attain  to  one-half  the  maxi- 
mum, and  the  coefficient  be  that  of  a horizontal  bed-joint 
upon  a concrete  foundation,  assumed  to  be  .62,  then  S = 

* Vide  % 353,  pp.  344,  345. 


LEVERAGE  STABILITY  OF  MASONRY. 


397 


(W  + e — .50Zi)  x c = 2.79  tons,  and  xx  — 2.2 5 tons,  and  the 
wall  has  a small  margin  of  frictional  stability. 

The  weight  of  the  wall  should  be  increased  until  it  is 
able  to  resist  a horizontal  thrust  of  at  least  1.5x1}  or  until 
8=  1.5a?i,  when  the  equation  of  frictional  stability  becomes 

8 = (W+  e — CiZi)  x c — 1.5xh  (8) 

in  which 

IV  is  the  weight  of  masonry  above  any  given  plane. 

e “ vertical  downward  water  pressure  resultant. 

Zi  “ maximum  upward  water  pressure  resultant. 

Ci  “ ratio  of  effective  upward  water  pressure  to  the 
maximum. 

c “ coefficient  of  friction  of  the  given  section  upon 
its  bed. 

Xj,  “ horizontal  water  pressure  resultant. 

S “ symbol  of  frictional  stability. 

400.  Pressure  Leverage  of  Water. — Since  the  hori- 
zontal resultant  of  the  water-pressure  has  its  point  of  appli- 
cation above  the  level  of  D,  in  JV,  its  moment  of  pressure 
leverage , L,  has  a magnitude  equal  to  DN,  or  Kx  — \h , 
into  the  horizontal  resultant. 

T . 7i  7i  7iz  /nN 

L = Am  2 X g-,=  -g-  Wl  (9) 

401.  Leverage  Stability  of  Masonry. — The  moment 
of  pressure-leverage  of  the  water  tends  to  overturn  the  wall 
about  its  toe,  I)  or  C\  Fig.  74,  opposite  to  the  side  receiving 
the  pressure  alone,  or  the  maximum  pressure. 

Let  the  weight  of  DCB,  per  cubical  foot,  be  assumed 
140  pounds,  an  approximate  weight  for  a mortared  rubble 
wall  of  gneiss,  or  mica-slate ; then  the  total  weight  above 
the  bed-joint  CD,  is  140rt  = 5.25  tons,  which  we  may  con- 


398 


PARTITIONS,  AND  RETAINING  WALLS, 


sider  as  acting  vertically  downward  through  G,  the  centre 
of  gravity  of  DCB. 

Plot  to  scale  this  vertical  resultant  of  weight  in  xe,  = 
5.25  tons  (neglecting  for  the  present  the  upward  and  down- 
ward pressures  of  the  water),  and  the  horizontal  resultant 
of  water  pressure  in  xN2  = 2.25  tons,  and  complete  the 
parallelogram  xN2Me2 ; then  the  diagonal  xJJ  is  in  mag- 
nitude and  direction  the  final  resultant  of  the  two  forces. 
The  resultant  arising  from  the  horizontal  pressure  on 
JO,  and  weight  of  the  masonry,  is  in  magnitude  and  direc- 
tion xO. 

If  the  directions  of  xM  and  xO  cut  the  lbase  DC,  then  the 
wall  has,  theoretically,  leverage  stability,  but  if  the  direc- 
tions of  these  diagonals  are  outside  of  DC,  then  the  wall 
lacks  leverage  stability  and  will  be  overturned. 

For  safety,  the  direction  of  xM  should  cut  the  base  at  a 
distance  from  K not  exceeding  one-half  KC,  and  the  direc- 
tion of  xO  cut  the  base  at  a distance  from  K not  exceeding 
one-half  KD. 

403.  Moment  of  Weight  Leverage  of  Masonry. — 

Since  the  vertical  resultant  of  weight  of  masonry  takes  its 
direction  through  G,  and  cuts  DC  at  a distance  from  C, 
the  point  or  fulcrum  over  or  around  which  the  weight  must 
revolve,  the  moment  of  weight  leverage  of  the  wall  has  a 
magnitude,  when  resisting  revolution  to  the  right,  equal  to 
the  distance  KI)  into  the  vertical  weight  resultant ; and 
when  resisting  revolution  to  the  left,  equal  to  the  distance 
KC  into  the  vertical  weight  resultant. 

Let  the  symbol  of  distance  of  K from  the  fulcrum,  on 
either  side,  be  du  and  its  value  be  computed  or  taken  by 
scale,  at  will ; and  let  the  symbol  of  moment  of  weight 
leverage  be  M,  then 


M = Awdx. 


(10) 


MOMENTS  OF  SECTIONS. 


399 


For  double  stability,  or  a coefficient  of  safety  equal  to  2, 

'must,  at  least,  be  equal  to  Axwx  or 
z o 

M=  ~wt. 


403.  Thickness  of  a Vertical  Rectangular  Wall 
for  Water  Pressure. 

Let  h be  the  height  of  the  wall  and  of  the  water. 

“ w “ weight  of  a cubic  foot  of  the  masonry. 

“ Wi  “ “ “ “ “ water. 

“ z “ required  thickness  of  the  wall. 

Then  hxzx-^-xw  = leverage  moment  of  weight  of 
z 

wall,  = ; and  h x ^ x w1  x ~ = leverage  moment  of 

Z Zo 


pressure  of  water  = for  double  effect, 


7i3Wi 

~3~' 


The  equation  for  a vertical  rectangular  wall,  Fig,  75, 
that  is  to  sustain  quiet  water  level  with  its  top,  and  that 
just  balances  a double  effect  of  the  water  is : 


liZ'VI  _ li3wx 


from  which  we  deduce  the  equation  of  thickness, 
(3  hw)  ( 1.5w ) 


(11) 


404.  Moments  of  Rectangular  and  Trapezoidal 
Sections. — Let  DCEB,  Fig.  75,  be  a vertical  rectangular 
wall  of  masonry,  of  sectional  area  exactly  equal  to  the  tri- 
angular section  of  wall  in  Fig.  74,  viz.,  15  feet  in  height  and 
5 feet  in  breadth,  and  weighing,  also,  140  pounds  per 
cubical  foot.  Let  the  depth  of  water  which  it  is  to  sustain 
upon  either  side,  at  will,  be  12  feet. 


400 


PARTITIONS,  AND  RETAINING  WALLS. 


The  horizontal  resultant  of  water  pressure  is 
7 

Wx-^r-  — 2.25  tons, 

£ 

and  the  vertical  resultant  of  weight  of  wall  into  the  coef- 
ficient (.62)  of  friction  is 

[ W - (.2 52,)]  x c = 2.96  tons. 

This  leaves  a small  margin  of  frictional  stability. 

The  vertical  weight  resultant  is 

(Aw)  — (.252,)  = 4.78  tons, 

or,  if  there  is  no  upward  pressur  e, 

Aw  = 5.25  tons. 

Plot  to  scale  the  horizontal  and  vertical  resultants  from 
their  intersection  in  x,  and  complete  the  parallelogram 

xPMe2 ; then  will  the  diagonal 
xM  be  the  final  resultant  of  the 
two  forces. 

* The  direction  of  the  diagonal 
now  cuts  the  base  very  near 
the  toe  C,  and  the  given  wall 
with  vertical  rectangular  sec- 
tion lacks  the  usual  coefficient 
of  leverage  stability,  though  it 
was  found  to  have  ample  lever- 
age stability  in  the  equal  tri- 
angular section. 

If  we  now  give  to  this  same 
wall  a slight  batter  upon  each 
side,  as  indicated  by  the  dotted  lines,  its  final  resultant, 
arising  from  the  horizontal  water  pressure,  will  lie  in  xOa 


Fig.  75. 


£■  B 

< s-o  > 


i 

o ^ 
\ 

© 

i 

i 

\ 

\ 

CO 

: - — __ 

1 

\ 

_ r~ 

ii 

i 

i 

i 

c 

\ 

\ 

\ 

>G 

/ 

l * 

j 

2.25 

X" 

\ 

*,  1 ? 

1 
1 
1 
/ 

\P  i 
1 / 
l ip  « 

1 / N 
! / » 

ri 

v i 

\ 

\ 

\ 

\ 

i y- 

CV 

hfli. 

\\i° 

L v'O 

MOMENTS  OF  SECTIONS. 


401 


and  its  direction  will  cut  the  base  farther  from  the  toe,  and 
the  leverage  stability  of  the  wall  will  be  increased. 

Let  JDCEB,  Fig.  76,  be  a section  of  a partition  wall  in  a 
reservoir,  subject  to  a pressure  of  water  whose  surface  coin- 
cides with  its  top,  on  either  side,  at  will.  Let  the  height  be 
12  feet,  and  the  thickness  at  top  4 feet. 


Fig.  76. 


The  side  EG  is  vertical  and  the  side  BD  has  a batter  of 
three  inches  to  the  foot. 

The  maximum  pressure  resultants  meet  the  respective 
sides  in  P and  Pb  in  directions  perpendicular  to  their  sides, 
and  at  depths  equal  to  two-thirds  the  vertical  depth  EC. 

26 


402 


PARTITIONS,  AND  RETAINING  WALLS. 


Plot  to  scale  tlie  horizontal  pressure  resultants  in  theii 
respective  directions  through  P and  Px , and  the  weight 
resultant  in  its  vertical  direction  through  the  centre  of  grav- 
ity,0 G,  and  complete  the  parallelograms.  The  diagonals 
then  give  the  directions  and  magnitudes  of  the  maximum 
leverage  effects. 

The  diagonal  xO  cuts  the  hase  CD  at  a distance  from  K 
less  than  half  KD  ; the  diagonal  xM  cuts  the  base  at  a 
distance  from  K more  than  half  the  distance  KC. 

The  leverage  stability  of  the  wall  is  therefore  satisfactory 
to  resist  pressure  from  the  left,  but  has  not  the  desired 
factor  of  safety  to  resist  pressure  from  the  right. 

405.  Graphical  Method  of  Finding  the  Leverage 
Resistance. — The  ratio  of  leverage  resistance  may  be 
obtained  from  the  sketch  by  scale,  as  follows : Extend  the 
base,  JO,  of  the  parallelogram  upon  the  right,  indefinitely ; 
draw  a broken  line  from  x through  I),  cutting  JOrx  in  rx ; 
then  the  ratio  of  leverage  stability  against  the  water  pressure 
upon  EC  is  to  unity  as  Jrx  is  to  JO. 

Also  extend  KO,  indefinitely  ; draw  a broken  line  from 
y,  through  the  toe  C,  cutting  K0,r2  in  r2 ; then  the  ratio  of 
leverage  stability  against  the  maximum  water  pressure 
uiion  BD  is  to  unity  as  Kr2  is  to  KO,. 

The  ratio  of  r20,  to  r2K  exceeds  .5.  but  the  ratio  of  r3f 
to  rJ  is  less  than  .5  ; therefore  the  effect  of  the  horizontal 
pressure  xxPx  to  overturn  the  wall  exceeds  the  effect  of  the 
maximum  pressure  yPx  to  overturn  the  wall. 

406.  Granular  Stability.— We  have  found  the  maxi- 

* The  centre  of  gravity  of  a rectangular  symmetrical  plane,  Fig.  75,  lies  in 
the  intersection  of  its  diagonals. 

The  centre  of  gravity  of  a trapezoidal  plane  DCEB , Fig.  76,  may  be  found 
graphically,  thus : Prolong  CD  to  i,  and  make  Ci  = EB.  Also  prolong  EB  to 
k,  and  make  Bk  = CD.  Join  ki.  Bisect  CD  and  EB.  in  d and  5.  and  join  db. 
The  centre  of  gravity  G lies  in  the  intersection  of  the  lines  db  and  ik 


COMPUTED  PRESSURE  IN  MASONRY.  403 

mum  water  pressure  resultant  upon  the  inclined  side,  JC 
(Fig.  74),  to  be  yl\  — y = 2.704  tons ; its  direction  to  be 
perpendicular  to  JC,  and  its  point  of  application  to  be  at 
two-tliirds  the  vertical  depth  JC,  or  iC. 

Plot  this  inclined  resultant,  in  the  prolongation  of  the 
line  yPx,  from  a vertical  through  G,  in  ?/2I\  = 2.704  tons ; 
and  plot  the  vertical  weight  resultant  of  the  wall  from  the 
intersection  y2,  in  y ju  = 5.25  tons  ; complete  the  parallelo- 
gram y2P  JJ2K:,  then  the  diagonal  y202  is  in  magnitude 
and  direction  the  maximum  pressure  resultant  of  the  two 
forces  tending  to  crash  the  granular  structure  of  the  wall 
and  its  foundation. 

The  following  table  of  data  relating  to  computed  pres- 
sures in  masonries  of  existing  structures,  is  condensed  and 
tabulated  from  memoranda*  given  by  Stoney  and  from 
other  sources : 


TABLE  No.  8 5. 


Computed  Pressures  in  Masonry. 


Kind  of  Masonry. 


Piers,  All  Saints  Church 

Pillar,  Chapter  House 

Pillars,  dome  St.  Paul’s  Church 
‘ “ St.  Peter’s  Church 

Aqueduct,  pier 

Arch  bricks,  bridge,  Charing  ) 

Cross f 

Pier  bricks,  Suspension  Bridge. 

Bridge  pier 

Arch  concrete,  bridge.  Char-) 

ing  Cross ) 

Arch  bricks,  viaduct 

Brick  chimney 

Bricks,  estimated  pressure  on  ) 
leeward  side  in  a gale. . . . ( 


Location. 

Material. 

Pressure 

IN  LBS.  PER 
SQ.  FOOT. 

Angers. 

Forneaux  stone. 

86,016 

Elgin. 

Red  sandstone. 

4.0, oq6 

London. 

Portland  limestone. 

39.4-4 

Rome. 

Calcareous  tufa. 

33,376 

Marseilles. 

Stone. 

30,240 

London. 

London  paviors. 

26,880 

Clifton. 

Staffordshire  blue  bricks. 

22,400 

Saltash. 

Granite. 

21,280 

London. 

Port.  Cement,  i;  gravel,  7. 

17,920 

Birmingham. 

Red  bricks. 

15,680 

Glasgow. 

Brick. 

20,160 

— 

33,600 

Long  span  bridges  have  sometimes  pressures  at  their  springing  exceeding 
125,000  pounds  per  square  foot. 


* The  Theory  of  Strains  in  Girders  and  Similar  Structures.  New  York,  1878. 


404  PARTITIONS,  AND  RETAINING  WALLS. 

Experimental  data  of  the  ultimate  strength  of  masonry 
in  large  masses  has  not  been  obtained  in  a sufficient  number 
of  instances  to  determine  a limit  generally  applicable  for 
safe  practice. 

Failure  first  shows  itself  by  the  spalting  off  of  the  angles 
or  edges  of  the  stones,  or  by  the  breaking  across  of  stones 
subjected  to  a transverse  strain,  and  next  by  the  crushing 
of  the  mortar. 

407.  Limiting  Pressures.— From  experiments  of  sev- 
eral engineers  upon  the  ultimate  crushing  strength  of  small 
cubes  of  dressed  stones  (1  inch  and  inch  square),  and 
from  computations  of  pressures  upon  the  lower  courses  of 
tall  stacks  and  spires,  the  data  of  the  following  table  has 
been  prepared : 

TAB  L E No.  86. 

Approximate  Limiting  Pressures  upon  Masonry. 


Av.  weight  laid 
in  mortar,  per 
cubic  foot. 

Approx,  ulti- 
mate resistance 
of  dry,  dressed, 
one-inch  cubes. 

Est.  safe  static 
pressure  per 
sq.  ft.  on  thick 
blocks,  unlaid. 

Est.  safe  pres- 
sure per  sq.  ft. 
in  coursed  rub- 
ble masonry,  at 
2 ft.  from  edge, 
when  laid  in 
strong  mortar- 

Limestone 

152  lbs. 

4,000  lbs. 

115,000  lbs. 

15,000  lbs. 

Sandstone 

132  “ 

6,000  “ 

170,000  “ 

15,000 

Granite 

154  “ 

10,000  “ 

280,000  “ 

20,000  “ 

Brick 

120  “ 

2,500  “ 

72,000  “ 

8,000  “ 

McMaster  mentions*  that  in  Spain,  and  in  some  instances 
in  France,  the  limit  of  pressure  in  stone  masonry  has  been 
taken  in  practice  as  high  as  14  kilogrammes  per  square 
centimeter  (—  28678  lbs.  per  square  foot) ; but  in  the  ma- 
jority of  cases  the  limit  is  taken  at  from  6 kilogrammes  to  8.50 
kilogrammes  per  sq.  centimeter,  or  say  15000  lbs.  per  sq.  ft. 


* Profiles  of  High  Masonry  Dams.  New  York,  1876. 


WALLS  FOR  QUIET  WATER. 


405 


The  ultimate  granular  resistance  of  the  masonry  is 
largely  dependent  upon  the  strength  of  the  mortar,  and 
upon  the  skill  applied  to  the  dressing  and  laying  of  the 
stones. 

It  is  not  advisable  to  allow  either  a direct  or  resultant 
pressure  exceeding  140  pounds  per  square  inch  within  one 
foot  of  the  face  of  rubble  masonry,  or  200  pounds  per  square 
inch  in  the  heart  of.  the  work ; and  these  limits  should  be 
approached  only  when  both  materials  and  workmanship 
are  of  a superior  class. 

The  resultant  of  the  horizontal  pressure  is  seen  to  cut 
the  base-line  nearer  to  the  toe,  or  fulcrum,  over  which  the 
resultant  tends  to  revolve  the  wall,  than  does  the  resultant 
of  maximum  pressure  ; the  crushing  strain  is  therefore 
greater  near  the  face  of  the  masonry  from  the  horizontal 
than  the  maximum  resultant. 

Care  must  be  exercised,  in  high  structures,  that  the  safe 
pressure  limit  near  the  edge  is  not  exceeded,  lest  the  edge 
spalt  off,  and  the  fulcrum  be  changed  to  a position  nearer 
the  centre  of  the  wall,  and  the  leverage  stability  thus  re- 
duced. 

408.  Table  of  Walls  for  Quiet  Water. — The  fol- 
lowing table  gives  dimensions  for  walls  to  sustain  quiet 
water  on  either  side,  and  also  on  the  back  only,  with  a 
limiting  face  batter  of  two  inches  per  foot  rise : 


406 


PARTITIONS,  AND  RETAIN Ln  li  WALLS. 


TAB  LE  No.  8 7. 

Approximate  Dimensions  of  Walls  to  Retain  Water. 

For  granite  rubble  walls,  in  mortar,  of  specific  gravity  2.25,  or  weight,  140  pounds 
per  cubic  foot ; to  retain  quiet  water  level  with  the  top  of  the  wall. 


Height  of 
water  and 
wall,  in  feet. 

Vertical 

Rectangular 

Wall. 

Pressure  on  either  side. 
Symmetrical  Partitions. 

Pressure  on  Back  only. 

Breadth  in 
feet. 

Top 

breadth  in 
feet. 

Bottom 
breadth  in 
feet. 

Top 

breadth  in 
feet. 

Face  batter 
in  inches 
per  ft.  rise. 

Bottom 
breadth  in 
' feet. 

4 

3-5 

3-5 

3-5 

3-5 

O 

3-5 

5 

3-5 

3-5 

3-5 

3-5 

O 

3-5 

6 

3-5 

3-5 

3-5 

3-5 

O 

3-5 

7 

4.0 

3-5 

4-25 

3-5 

i 

4.0 

8 

4-5 

3-5 

5-25 

3-5 

li 

5-o 

9 

5-o 

3-5 

6.00 

3-5 

2 

5-75 

10 

5-5 

3-5 

6.50 

3-5 

2 

6-75 

11 

6.0 

3-5 

7-25 

3-5 

2 

7-25 

12 

6-75 

4.0 

7-75 

4.0 

2 

7-83 

13 

7-25 

4.0 

8.50 

4.0 

2 

8.67 

14 

7-75 

4.0 

9-25 

4.0 

2 

9-5° 

i5 

8.25 

4.0 

10.00 

4.0 

2 

10.50 

16 

9.00 

4.0 

10.75 

4.0 

2 

11.50 

17 

9-5o 

4.0 

1 1.67 

4.0 

2 

12.00 

18 

10.00 

5-o 

n-75 

5-° 

2 

12.50 

19 

10.50 

5-o 

12.67 

5-° 

2 

13-67 

20 

1 1. 00 

5-o 

13-33 

5-° 

2 

14.50 

21 

11.50 

5-° 

14.00 

5-o 

2 

15-25 

22 

12.25 

5-° 

14.83 

5-° 

2 

16.25 

23 

12.75 

5-° 

15-75 

5-o 

2 

17-25 

24 

13-25 

5-° 

16.50 

5-0 

2 

18.25 

Tlie  top  thickness  is  to  Tie  increased  if  the  top  of  the 
wall  is  exposed  to  ice-thrnst ; and  the  -wliole  thickness 
must  lbe  increased  if  water  is  to  flow  over  the  crest,  accord- 
ing to  the  depth  of  water  upon  the  crest,  and  its  initial 
velocity  of  approach. 

Unless  partition-walls  rest  on  solid  rock,  or  on  imper- 
vious strata  of  earth,  as  they  should,  percolation  under  the 


ECONOMIC  PROFILES. 


407 


wall  must  be  prevented  by  a concrete  or  puddle  stop-wall, 
or  by  sheet-piling ; or  the  pervious  strata  must  be  effectu- 
ally sealed  over. 

409.  Economic  Profiles.— It  is  evident,  from  the 
above  investigations,  that  the  profile  has  an  important  influ- 
ence upon  the  leverage  stability  of  a wall  of  given  weigh  1 
of  material,  and  therefore,  for  a given  stability,  upon  econ- 
omy of  material. 

The  leverage  stability  against  pressures  of  water  upon 
the  vertical  sides  of  triangular  or  trapezoidal  sections  of 
masonry  is  greater  than  the  leverage  resistances  to  pressures 
upon  their  inclined  sides,  as  is  graphically  illustrated  in  the 
above  sketches ; hence  there  is  an  advantage  in  giving  all 
the  batter  to  the  side  opposite  to  the  pressure. 

The  vertical  rectangular  sections  are  least  economic,  and 
the  triangular  sections  most  economic  of  material. 

When  some  given  thickness  is  assumed  for  the  top  of  a 
retaining  wall,  to  give  it  stability  against  frost,  or  displace- 
ment from  any  cause,  then  theory  makes  both  sides  vertical 
from  the  top  downward  until  the  limiting  ratio  of  leverage 
stability  is  reached,  and  then  gives  to  the  side  opposite  to 
the  pressure  a parabolic  concave  curve. 

It  may  be  necessary  to  widen  the  base  of  high  walls 
upon  both  sides  beyond  the  breadth  required  for  leverage 
stability,  to  distribute  the  weight  sufficiently  upon  a weak 
foundation.  Practical  considerations,  in  opposition  to 
theory,  tend  to  rectangular  vertical  sections. 

The  engineer  who  is  familiar  with  both  theory  and  prac- 
tice, adjusts  the  profile  for  each  given  case,  so  as  to  attain 
the  requisite  frictional,  leverage,  and  granular  stabilities,  in 
the  most  substantial  and  economical  manner,  having  due 
regard  to  the  quality  and  cost  of  materials,  and  the  skill 
and  cost  of  the  required  labor. 


408 


PARTITIONS,  AND  RETAINING  WALLS. 


410.  Theory  of  Earth  Pressures. — Earth  filling  of 
the  different  varieties  behind  retaining  walls,  is  met  in  all 
conditions  of  cohesiveness  between  that  of  a fluid  and  that 
of  a solid. 

The  same  filling,  in  place,  is  subject  to  constant  changes 
in  its  degree  of  cohesion,  as  its  moisture  is  increased  or 
diminished,  or  as  its  pressure  and  condensation  is  increased, 
or  as  it  is  subjected  to  the  tremulous  action  of  traffic  over  it. 
The  theory  of  earth  pressure,  therefore,  leads  to  less  certain 
results  than  does  the  theory  of  water  pressure. 

We  have  seen  (§  353)  that  different  earths  have  dif- 
ferent natural  angles  of  repose  when  exposed  to  atmos- 
pheric influences,  and  they  also  tend  to  assume  their  natural 
f rictional  angle  wdien  deposited  in  a bank.  If  we  make  a 
broad  fill  with  earth,  behind  a vertical  wall  and  then  sud- 
denly remove  the  wall,  a portion  of  the  earth,  of  triangular 
section,  will  at  once  fall,  and  the  slope  will  assume  its  natu- 
ral frictional  angle.  If  we  make  such  a fill  even  with  the 
top  of  a vertical  rectangular  wall,  whose  thickness  is  only 
equal  to  one-fourth  of  its  height,  then  the  earth  will  over- 
turn the  wall.  This  is  evidence  that  a portion  of  the  earth 
produces  a lateral  pressure.  If  the  earth  is  fully  saturated 
with  water,  its  lateral  pressure  may  be  nearly  like  that  of  a 
fluid  of  equal  specific  gravity.  If  the  earth  is  compact  like 
a solid,  its  thrust  may  be  nearly  like  that  of  a rigid  wedge. 

Let  LBBJ , Fig.  77,  be  an  earth-fill  behind  a vertical 
retaining  wall  I)B.  Let  LB  I7,  be  the  natural  frictional 
angle  = <f>,  of  that  earth  filling.  It  is  evident  that  the  por- 
tion of  earth  LB  Vx  will  produce  no  thrust  upon  the  ma- 
sonry, because  it  would  remain  at  rest  if  the  wall  was 
removed.  Suppose  all  the  filling  above  D Vl  to  be  divided 
into  an  infinite  number  of  laminae  whose  planes  of  cleavage 
all  meet  at  one  edge  in  B,  and  radiate  from  B.  Then  the 


THEORY  OF  EARTH  PRESSURES. 


409 


thin  lamina  adjoining  DVX  will  exert  the  minimum  thrust 
against  the  masonry  and  the  maximum  weight-pressure 
upon  I)  Vi.  The  thin  lamina  adjoining  BD  will  exert  the 


Fig.  77. 


maximum  wedge-thrust  against  the  masonry  and  minimum 
weight-pressure  upon  D V,. 

Suppose  the  mass  VXDBJ  to  be  divided  into  two  parts 


410 


PARTITIONS,  AND  RETAINING  WALLS. 


by  the  plane  DJ,  which  bisects  the  angle  BD  Vx.  Let  the 
wedge  BDJ , then  be  increased  in  dimensions  by  revolving 
the  side  JD  to  the  right,  around  I)  ; then  its  weight,  as  a 
solid,  will  rest  more  upon  F,D,  and  its  lateral  thrust  will 
not  be  increased.  Let  the  wedge  BDJ , then  be  reduced  in 
dimensions  by  revolving  the  side  JD  to  the  left ; then  its 
total  weight  and  its  ability  to  produce  lateral  thrust  upon 
the  masonry  will  be  reduced.  We  may  therefore  assume 
that  that  portion  of  the  mass  VYDBJ.  included  in  the  upper 
wedge  formed  by  bisecting  the  angle  VXDB  will  be  the 
maximum  portion  of  the  earth  that  will  first  fall  if  the  wall 
is  suddenly  removed,  and  that  the  thrust  of  the  wedge  BDJ , 
if  considered  alone,  and  as  devoid  of  friction  upon  the  plane 
JD , will  give  a safe  theoretical  maximum  effect  upon  the 
masonry  of  the  whole  mass  V^DBJ. 

The  practical  value  of  such  assumption  has  been  ably 
demonstrated  by  Coloumb,  Prony,  Canon  Moseley,  Kan- 
kine,  Neville,  and  others. 

411.  Equation  of  Weight  of  Earth-Wedge. — The 

weight  W2  of  the  wedge  of  earth  (considered  as  one  foot 
in  length),  in  pounds,  equals  its  surface  area  DBJ.  in  square 
feet,  = Aa,  into  the  weight  of  one  cubical  foot  of  the  mate- 
rial = w2. 

Wo  = AoWo.  (12) 

Let  the  symbol  of  the  frictional  angle  LDV  of  the 
earth  filling  be  <j> , and  of  VXDJ  be  <r  ; then  will  the  angle 

BDJ  = [=9  = angle  VXDJ=  <r. 

Let  the  height  BD  equal  12  feet,  = 7i ; then  the  area  of 
DBJ  will  equal  DB  into  one-half  BJ  = 

Ao  = 7i  x ^ tan  d = ^ cotan  (<(>  + ?).  (13) 


PRESSURE  OF  EARTH-WEDGE. 


411 


412.  Equation  of  Pressure  of  Earth -Wedge. — 

Assume  the  weight  of  the  wedge  DBJ  — Aw,  = W,  to  be 
gathered  into  its  vertical  resultant  passing  through  its  cen- 
tre of  gravity,  g ; then  the  thrust  P of  the  wedge  equals 
its  weight  into  its  horizontal  breadth  BJ , divided  by  its 
vertical  height  BD  — 

P = A2w2  tan  0 — W2  cotan  (<p  + <p).  (14) 

Draw  the  vertical  resultant  W2  to  scale  in  eP,  meeting 
the  inclined  plane  JD , in  P. 

The  thrust  effect  of  W,  will  have  its  maximum  action  in 
a line  parallel  to  the  line  I)  Vx , since  the  mass  VXDBJ , as 
a whole,  tends  to  move  down  the  plane  ViD. 

The  theoretical  reaction  from  the  wall,  necessary  to  sus- 
tain W,,  will  then  be  in  a direction  parallel  to  DV,  cutting 
the  vertical  resultant  in  P.  Draw  the  reaction  of  the  wall 
to  scale  in  nP.  The  reaction  of  the  plane  JD  is  in  direc- 
tion and  magnitude  equal  to  the  diagonal  Py,  of  the  paral- 
lelogram of  which  W2  and  P form  two  sides.  Draw  the 
reaction  of  JD  to  scale  in  VP.  Then  will  the  three  result- 
ants eP,  nP,  and  VP  be  in  equilibrium  about  the  point  P. 

Let  <p  = 30°. 

Assume  the  tilling  to  be  of  gravel,  weighing  125  pounds 
per  cubic  foot,  and  that  after  a storm,  its  drains  being 
obstructed,  its  voids  are  filled  with  water,  increasing  the 
weight  to  140  pounds  per  cubic  foot,  = w2 ; then 

W2  = -g  cotan  (0  + q>)  w2  = . tan  — ^ — 

12 

= 12  feet  x -Q-  feet  x .57735  x 140  pounds 
£ 

— 5,820  pounds  = 2.91  tons. 

The  reaction  from  the  wall  necessary  to  sustain  the 
weight  of  the  wedge  JBD  = 


412 


PARTITIONS,  AND  RETAINING  WALLS. 


P = W2  tan  0 = — cotan2  (</>  + g>)  w s (15) 

= 2.91  tons  x .57735 
= 1.68  tons. 

The  horizontal  effect  of  P — 

x — P cos  (p  = A2w2  tan  6 cos  $ (16) 

= 1.68  tons  x .86602  = 1.45  tons. 

The  thrust  of  the  wedge  tending  to  push  away  and  to 
overturn  the  wall  is  equal  to  the  reaction  from  the  wall 
necessary  to  sustain  the  wedge  in  position.  We  find  its 
horizontal  effect  in  this  case  to  "be  1.45  tons,  and  this  is  the 
maximum  effect,  = x,  tending  to  displace  the  wall  hori- 
zontally. 

413.  Equation  of  Moment  of  Pressure  Leverage. 

— The  maximum  moment  of  pressure  leverage , L , tending 
to  overturn  the  wall  around  its  toe,  equals  x into  the  height, 
in  feet,  above  D at  which  x meets  the  wall. 

When  the  wall  is  vertical  and  the  surface  of  filling  hori- 
zontal, x always  meets  BD  at  one-third  h from  Z>,  — \f 

therefore  the  equation  of  moment  of  pressure  leverage 
becomes 

Lx  — x \ = (. A2w2  tan  0 cos  <£)  \ (17) 

O O 

19  ft 

. = 1.45  tons  x — — ^ = 5.80  tons. 

O 

414.  Thickness  of  a Vertical  Rectangular  Wall 
for  Earth  Pressure. — The  moment  of  weight  leverage  of 

a vertical  rectangular  wall  is  , in  which  z is  the  thick- 

ness  of  the  wall. 


SURCHARGED  EARTH-WEDGE. 


413 


The  double  moment  of  pressure  leverage  of  earth  level 
with  the  top  of  the  wall  is 

h h3 

(h2w2  tan2  d cos  0)  x — = — w2  tan2  6 cos  0. 

d O 

When  the  wall  just  balances  the  theoretical  double 
pressure  of  the  earth  level  with  its  top, 

hz2w  Ji3  , , . 

— = — w2  tan2  6 cos  0, 

/d>  O 

from  which  is  deduced  the  equation  of  thickness  for  a ver- 
tical rectangular  wall, 


j 2 hsw2  tan2  6 cos  <p  [i  _ 

j h2w2  tan2  6 cos  0 ) 

( 3 hw  S 

| 1.5m  j 

415.  Surcharged  Earth-Wedge. — When  the  earth- 
fill  behind  a wall  is  carried  up  above  the  top  level  BJ  of 
the  wall,  and  is  sloped  down  against  the  top  angle  B,  or 
upon  the  top  of  the  wall,  the  fill  DBF  is  then  termed  a 
surcharged  fill. 

Its  weight  W2  is,  as  in  the  case  of  the  level  fill,  per  lineal 
foot, 

W2  = A2w2.  (19) 

To  compute  the  pressure  of  the  surcharged  fill,  we  may 
divide  the  mass  Vx DBF  into  two  wedges  by  a plane  DF, 
bisecting  the  angle  YVDB , and  take  the  action  of  the  wedge 
FDB  as  equivalent  to  the  effective  action  of  the  whole  mass 
VDBF. 

Let  the  natural  frictional  angle  of  the  earth-fill  be 
< 6 = 30°. 

The  area  A2  of  the  wedge  FDB  may  be  computed  by 
any  method  of  ascertaining  the  area  of  a triangular  super- 


414 


PARTITIONS,  AND  RETAINING  WALLS. 


ficies.  If,  with  a given  slope  BF , the  fill  does  not  rise  as 
high  as  F,  and  its  surface  level  cuts  FB  and  FJ  between 
the  levels  of  F and  B , then  its  area  is  ascertained  by  any 
method  of  ascertaining  the  superficies  of  a trapezium. 

Let  fall  upon  BF  a perpendicular  from  B,  meeting  BF 
in  i ; then  the  distances  Bi  and  IF  are  equal,  each,  to  the 

Q0O  £ 

cosine  of  the  angle  BBF  = cos.  - — = — - =.  cos  ft  ; and  the 

distance  IB  is  equal  to  sin  — - = sin  ft. 

Let  the  height  BB  = h — 12  feet. 

The  area  BBF  equals  the  length  BF  into  one-half  IB  = 

A2  — h x 2 cos  ft  x h \ sin  ft  — h cos  ft  x It  sin  ft  (20) 
= (12  x .866)  x (12  x .5)  = 62.53  sq.  ft, 

I 

Let  the  mean  weight  of  the  fill,  which  is  quite  sure  to  be 
drained  above  the  level  BJ,  be  assumed  130  pounds  per 
cubical  foot. 

416.  Pressure  of  a Surcharged  Earth-Wedge.— 

Suppose  the  weight  to  be  gathered  into  its  vertical  resultant 
passing  through  the  centre  of  gravity  g2,  of  the  mass  BFB. 
This  vertical  resultant  will  meet  the  plane  FB  in  at  a 
level  higher  than  P. 

The  wedge-thrust  P1}  due  to  the  weight  W2,  equals  the 
weight  into  the  horizontal  breadth  BJ,  divided  by  the 
height  BB  = 

Pl  = W2  tan  90  - = A2w2  cotan  (9  + <r)  — (21) 

z 

62.53  sq.  ft.  x 130  lbs.  x .577  = 4690.38  lbs.  = 2.345  tons. 


The  maximum  pressure-action  of  the  weight  upon  the 
wall  is  in  a direction  parallel  to  T"P,  the  natural  frictional 
angle  4>,  of  the  filling  material.  Its  horizontal  pressure 
effect,  X\,  is  therefore  - 


PRESSURE  OF  AN  INFINITE  SURCHARGE. 


415 


Xx  = 1\  x cos  (p  = A2w2  tan  0 cos  </>  = (22) 

2.345  tons  x .866  = 2.03  tons. 

The  maximum  horizontal  pressure  resultant  takes  its 
direction  through  Px  and  meets  the  wall  at  the  altitude  of 

P„  which  is  greater  than 

6 

We  may  here  observe  that,  even  though  the  fill  DBF 
is  of  lighter  material  than  the  fill  DBf  so  that  the  total 
weight  of  one  is  exactly  equal  to  the  total  weight  of  the 
other,  the  pressure  leverage  effect  from  the  surcharged  fill 
will  exceed  the  pressure  leverage  effect  from  the  level  fill, 
because  its  centre  of  gravity  g2  will  be  higher  than  g,  its 
vertical  resultant  W,  will  meet  the  plane  JD  in  P,  at  a point 
higher  than  P,  and  its  horizontal  resultant  xx  will  meet  the 
wall  at  a greater  altitude  from  D than  will  the  resultant  x. 

Let  rh  be  the  symbol  of  the  ratio  of  h at  which  xx  meets 
the  wall  from  D ; then  if  xx  meets  DB  at  \h,  rh  — .3333  ; 
and  if  x{  meet  DB  at  fh,  rh=  .5,  etc. 

417.  Moment  of  a Surcharge  Pressure  Lev  erage. 
— The  maximum  moment  of  pressure  leverage  P„  of  a sur- 
charged fill,  tending  to  overturn  the  wall  around  its  toe, 
equals  xx  into  the  height,  in  feet  = (rh?t)  above  D,  at  which 
xx  meets  the  wall. 

• __ 

Li  = xx  x (rhh)  = Am2  tan  6 cos  <t>  (rh7i)  = (23) 

2.03  tons  x 5.98  = 12.14  tons. 

418.  Pressure  of  an  Infinite  Surcharge. — Let  PP, 
Fig.  78,  be  the  natural  slope  of  the  filling  material,  and 
parallel  with  DI,  which  makes  with  DL  the  natural  fric- 
tional angle  LDI  = 0.  Let  BF  extend  indefinitely. 

If  IDBF  is  a perfect  solid  it  will  be  just  upon  the  point 
of  motion  down  the  slope  ID ; on  the  other  hand,  if  IDBF 


416 


PARTITIONS,  AND  RETAINING  WALLS. 


is  liquid,  of  specific  gravity  equal  to  the  specific  gravity  of 
the  filling  material,  it  will  then  exert  its  maximum  pressure 
upon  the  wall-face  DB. 

Let  the  filling  be  considered  liquid,  resting  upon  the 
equivalent  horizontal  base  DI,  and  having  the  equivalent 
horizontal  surface  BF 

Let  fall  upon  DI  a perpendicular  from  B , meeting  Dl 
in  j ; then  will  Bj  be  an  equivalent  vertical  projection,  or 
trace,  of  BD.  The  angle  DBJ  equals  the  angle  LDI  — cp. 
The  distance  Bj  = hx  equals  the  distance  BD  (—h)  into  the 
cosine  of  the  angle  DBj  — h cos  </>. 


h 2 

The  direct  liquid  pressure  Px  upon  Bj  equals  D-  w2  = 

d 


-D  W 
Px  =z  W2-„-  cos 


(24) 


and  the  pressure  upon  BD  in  the  same  direction  is 


h2 

= w2  cosa  <P, 
d 


and  its  maximum  resultant  has  a direction  parallel  with 
ID,  and  meets  Bj  at  one-third  the  height  jB,  in  m,  and  BD 
at  one-third  the  height  DB,  in  Px. 

The  horizontal  pressure  effect  xx  upon  the  wall  BD,  is 

xx  — Pj  cos  (p  = w2  \ cos3  <p  = (25) 

102 

130  lbs.  x ~ x .6495  = 6079.32  lbs.  = 3.036  tons. 
d 

The  maximum  moment  of  liquid  pressure  leverage  L: 
of  the  infinite  surcharged  fill  tending  to  overturn  the  wall 
around  its  toe,  equals  xx  into  one-third  the  height  BD. 


T h l « 3 A a 

Di  = xx  — = — cos *<p)  x — = 

19  ft 

3.036  tons  x —7.—  — 12.14  tons. 


(26'1 


3 


RESISTANCE  OF  MASONRY  REVETMENTS. 


417 


419.  Resistance  of  Masonry  Revetments. — The 

elements  of  stability  of  a revetment  that  enables  it  to  sus- 
tain the  thrust  of  an  earth-filbug  behind  it,  are  identical 
with  those  we  have  already  examined  (§  401),  that  enable 
it  to  sustain  a pressure  of  water. 

There  must  be  sufficient  weight,  W}  to  give  it  frictional 
stability,  8,  and  the  profile  must  be  adjusted  so  that  with 
the  given  weight  the  mass  shall  have  the  requisite  moment 
M of  weight  leverage,  with  an  ample  coefficienty  of  safety, 
to  resist  the  thrust  of  the  earth-filling,  at  its  maximum. 

The  weight  of  wall  above  any  given  horizontal  plane 
between  B and  D (Fig.  77)  equals  the  area  of  the  section 
above  that  plane  in  square  feet,  into  the  weight  of  a cubical 
foot  of  the  materials  of  the  wall  (§  398), 

= W=  Aw. 

The  frictional  stability , S,  of  the  wall  at  the  given  hori- 
zontal plane,  that  has  to  resist  the  horizontal  pressure  of 
the  earth  filling,  equals  the  weight  of  masonry  above  that 
plane,  plus  the  vertical  downward  pressure  of  any  water 
that  may  rest  upon  its  front  batter  (BJC,  Fig.  80),  less  the 
vertical  resultant  of  upward  pressure  beneath  the  plane  or 
in  the  bed-joints,  and  into  the  coefficient  of  friction  of  the 
given  section  upon  its  bed  (§  398), 

8 = ( TF  + e — cxz j) . c. 

The  moment  of  weight  leverage  of  the  wall  that  has  to 
resist  the  overturning  tendency  of  the  earth-thrust,  equals 
the  weight  of  the  masonry  above  the  given  plane  into  the 
horizontal  distance  of  the  centre  of  gravity  of  the  masonry 
from  the  toe,  or  fulcrum,  over  which  the  thrust  tends  to 
revolve  it  (§  402), 


27 


M — Awd. 


418 


PARTITIONS,  AND  RETAINING  WALLS. 


In  tliese  equations : 

W is  the  weight  above  the  given  plane. 

S “ “ frictional  stability  of  the  given  section. 

M “ “ moment  of  weight  leverage  of  the  given  section. 
e “ “ vertical  downward  water  pressure  resultant. 

Z\  “ “ vertical  upward  water  pressure  resultant. 

<?!  “ “ ratio  of  effective  vertical  upward  water  pressure. 
c “ “ coefficient  of  friction  of  the  given  section  upon 
its  bed. 

The  moment  of  weight  leverage  of  the  wall  must,  for  a 
safe  coefficient  of  stability,  be  equal  to  double  the  moment 
of  pressure  leverage  of  the  earth  fill ; that  is,  for  a level  fill 
we  must  at  least  make 

Awd  . , n , h 

— = — = A2w2  tan.  0 cos.  <f> 

/y  O 

and  for  a surcharged  fill. 


Awd 

~¥~ 


= A2w2  tan.  6 cos.  <p  ( rji ), 


and  a like  margin  of  frictional  stability  should  be  secured. 

420.  Final  Resultants  in  Revetments. — The  height 
of  the  wall  (Fig.  79)  is  the  same,  by  scale,  as  the  wall  in 
Fig.  77,  whose  reactions  to  sustain  the  level  and  surcharged 
fills  we  have  investigated. 

The  back  of  the  wall  (Fig.  79)  is  vertical,  and  the  hori- 
zontal earth-thrusts  against  it  are  as  before  computed— viz., 
1.45  tons  for  the  level  till,  and  2.03  tons  for  the  surcharged 
fill.  Draw  these  horizontal  earth-thrust  resultants  to  the 
left  from  a vertical  line  passing  through  the  centre  of  gravity 
of  the  masonry,  in  their  respective  directions  and  at  their 
respective  altitudes.  Draw  in  the  vertical  line  the  vertical 
weight  resultant  of  the  masonry  in  PK:  complete  the  paral- 
lelogram PK0_x ; then  will  the  diagonal  P02  represent,  in 


TRAPEZOIDAL  REVETMENTS. 


419 


magnitude  and  direction,  the  resultant  effect  of  the  level  fill 
LDBJ. 

Draw  the  vertical  weight  resultant  of  masonry,  also,  in 
P3e>,  and  complete  the  parallelogram  P^Mx% ; then  will  the 
diagonal  P?M  represent,  in  magnitude  and  direction,  the 
resultant  effect  of  the  surcharged  fill  LDBF. 

The  comparative  thrust  effects  of  the  level  and  sur- 
charged fills  upon  the  masonry  are  shown  by  the  positions 
of  the  respective  final  resultants,  and  the  comparative  re- 
sistances of  the  wall  against  each,  by  the  distances  from 
C,  at  which  their  directions  cut  the  plane  CP. 


Fig.  79. 


431.  Table  of  Trapezoidal  Revetments. — The  fol- 
lowing table  of  dimensions  of  walls,  to  sustain  earth,  in 
which  the  sections  are  trapezoidal,  and  face  batters  limited 
to  two  inches  per  foot  rise,  is  adapted  for  walls  to  sustain 
gradings  about  pump-houses,  reservoir-grounds,  etc.,  and 
will  give  approximate  dimensions  for  plotting  trial  sections 
when  it  is  desired  to  resolve  the  profile  into  other  forms. 


420 


PARTITIONS,  AND  RETAINING  WALLS. 


TABLE  No.  88. 

Approximate  Dimensions  of  Walls  to  Sustain  Earth. 

For  granite  rubble,  walls,  in  mortar,  of  specific  gravity  2.25,  or  weight  140  pounds 
per  cubic  foot,  to  retain  earth  level  with  the  top  of  the  wall. 


Height  of  wall, 
in  feet. 

Top  breadth  of 
wall,  in  feet. 

Face  batter  of 
wall,  in  inches 
per  foot  rise. 

Base  breadth  of 
wall  at  lower  earth 
surface,  in  feet. 

Thickness  of  a 
vertical  rectangular 
wall,  in  feet. 

4 

3-° 

O 

3-° 

3-° 

5 

3-o 

O 

3° 

3-o 

6 

3-o 

O 

3-o 

3-o 

7 

3-o 

O 

3-25 

3-5° 

8 

3 • 0 

2 

3-83 

4.00 

9 

3-33 

It 

4-83 

4 25 

10 

3-33 

5.0° 

4-5° 

11 

3-5 

li 

5-25 

5.00 

12 

3-5 

2 

5-67 

5-5° 

13 

3-5 

2 

6-33 

5 83 

14 

3-5 

2 

7 .00 

6.25 

15 

3-5 

2 

7-5° 

6-75 

16 

4.0 

2 

8.00 

7-25 

17 

4.0 

2 

8.67 

7 ■ 75 

18 

5-° 

2 

9.00 

8.25 

19 

5-o 

2 

9-5° 

8-75 

20 

5-° 

2 

9.87 

9.00 

21 

5.0 

2 

10.50 

9. 50 

22 

5 -° 

2 

11 .00 

10.25 

23 

5 ° 

2 

n-33 

10.50 

24 

5-° 

2 

11.78 

io-75 

It  will  rarely  be  advisable  to  reduce  tlie  top  thicknesses 
given  in  the  table,  with  a view  only  to  economizing  ma- 
terial lest  the  top  courses  be  too  light  to  withstand  the 
variety  of  shocks  to  which  they  will  be  liable,  and  which 
are  not  recognized  in  the  common  formulas. 

Several  eminent  professors  who  have  written  upon  the 
theory  of  retaining  walls,  give  formulas  for  determining  their 
proportions ; but  such  formulas  usually  give  too  small  top 
breadths,  for  practical  adoption,  for  low  walls,  and  objec- 
tionably great  top  breadths  for  high  walls. 


CURVED  FACE— BATTER  EQUATION, 


421 


Each  class  of  wall  has  its  own  most  convenient  top 
breadth,  which  remains  nearly  constant  through  a large 
range  of  height. 

Common  uncoursed  rubble  walls  of  granite,  laid  dry, 
should  be  increased  from  the  above  dimensions  six  inches 
in  the  top  breadth  and  thirty-three  per  cent,  in  the  bottom 
breadth.  If  the  level  earth-filling  behind  the  wall  is  to  be 
loaded,  or  subject  to  traffic,  the  weight  and  leverage  resist- 
ance of  the  wall  are  to  be  increased  accordingly. 

The  thrust  of  the  filling  material  behind  a retaining  wall, 
upon  the  wall,  will  be  lessened  if  the  filling  next  the  wall 
is  spread  in  thin  horizontal  layers  and  well  settled,  instead 
of  being  allowed  to  slope  against  it,  as  it  falls  at  the  head 
of  a dump. 

422.  Curved  Face — Batter  Equation. — When  it  is 
desired  to  give  to  the  face  a curve,  the  back  being  perpen- 
dicular, and  the  top  breadth  constant,  the  following  equa- 
tion will  assist  in  determining  ordinates  at  any  given  depths 
for  plotting  a trial  section  (vide  § 392,  p.  387). 

Let  b be  the  assumed  top  breadth,  and  l the  thickness 
at  any  given  depth  d , then 

t = b + .075  Vd\  (27) 

For  illustration,  assume  the  top  breadth  not  less  than 
3.5  feet ; then  for  several  given  depths,  from  0.0  to  30  feet, 
we  have  ordinates,  or  thicknesses,  as  given  in  Table  No.  89. 

Upon  the  curve  thus  obtained,  steps  may  be  laid  off  with 
either  vertical  or  battered  risers. 

Tests  with  the  equation  for  moment  of  leverage  stability, 
will  determine  whether  the  risers  may  cut  the  curve,  or  if 
the  inner  angle  of  tread  and  riser  shall  lie  in  the  curve. 

A slight  increase  or  reduction  of  the  top  breadth,  or  of 
the  fractional  multiplier,  will  increase  or  reduce  the  wall- 
section,  as  desired. 


422 


PARTITIONS,  AND  RETAINING  WALLS. 


TABLE  No.  89. 

Thickness  at  Given  Depths  of  a Curved  Face  Wall. 


Depths. 

Thickness. 

Feet. 

(6.)  .075  \/d? 

Feet. 

0 

3-5  H-  = 

3-5° 

4 

3-5  + -6  = 

4.10 

6 

3.5  + X.IO  = 

4.60 

8 

3.5  + 1.69  = 

5-*9 

10 

3-5  + 2-37  - 

5-8? 

12 

3.5  + 3.12  = 

6.62 

r5 

3.5  + 4.36  = 

7.86 

20 

3.5  + 6.71  — 

10.21 

25 

3-5  + 9-38  - 

12.88 

3° 

3-5  + I2-32  = 

15.82 

423.  Back  Batters,  and  their  Equations. — When 
for  practical  or  other  reasons  there  is  objection  to  giving  all 
the  batter  to  the  front  of  the  wall,  and  a portion  of  it  is 
placed  upon  the  back,  then  it  is  usually  arranged  in  a 
series  of  offsets  or  steps  BDX , Fig.  80. 

In  such  case,  the  weight  of  the  triangle  of  earth  BJ)[  B 
may  be  assumed  to  be  supported  entirely  by  the  wall,  and 
as  producing  no  lateral  thrust  upon  the  wall.  This  triangle 
increases  the  weight  leverage  of  the  wall,  and  moves  its 
weight  resultant  farther  back  from  the  toe  C. 

Find  the  centre  of  gravity  of  the  masonry,  in  g,  and  find 
the  centre  of  gravity  of  the  triangle  of  earth,  in  g2 ; then  will 
the  centre  of  gravity  of  the  two  united  bodies  be  in  G. 

Let  LDJ  be  the  natural  frictional  angle  of  the  material. 
Bisect  the  angle  IDXB2  by  the  plane  T\F ; then  we  may 
assume  the  trapezium  T)x  B2FX  F to  be  that  portion  of  the 
earth-filling  that,  considered  alone,  will  produce  the  maxi- 
mum thrust  effect  upon  the  Avail,  and  its  horizontal  and 
leverage  effects  may  be  computed  by  equations  21  and  23. 


INCLINATION  OF  FOUNDATION. 


423 


Fig.  80. 


Prof.  Moseley’s  equation55  for  the  maximum  pressure  of 
a surcharge  similar  to  this  is 

Px  z=  ±w2  \Jix  sec  <p  — (hi*  tan2  </>  + C22)1}2,  (28) 

in  which  c2  is  the  height  B2c2. 

Pv  “ maximum  pressure  of  the  earth. 

w2  “ weight  of  one  cubic  foot  of  earth. 

7i\  1 vertical  distance  Pxc2. 

<f>  11  frictional  angle  of  the  earth. 

424.  Inclination  of  Foundation.  — The  frictional 
stability  of  a wall  upon  its  foundation  is  materially  in- 


* Mechanics  of  Engineering,  p.  426.  Van  Nostrand,  New  York,  1860. 


424 


PARTITIONS,  AND  RETAINING  WALLS. 


creased,  and  its  pressure  is  more  evenly  distributed  upon 
the  foundation  stratum,  if  an  inclination  is  given  to  the  bed 
nearly  at  right  angles  to  the  final  thrust  resultant,  as  in 
Fig.  80.  Bed-joints  may  often  be  similarly  inclined  with 
advantage. 

A sliding  motion  in  such  case  involves  the  additional 
work  of  lifting  the  whole  weight  up  the  inclined  plane. 

425.  Front  Batters  and  Steps.— Masons  experience 
a very  considerable  difficulty  in  laying  the  face  of  nibble 
walls  with  batters  exceeding  two  inches  to  the  foot,  and 
often  with  batters  exceeding  one  and  one-half  inches  to  the 
foot,  unless  with  stones  from  a quarry  where  the  transverse 
cleavage  varies  several  degrees  from  a perpendicular  to 
the  rift. 

The  difficulty  is  increased  when  the  bed-joints  of  the 
work  are  level  from  front  to  rear,  as  the  workmen  prefer  to 
make  them. 

it  is  especially  troublesome  to  the  workmen,  and  expen- 
sive as  well,  to  make  face-batters  of  high  walls  conform  to 
the  theoretical  curved  batters  deduced  from  the  logarithmic 
equations. 

It  is  better,  therefore,  to  transpose  the  curve  into  a series 
of  steps  when  its  tangent  inclination  exceeds  two  inches  to 
the  foot,  in  which  case  the  steps  may  have  equal  heights 
and  varying  projections,  as  in  Fig.  81,  which  is  a revetment 
upon  a navigable  river,  or  may  have  both  varying  rise  and 
projection,  with  batter  upon  the  rise,  as  in  the  weir.  Fig.  72. 

426.  Top  Breadths. — The  thickness  at  the  top  of  a 
revetment  should  in  all  cases  be  sufficient,  so  that  its  weight 
will  be  able  to  resist  the  frost  expansion  thrust  of  the  sur- 
face layers  of  the  earth.  Sometimes  a batter  is  given  to  the 
back  of  the  wall,  three  or  four  feet  down  from  the  top.  to 
enable  the  earth  to  expand  readily  in  a vertical  direction, 


26— FEET. 


TOP  BREADTHS. 


425 


and  thus  act  with  less  force  horizontally  against  the  backs 
of  the  cap-stones. 

An  increased  thickness  at  the  top  of  the  wall,  and  at  all 
points  of  depth,  is  also  necessary  when  the  filling  is  liable 
to  be  loaded  with  construction  materials,  fuel,  merchandise, 

Fig.  81. 

E 


or  other  weights,  or  if  it  is  to  sustain  traffic  of  any  kind. 
The  additional  weight  may  in  such  case  be  considered 
equivalent  to  a surcharge  weight,  and  the  centre  of  gravity 
of  the  filling  and  of  the  additional  weight  will  be  resolved 
into  their  united  centre  of  gravity  and  the  vertical  resultant 


426 


PARTITIONS,  AND  RETAINING  WALLS. 


be  considered  as  passing  through  this  new  centre  of  gravity. 
The  new  horizontal  thrust  resultant  will  then  act  upon  the 
wall  at  a greater  altitude,  and  with  greater  leverage  than 
the  horizontal  resultant  of  filling  alone  (§  416),  as  has 
been  already  demonstrated. 

In  the  cases  of  discharge  weirs  the  floods  are  considered 
as  surcharge  weights,  and  not  only  the  depth  of  water 
behind  the  weir  and  upon  its  crest  is  to  be  considered,  but 


Fig.  82. 


the  additional  height  to  which  the  velocity  of  approach  of 
the  water  is  due. 

If  there  is  but  one  or  two  feet  depth  of  water  flowing 
over,  then  the  cap-stones  may  be  subject  to  the  blows  of 
logs,  cakes  of  ice,  and  such  debris  as  the  floods  gather. 

427.  Wliarf  Walls. — When  a wall  is  to  be  generally 


ELEMENTS  OF  FAILURE. 


427 


nsed  for  wharf  purposes,  its  face  should  be  protected  by 
fender  piles,  both  for  its  own  advantage  and  that  of  the 
vessels  that  lie  alongside. 

Fig.  82  illustrates  the  method  of  piling  and  capping, 
adopted  by  the  writer,  in  an  extensive  wharf -pier  of  one- 
half  mile  frontage  in  one  of  the  deep  harbors  upon  the  New 
England  coast.  The  caps  are,  in  this  case,  dressed  dimen- 
sion stones,  three  and  one-lialf  feet  wide  and  one  foot  thick. 
The  wharf  log  is  made  up  of  12”  x 10"  and  12"  x 8"  hard 
pitch  pine,  placed  one  upon  the  other  so  as  to  break  joints, 
and  tre-nailed  together.  The  anchors  of  the  pile-heads  pass 
through  the  cap-log,  and  their  bolts  pass  through  the  cap- 
stones into  headers  specially  placed  to  receive  them.  The 
piles  are  placed  eight  feet  between  centres,  and  each  fourth 
pile  extends  above  the  log  for  a belay  pile.  Waling 
pieces  of  6 ' x 12"  hard  pine  are  fitted  between  the  pile-heads, 
and  spiked  to  the  face  of  the  cap-log  to  confine  the  pile- 
heads  rigidly  in  place.  Midway  between  the  belay  piles 
are  belay  rings,  whose  bolts  pass  through  the  cap-logs  into 
headers,  and  are  also  anchored  by  straps  to  cap-stones. 

428.  Counter-forted  Walls. — There  is  so  rarely  an 
economic  advantage  in  counter-forting  a wall,  except  in 
those  cases  of  brick  walls  where  the  counter-fort  may  take 
the  form  of  a buttress  upon  the  exterior  face,  that  we  shall 
not  here  devote  space  to  their  special  theoretical  investiga- 
tion, which,  by  graphical  analysis,  is  a simple  reapplication 
of  the  principles  already  laid  down. 

429.  Elements  of  Failure. — In  our  theoretical  inves- 
tigation of  the  resistances  of  masonry  to  sliding  or  overturn- 
ing we  have  supposed  the  walls  to  be  laid  in  mortar  and 
solid,  and  well  bonded,  so  that  the  mass  was  practically 
one  solid  piece,  considered  as  one  foot  long. 

If  any  given  foot  of  length,  considered  alone  as  a unit 


428 


PARTITIONS,  AND  RETAINING  WALLS. 


of  length,  is  found  stable,  and  each  other  foot  is  equal  to  it, 
then  evidently  the  whole  length  will  be  stable. 

The  joints  from  front  to  rear  in  cut  and  lirst-class  rubble 
walls  are  usually  laid  level,  and  the  workmen  intend  to  give 
a good  bond  of  one  course  upon  another.  When  consider- 
ing the  leverage  stability  of  a high  wall,  at  the  respective 
joints,  working  from  top  downward,  we  usually  treat  the 
joints  as  horizontal  planes.  Let  us  turn  again  to  the  sketch 
of  the  partition  wall,  Fig.  76,  which  has  joints  laid  off  upon 
it  showing  an  average  class  of  rubble  work.  Suppose  the 
water  to  be  drawn  off  from  the  side  EC,  and  the  full  water 
upon  the  opposite  side  to  be  freezing,  and  the  ice  exerting  a 
thrust  upon  the  upper  courses  of  the  wall.  We  investigate 
the  leverage  stabilty  at  the  joint  jj\,  and  find  that  it  will 
resist  a considerable  leverage  strain,  which  for  further  illus- 
tration we  assume  to  be  ample.  Examining  critically  the 
building  of  the  wall,  we  find  that  jj\  is  not  the  real  joint, 
and  j\  the  fulcrum  to  be  considered  in  connection  with 
pressure  upon  Bj,  but  in  consequence  of  faulty  workman- 
ship, jjiji  is  the  zigzag  joint  and  the  fulcrum,  and  that 
the  joint,  instead  of  being  horizontal,  is  an  equivalent  in- 
clined plane  on  which  the  wall  is  quite  likely  to  yield  by 
slipping  slightly  with  each  extra  lateral  strain  put  upon  it. 

If  in  a high  and  long  wall  such  weaknesses  are  repeated 
several  times,  the  result  will  be  a bulge  upon  the  face  of 
the  wall,  ordinarily  reaching  its  maximum  at  about  one- 
third  the  height  of  the  wall,  the  portion  above  that  level 
appearing  to  have  been  moved  bodily  forward,  and  retain-  • 
ing  nearly  its  true  batter. 

When  walls  are  so  high  as  to  require  a thickness  in  a 
considerable  portion  of  their  height  exceeding  seven  or 
eight  feet,  careless  wall-layers,  who  are  not  entitled  to  the 
honorable  name  mechanic , often  pile  up  an  outside  and 


FACED,  AND  CONCRETE  REVETMENTS. 


429 


inside  course,  and  fill  in  the  middle  with  their  refuse  stone, 
thus  producing  a miserable  structure,  especially  if  it  is  dry 
rubble,  that  is  almost  destitute  of  leverage  stability,  unless 
a great  surplus  of  stone  is  put  into  the  wall  sufficient  to 
resist  the  thrust  of  an  earth-backing  by  compounded  weight 
alone. 

Short  walls  supported  at  each  end  may  by  such  trans 
verse  motion  be  brought  into  an  arched  form,  concave  to 
the  pressure,  but  at  the  same  time  into  a state  of  longitudi- 
nal tension  that  will  assist  in  preventing  further  motion. 

If  there  is  the  least  transverse  motion  in  a mortared  wall 
sustaining  water,  the  masonry  ceases  from  that  instant  to 
be  water-tight,  and  if  the  stones  are  in  the  least  disturbed 
on  their  bed  after  their  mortar  has  begun  to  set,  the  wall 
will  never  be  tight. 

430.  End  Supports. — Well  constructed  short  walls, 
supported  at  each  end,  such  as  gate-chamber  and  wheel-pit 
walls,  have  an  appreciable  amount  of  that  transverse  resist- 
ance prominently  recognized  in  a beam,  which  permits 
their  sections  to  be  reduced,  an  amount  dependent  on  the 
effective  value  of  such  transverse  support.  The  supported 
ends  of  long  walls  transmit  the  influence  of  the  support  in  a 
decreasing  ratio,  out  to  some  distance  from  the  supports, 
and  walls  whose  ends  abut  upon  inclines,  as  in  the  case  of 
stone  weirs  across  valleys,  may  be  reduced  in  thickness, 
ordinarily,  at  the  top  and  through  their  whole  height,  as 
the  height  reduces. 

431.  Faced,  and  Concrete  Revetments. — Walls  on 
deep  water-fronts,  as  in  Fig.  81,  for  instance,  when  laid 
within  coffer-dams,  are  often  faced  with  coursed  ashler 
having  dressed  beds  and  builds,  and  backed  up  with  either 
rubble-work  laid  in  mortar,  or  with  concrete,  the  headers  of 
the  ashler  being  intended  to  give  the  requisite  bond  between 


430 


PARTITIONS,  AND  RETAINING  WALLS. 


the  two  classes  of  work.  Much  care  must  be  exercised  in 
sucli  composite  work,  lest  the  unequal  settlement  of  the 
different  classes  of  work  entirely  destroy  the  effective  bond 
between  them  and  thus  lead  to  failure. 

Such  walls  have  been  constructed  with  perfect  success 
without  coffer-dams,  of  heavy  blocks  of  moulded  beton,  and 
also  successfully  by  depositing  concrete  in  place  in  the  wall, 
under  water,  with  the  assistance  of  a caisson  mould,  or 
sheet-pile  mould,  thus  forming  a monolithic  revetment. 

Foundations  under  water  to  receive  masonry  structures 
have  also  been  successfully  placed  by  the  last-mentioned 
system. 

Concrete  structures  under  water  laid  without  coffers, 
however,  demand  the  exercise  of  a great  deal  of  good  judg- 
ment, educated  both  in  theory  and  by  practice,  and  admit 
only  of  the  most  faithful  workmanship. 


Fig.  83. 


Fig.  84. 


CONDUIT  SECTIONS. 


CHAPTER  XX. 

i 

MASONRY  CONDUITS. 

432.  Protection  of  Channels  for  Domestic  Water 
Supplies. — The  observations,  sound  reasonings,  and  good 
judgments  that  influence  municipalities  to  seek  and  secure 
the  most  wholesome1  and  coolest  waters  for  their  domestic 
uses,  compel  them  also  to  guard  the  purity  and  maintain 
the  equable  temperature  of  the  waters  as  they  flow  to  the 
point  of  distribution. 

The  larger  cities,  with  few  exceptions,  must  lead  their 
waters  in  artificial  conduits,  from  sources  in  distant  hills, 
where  neither  the  soils  nor  atmosphere  are  tainted  by 
decompositions  such  as  are  always  in  progress  in  the  midst 
of  large  concourses  of  human  beings  and  animals. 

Such  long  water-courses  ought  to  be  paved  or  revetted, 
or  their  currents  will  be  impregnated  with  the  minerals 
over  which  they  flow,  and  will  cut  away  their  banks  where 
the  channels  wind  out  and  in  among  the  hills.  An  arch  of 
masonry  spanning  from  wall  to  wall  is  then  the  most  sure 
protection  from  inflowing  drainage,  the  approach  of  cattle 
and  vermin,  the  heating  action  of  the  summer  sun,  and  the 
growth  of  aquatic  plants  in  too  luxuriant  abundance. 

433.  Examples  of  Conduits. — When  proper  grades 
are  attainable  to  permit  the  waters  to  flow  with  free  sur- 
faces, such  conduits,  requiring  more  than  six  or  eight  square 
feet  sectional  area  are  usually,  and  most  economically,  con- 
structed of  hydraulic  masonry. 


432 


MASONRY  CONDUITS. 


Figures  83  to  89  illustrate  some  of  the  forms  adopted  in 
American  masonry  conduits. 

Fig.  87  is  a section  of  the  Croton  conduit,  at  a point 
where  it  is  raised  upon  embankment.  This  conduit  is  7 -5" 
wide  and  8 -5J"  high,  and  conveys  from  Croton  River  to  the 
distributing  reservoir  in  Central  Park,  New  York  city, 
about  one  hundred  million  gallons  of  water  daily.  The 
combined  length  of  conduit  and  of  siphons  between  Croton 
Dam  and  Central  Park  is  about  thirty-eight  miles,  and  they 
were  completed  in  1842. 

Fig.  88  is  a section  of  the  Washington  conduit,  which  is 
circular,  of  9 feet  internal  diameter.  This  leads  water  from 
a point  in  the  Potomac  River  about  sixteen  miles  from  the 
capital,  to  a distributing  reservoir  in  Georgetown,  from 
whence  the  water  is  led  to  the  Government  buildings  and 
grounds,  and  throughout  the  City  of  Washington,  in  iron 
pipes.  This  conduit  was  constructed  in  1859. 

Fig.  84  is  a section  of  the  Brooklyn,  L.  I.,  conduit  lead- 
ing the  waters  of  Jamaica  and  other  ponds  to  the  basin  ad- 
joining the  well  of  the  Ridgewood  pumping-engines.  This 
conduit  increases  in  dimensions  at  points  where  its  volume 
of  flow  is  augmented  from  8-2"  wide  to  10-0"  wide,  and  to 
a maximum  height  of  8 -8".  It  was  constructed  in  1859. 

Fig.  86  is  a section  of  the  Charlestown,  Mass.,  conduit, 
leading  the  water  of  Mystic  Lake  to  the  well  of  the  Mystic 
pumping-station.  This  conduit  is  5-0  wide  and  5-8  high, 
and  was  constructed  in  1864. 

Fig.  85  is  a section  of  the  Lowell,  Mass.,  conduit,  of 
4-3"  diameter.  This  leads  water  from  a subterranean 
infiltration  gallery  along  the  margin  of  the  Merrimack 
River,  a short  distance  above  Lowell,  a portion  of  the  dis- 
tance to  the  pumping-station.  It  was  constructed  in  1872. 

Fig.  89  is  a section  of  the  second  Chicago  tunnel,  extend- 


FOUNDATIONS  OF  CONDUITS. 


433 


ing  under  Lake  Michigan  two  miles  from  the  shore  to  the 
lake  crib,  and  underneath  the  city  to  the  side  opposite  to 
the  shore  of  the  lake.  It  is  7 -0''  wide  and  7-2"  high  in  the 
clear.  The  masonry  of  this  tunnel  consists  of  three  rings  of 
brickwork,  the  two  inner  of  which  have  the  sides  of  their 
bricks  in  radial  lines,  and  the  outer  having  its  sides  of 
brick  at  right  angles  to  radial  lines.  This  tunnel  was  com- 
pleted in  1874. 

Fig.  83  is  a section  of  the  Boston  conduit,  commenced  in 
1875,  to  lead  an  additional  supply  from  Sudbury  River  to 
the  Chestnut  Hill  reservoir.  Its  length  is  sixteen  and  one- 
half  miles,  its  width  9'-0",  and  height  7-8". 

The  new  Baltimore  conduit,  as  in  progress  in  1876,  is  to 
be  36,495  feet  in  length,  entirely  in  tunnel,  extending  from 
Gunpowder  River  to  the  receiving  reservoir.  The  portions 
lined  with  masonry  are  circular  in  section,  of  12  feet  clear 
diameter.  The  inclination  is  1 in  5000,  and  the  anticipated 
capacity  about  170,000,000  gallons  per  24  hours. 

The  Cochituate  conduit  of  the  Boston  water  supply  is 
5 feet  wide,  6 -4"  high,  of  oviform  section,  and  has  an  incli- 
nation of  3£  inches  to  the  mile.  Its  capacity  is  16,500,000 
gallons  per  24  hours. 

434.  Foundations  of  Conduits. — The  foundations  of 
masonry  conduits  must  be  positively  rigid,  since  the  super- 
structures are  practically  inelastic,  and  any  movement  is 
certain  to  produce  rupture.  A crack  below  the  water-line 
admits  water  into  the  foundation,  and  tends  to  soften  or 
undermine  the  foundation,  and  to  further  settlement,  and 
to  additional  leakage.  So  long  as  the  foundation  yields, 
the  conduit  cannot  be  maintained  water-tight,  for  the  set- 
tling away  of  the  support  at  any  point  results  in  an  undue 
transverse  strain  upon  the  shell,  and  the  adhesion  of  the 
mortar  to  the  masonry  is  overcome  and  the  work  cracks. 

28 


434 


MASONRY  CONDUITS. 


435.  Conduit  Shells.  — A perfect  shell  should  have 
considerable  tensile  strength  in  the  direction  of  its  circum- 
ference ; but  when  a longitudinal  crack  is  produced  its 
tensile  strength  is  destroyed  at  that  point,  and  cannot  again 
be  fully  restored  except  by  rebuilding. 

When  the  side  walls  are  of  rubble  masonry  they  are 
usually  lined  with  a course  of  brick-work  laid  in  mortar,  or 
with  a smooth  coat  of  hydraulic  cement  mortar.  The  bot- 
toms are  frequently  lined  with  a nearly  flat  invert  arch  of 
brick. 

All  the  materials  and  workmanship  entering  into  this 
class  of  structures  should  be  of  superior  quality. 

436.  Ventilation  of  Conduits.— Conduits  of  form  and 
construction  similar  to  those  above  illustrated  are  usually 
proportioned  so  that  they  are  capable  of  delivering  the  max- 
imum volume  of  water  required  when  flowing  about  two- 
thirds  full.  Provision  is  then  made  for  the  free  circulation 
of  a stratum  of  air  over  the  water  surface  and  beneath  the 
covering  arch. 

Fig.  90.  Fig.  91. 


Figs.  90  and  91  illustrate  the  form  of  ventilating  shaft 
and  cover  used  upon  the  New  Bedford,  Mass.,  conduit. 


CONDUITS  UNDER  PRESSURE 


435 


These  shafts  may  he  used  also  for  man-hole  shafts,  which 
are  required  at  frequent  intervals  for  inspection  and  care  of 
the  conduit. 


Fig.  92. 


437.  Conduits  under  Pressure.— Fig.  92  illustrates  a 
conduit  of  locked  bricks,  designed  by  the  writer  to  convey 
water  under  pressure.  The  specially  moulded  bricks  are 
eight  inches  long  and  eight  inches  wide  and  two  and  one- 
half  inches  thick.  They  have  upon  one  side  a mortise  six 
inches  long,  four  and  one- quarter  inches  wide,  and  one-half 
inch  deep,  and  upon  the  opposite  side  two  tenons,  each 
matching  in  form  a half  mortise.  When  the  bricks  are  laid 


436 


MASONRY  CONDUITS. 


in  the  shell  the  tenons  at  the  adjoining  ends  of  two  "bricks 
fill  the  mortise  in  the  brick  over  which  the  joint  breaks. 

In  brick  conduits  as  usually  constructed  the  bricks  have 
their  greatest  length  in  a longitudinal  direction,  but  here  the 
length  is  in  circumferential  direction.  The  object  here  is  to 
utilize  to  the  fullest  extent  the  tensile  bonding  strength  of 
the  masonry,  and  then  to  reinforce  this  strength  by  inter- 
locking the  bricks  themselves.  The  conduit  cannot  be  rup- 
tured by  pressure  of  water  without  shearing  off  numerous 
tenons  in  addition  to  overcoming  the  cohesive  strength  of 
the  masonry. 

This  system  permits  of  vertical  undulations  in  the  grade 
of  the  conduit  within  moderate  limits,  and  reduces  mate- 
rially the  amount  of  lift  of  the  conduit  required  upon  em- 
bankments. 

Upon  long  conduits  it  permits  the  insertion  of  stop-gates 
and  the  examination  and  repair  of  any  one  section  while 
the  other  sections  remain  full  of  water.  Also  when  of 
a given  sectional  area  and  flowing  full,  and  delivering 
to  a pump-well  or  directly  into  distribution-pipes  a given 
volume  of  water,  it  transfers  more  of  the  pressure  due 
to  the  head  than  the  usual  form  of  construction  of  like 
sectional  area,  and  thus  reduces  the  lift  of  the  pump  or 
increases  the  head  upon  the  distribution.  This  is  more 
especially  the  case  when  the  consumption  is  less  than  the 
maximum. 

438.  Protection  from  Frost. — The  masonry  of  con- 
duits must  be  fully  protected  from  frost,  or  its  cement 
mortar  will  be  seriously  disintegrated  by  the  freezing  and 
expansion  of  the  water  filling  its  pores.  The  frost  coverings 
are  usually  earthen  embankments,  of  height  above  the  top 
of  the  masonry  equal  to  the  greatest  depth  to  which  frost 
penetrates  in  the  given  locality.  The  level  breadth  of  the 


MASONRY  TO  BE  SELF-SUSTAININO. 


437 


top  of  the  embankment  should  equal  the  breadth  of  the 
conduit,  and  the  side  slopes  be  not  less  than  1-|-  to  1. 

43J>.  Masonry  to  be  Self-sustaining. — When  the 
conduit  is  in  part  or  wholly  above  ground  surface,  its  ma- 
sonry should  be  self-sustaining  under  the  maximum  pres- 
sure, indepeudent  of  any  support  that  may  be  expected 
from  the  embanked  earth.  The  winds  of  winter  generally 
clear  the  embankments  very  effectually  of  their  snow  cover- 
ings, and  leave  them  exposed  to  the  most  intense  action 
of  frost. 

In  periods  of  most  excessive  cold  weather  the  entire  em- 
bankment may  be  frozen  into  a solid  arch,  and  by  expan- 
sion rise  appreciably  clear  of  the  masonry,  and  possibly 
exert  some  adhesive  pull  upon  the  liances  of  the  arch.  If 
the  conduit  is  then  under  full  pressure,  and  not  wholly 
independent  of  earth  support,  a change  of  form,  and  rup- 
ture of  the  arch  may  result. 

Each  quadrant  of  the  covering  arch,  above  its  springing 
line,  exerts  a horizontal  thrust  at  the  springing  line  as  indi- 
cated in  Fig.  92  by  the  shorter  arrow,  and  the  water  pres- 
sure exerts  an  additional  horizontal  thrust,  as  indicated  by 
the  lower  arrow  in  Fig.  92.  When  the  conduit  is  just  even 
full,  the  point  of  mean  intensity  of  this  latter  pressure  is  at 
one-third  the  height  from  the  bottom  of  the  conduit. 

The  amount  of  horizontal  pressure  upon  each  side  in 
each  unit  of  length  is  equal  to  the  vertical  projection  of  the 
submerged  portion  of  that  side,  per  unit  of  length  into 
the  vertical  depth  from  free  water  surface,  of  the  centre  of 
gravity  of  the  submerged  surface,  into  the  weight  of  one 
cubic  foot  of  water ; the  depths  being  in  feet,  and  weight 
and  pressure  in  pounds. 

The  product  of  weight  of  backing  masonry  at  any  given 
depth  below  the  crown  of  the  arch  into  its  coefficient  of 


438 


MASONRY  CONDUITS. 


friction,  should  be  greater  than  the  sum  of  thrusts  at  that 
depth,  and  for  a safe  margin  to  insure  frictional  stability 
should  be  equal  to  double  the  sum  of  thrusts. 

The  backing  masonry  is  liable  to  receive  some  pull  from 

the  embankment,  if  one 
side  of  the  embankment 
settles  or  slides,  but  if  the 
foundations  of  the  sides  of 
the  embankments  are  rea- 
sonably firm,  the  earth  at 
the  sides  of  the  backings 
may  be  assumed  capable 
of  neutralizing  the  thrusts 
due  to  the  weight  of  cover- 
ing earth  upon  the  liances 
of  the  arch. 

440.  A Concrete  Conduit. — The  use  of  hydraulic 
concrete,  or  beton , is  at  present  being  more  generally  intro- 
duced into  American  hydraulic  constructions,  in  those 
localities  where  good  quarried  stones  are  not  readily  and 
cheaply  accessible,  than  has  been  practiced  in  years  past. 

Fig.  93  is  introduced  here  as  a matter  of  especial  interest, 
since  it  illustrates  the  form  of  a conduit  constructed  entirely 
of  beton,  in  the  new  Yanne  water  supply  for  the  city  of 
Paris.  This  conduit  is  two  meters  (6.56  feet)  in  diameter. 

The  beton  agglomere  of  this  conduit  is  a very  superior 
quality  of  hydraulic  concrete,  which  lias  resulted  from  the 
experiments  and  researches  of  M.  Francois  Coignet,  of  Paris. 

Gen.  Q.  A.  Gillmore  has  described*  in  Professional 
Papers,  Corps  of  Engineers,  U.  S.  Army,  No.  19,  the  mate- 
rials, compositions,  manipulations,  and  properties  of  this 


Fig.  93. 


* Report  on  Beton  Agglomere,  or  Coignet  Beton.  Washington,  1871. 


EXAMPLE  OF  CONDUIT  UNDER  HEAVY  PRESSURE.  439 


beton  in  a masterly  manner,  and  has  given  several  plates 
illustrating  some  of  the  magnificent  monolithic  aqueducts 
of  concrete,  spanning  valleys  and  quicksands,  in  the  great 
forest  of  Fontainebleau,  on  the  line  of  the  Vanne  conduit, 
between  La  Vanne  River  and  the  city  of  Paris. 

441.  Example  of  Conduit  under  Heavy  Pressure. 
—The  details  of  the  Penstock,  leading  water  from  the  canal 
above  referred  to  (§  382),  to  the  Manchester,  N.  II.,  turbines 
and  pumps,  are  shown  in  Fig.  94. 

This  penstock  is  six  hundred  feet  long,  and  six  feet  clear 
internal  diameter.  Its  axis  at  the  upper  end  is  under 
twelve  feet  head  of  water,  and  at  the  lower  end  under  thirty- 
eight  feet  head  of  water.  It  was  constructed,  in  place,  in  a 
trench  averaging  thirteen  feet  deep.  The  staves,  which  are 
of  southern  pitch-pine,  4 inches  thick,  were  machine-dressed 
to  radial  lines,  and  laid  so  that  each  stave  breaks  joint  at  its 
end  at  a distance  from  the  ends  of  the  adjoining  staves,  after 
the  usual  manner  of  laying  long  floors.  The  end-joints 
where  each  two  staves  abut  are  closed  by  a plate  of  flat 
iron,  one  inch  wide,  let  into  saw-kerfs  cut  in  the  ends  of  the 
staves  at  right  angles  to  radius.  Thus  a continuous  cylin- 
der is  formed,  except  at  the  two  points  where  changes  of 
grade  occur.  The  hoops  are  of  2|  x y-inch  rolled  iron,  each 
made  in  two  sections  with  clamping  bolts,  and  they  are 
placed  at  average  distances  of  eighteen  inches  between 
centres. 

Its  capacity  of  delivery  is  sixty-five  million  gallons  in 
twenty-four  hours,  with  velocity  of  flow  not  exceeding  four 
feet  per  second.*  It  was  completed  in  the  spring  of  1874, 
and  has  since  been  in  successful  use,  requiring  no  repairs. 
It  lies  in  a ground  naturally  moist,  and  sufficiently  satu- 

* This  penstock  is  more  fully  described  in  a paper  read  before  the  Ameri- 
can Society  of  Civil  Engineers  in  January,  1877.  Vide  Trans.,  March,  1877. 


VERTICAL«SEXTION 


CYLINDRICAL  WOODEN  PENSTOCK. 


MEAN  RADII  OF  CONDUITS. 


441 


rated  to  fully  protect  the  wood-work  from  the  atmospheric 
gases. 

The  city  of  Toronto,  Canada,  has  just  completed  a con- 
duit of  wood,  which  conveys  water  under  pressure  from  the 
filtering  gallery  on  an  island  in  Lake  Ontario,  opposite  to 
the  city,  about  7,000  feet,  to  the  pumping-station  on  the 
main  land.  The  internal  diameter  of  this  conduit  is  4 feet. 

442.  Mean  Radii  of  Conduits. — In  the  formula  of 
flow  for  open  canals  (§  323),  the  influence  of  the  air  pe- 
rimeter is  taken  into  consideration  in  establishing  the  value 

„ , , , , , . -j  t-w  sectional  area,  S 

of  the  hydraulic  mean  depth , r = r W — , and  a 

^ contour,  C 

fractional  portion  of  the  air  perimeter,  equal  to  its  propor- 
tional resistance,  is  added  to  the  solid  wet  perimeter. 

It  is  more  especially  necessary  that  the  resistance  of  the 
air  perimeter  be  recognized  in  conduits  partially  full.  As 
the  depth  of  water  increases  above  half-depth,  the  influence 
of  the  confined  air  section  is,  apparently,  inversely  as  the 
mean  hydraulic  radius  of  the  stream. 

If  we  compute,  for  circular  conduits,  values  of  r,  as  equal 

to  — j — section  — — we  pave  0 qeptb  r = 0d  ; at  one- 

wet  solid  perimeter  r 

fourth  depth,  r — .14734 d ; at  one-half  depth,  r = .2 5d ; at 
three-fourths  depth,  r = .30133 d ; and  at  full  depth,  r — .2 5d. 
This  series  gives  a maximum  value  of  r at  about  eight-tenths 
depth  and  a decrease  in  its  value  from  thence  to  full. 

The  relative  discharging  powers,  in  volume,  of  a circular 
conduit,  with  different  depths  of  water,  are  as  the  product 


when  S is  the  sectional  area  of  the  stream  ; r,  the 


mean  hydraulic  radius  ; and  m,  a coetficient. 

If  for  a given  series  of  depths,  in  the  same  conduit,  we 
compute  its  series  of  volumes  of  discharge,  neglecting  the 


442 


MASONRY  CONDUITS. 


influence  of  the  air  perimeter,  we  arrive  at  the  paradoxical 
result  that  when  the  depth  is  eighty-eight  hundredths  of 
full  the  volume  flowing  is  ten  per  cent,  greater  than  when 
the  conduit  is  full.  This  theoretical  result  has  misled  sev- 
eral hydraulicians  who  have  written  upon  the  subject. 

With  a true  value  of  r,  the  discharge  has  some  ratio  of 
increase  so  long  as  sectional  area  of  column  of  water  in  a 
circular  conduit  increases ; but  the  maximum  capacity  of 
discharge  of  a conduit,  not  under  pressure,  is  very  nearly 
reached  when  it  is  seven-eighths  full.  (See  flow  in  Croton 
Conduit,  p.  444.) 

TA  B L E No.  90. 

Hydraulic  Mean  Radii  for  Circular  Conduits,  Part  Full. 

(- Expressed  in  decimal  parts  of  the  diameter.) 

. Ratio  of  Full  Depth. 

o I .i  | .2  | .25  I .3  | .4  | .5  I .55  | .6  I .65  | .7  I .75  I .8  | .85  I .875  | .9  | .95  | FuiL 
Hydraulic  Mean  Radii. 

o | .063I  . 121 1 .147I  .171  [ .214I  .250I  .264I  .378!  ,28S|  .296I  .302!  .304]  .308]  .301!  .298I  .286I  .250 

443.  Velocities  of  Flow  in  Conduits. — The  table 

of  dimensions  and  coefficients  of  Lined  Channels,  on  page 
373,  gives  varied  data  relating  to  masonry  contours  here- 
tofore constructed.  Following  the  table  is  a classification 
of  the  roughness  of  sueh  channel  linings,  and  a series  of 
exponential  formulas  applicable  to  such  surfaces,  and 
varied  cross-sections  in  open  channels. 

The  formulas  for  velocity  of  flow  in  rough  pipes,  on 
page  267,  and  classified  coefficients,  on  page  272,  are  also 
applicable  to  the  respective  classes  in  roughness  of  con- 
tours of  conduits  for  full  depths.  When  hydraulic  radius, 
r,  is  taken  instead  of  diameter,  d,  in  feet,  then  the  value 
of  c for  r equals  c for  .25 d. 


MASONRY  CONDUITS. 


443 


The  masonry  linings  of  conduits  may  be  classified  as 
follows : 

B.  Smooth  Cement. 

I).  Planed  Wood;,  length  with  current. 

E.  Very  smooth  Brickwork. 

G.  Smooth  Concrete. 

H.  Smooth  Brickwork. 

H.  Unplaned  AVood,  laid  across  the  current. 

I.  Smooth  Ashlar. 

I.  Ordinary  Brickwork. 

J.  Rough  Brickwork. 

K.  Smooth  Rubble  in  mortar. 

Formulas  for  velocity,  v,  with  varying  coefficients  are 
as  follows : 

v = v — x 4/  ri  = c Vri. 
r m r 

A table  of  values  of  c classified  for  roughness  may  be  found 
in  Chapter  XIII,  on  page  269a,  which  will  apply  for  con- 
duits one-fourth  to  three-fourths  full. 

The  following  valuable  tables  relate  to  the  Croton  and 
Sudbury  Conduits,  and  are  based  on  the  tests  by  Messrs. 
Fteley  and  Fitzgerald. 


TABLE  No.  9 O a. 
Velocities  in  the  Sudbury  Conduit. 


Total  width,  9.0  ft.;  total  depth,  7.667  ft.;  depth  below  spring  of  arch,  3.167  ft. 


Depth  in  feet 

Volume,  cu.  ft.  per  sec 

Maximum  velocity  in  feet 

Mean  velocity  in  feet 

Center  surface  velocity 

Ratio  of  mean  to  maximum  veloc. 
Ratio  of  mean  to  surface  velocity. 


4-539 

4.007 

3.002 

2.026 

1.508 

III. 470 

94.720 

62.430 

33-408 

20.158 

3-370 

3-317 

3.061 

2.470 

2.140 

2-973 

2.896 

2.620 

2.180 

1.897 

3,050 

3.000 

2.870 

2.420 

2.150 

88.2$ 

87-3$ 

85.6^. 

88. 3$ 

88.6# 

97-5$ 

96.5$ 

90.1$ 

90.1# 

88.2# 

444 


MASONRY  CONDUITS. 


TABLE  No.  9 O b . 

Coefficients  of  Flow  for  the  Croton  New  Aqueduct. 

The  depths  given  are  above  the  center  of  the  invert.  Greatest  width, 
13.6  feet,  and  greatest  height,  13.53  feet.  Slope  .00013257. 


Depth. 

- 

C. 

V. 

1.0 

0. 6582 

102.  70 

o-9593 

7-7I3 

I.  I 

• 7434 

I IO.  49 

1. 0969 

io-i35 

. . 

1. 0 

119.25 

1.6 

1. 1404 

121.98 

1.4998 

23.022 

. . 

1.25 

123.50 

1.9 

1-3544 

124.  9O 

1.6736 

3i-9l6 

i-5 

126. 30 

2.4 

1.6788 

127.79 

1. 9064 

48.328 

. . 

1 - 7 5 

128.30 

.... 

2.7 

1.8562 

1 28. 99 

2.0234 

59-°44 

. . 

2.0 

129.80 

3-2 

2.1303 

i30-47 

2. 1926 

78.143 

. . 

2.25 

131.00 

3-7 

2-3763 

I3I-52 

2-3343 

98.463 

. . 

2-5 

I3I-  9° 

.... 

4.4 

2.6852 

132.57 

2.5012 

1 28. 69 

. . 

2-75 

132.70 

.... 

4.9 

2.8850 

133.06 

2.6022 

x5 1-34 

3-o 

133-25 

5.6. 

3-1345 

I33-58 

2.7230 

184. 10 

3-25 

133-75 

6.4 

3-3863 

134.00 

2.8392 

222.76 

3-5 

134. 10 

7-5 

3.6796 

r34-.3° 

2. 9662 

277.01 

. . 

3-75 

134-35 

8.4 

3-8743 

134-39 

3-0457 

321.08 

4-o 

134-43 

10.4 

4. 1260 

134-5° 

3-I456 

409.88 

I I . O 

4. 1417 

I34-5I 

3-I5I9 

431-58 

11. 6 

4. 1211 

134-5° 

3-!438 

449-43 

12.0 

4.0847  ■ 

134-5° 

3.1299 

458  81 

12.3 

4.0407 

134-49 

3.H27 

463.86 

12.6 

3.9880 

134.46 

3-°9I7 

467.65 

12.842 

3.9161 

i34-4r 

3.0625 

467.99 

444.  Table  of  Conduit  Data.— The  following  table 
gives  data  respecting  well  known  conduits  of  masonry. 


CONDUITS. 


444:01 


WOOD  STAVE  PIPE.— Siphon,  4 ft.  diam. 


CONDUIT  DATA. 


445 


TABLE  No.  9 1. 
Conduit  Data. 


Locality. 

Width. 

Height. 

Depth  of 
Water. 

r. 

i. 

V 

per 

sec. 

m. 

Daily  de- 
livery at 
given 
depth. 

Total 

daily 

capacity. 

Feet. 

Feet. 

Feet. 

Feet. 

U.  S.  gal. 

U.  S.  gal. 

Cochituate,  Boston  

5 

6-333 

6-333 

1. 417 

.000049 

1 .0 

.00452 

16,398,980 

16,500,000 

Croton,  New  York 

7-417 

8.458 

6.083 

2.3415 

.00021 

2.218 

.006435 

59,340,243 

100,000,000 

Washington  Aq.,  D.  C.. . 

9 

9 

3-465 

t.8735 

.00015 

1.893 

. 00505 

27,559.364 

100,000,000 

Brooklyn,  L.  I 

Sudbury,  Boston 

10 

8.667 

5.00 

2.5241 

.0001 

1.588 

.00645 

48,205,128 

70,000,000 

9 

7.667 

5-3 

2.4588 

.0002 

3.029 

•00345 

86,300,000 

100,000,000 

Baltimore 

12 

12 

12.00 

3.0000 

.0002 

170,000,000 

Loch  Katrine,  Glasgow.. 
Canal  of  Isabel  II,  Madrid 

8 

8 

6.85 

2.5253 

.000157 

1.7126 

.00876 

60,000,000 

60  000,00c 

7.052 

9.184 

52,000,00c 

Vienna 

5.667 

6.0 

.000435 

Vanne,  Paris 

6.6 

6.6 

5.00 

I.482 

.0001 

1.436 

.00462 

19,124,152 

23,500,000 

Dhuis,  “ 

2-3 

3-5 

, . . . 

.0001 

5,500,000 

Pontdu  Gard,  Nimes 

4.00 

3-333 

1.250 

.0004 

2 

.00809 

17,234,136 

Pont  Pyla,  Lyons 

1.833 

1.833 

.6ll 

.00166 

2-95 

.00751 

6,405,657 

Metz 

3- 167 

2 . 167 

•915 

.001 

2.783 

.00761 

12,343,270 

Roquencourt,  Versailles  . 
Caserte,  Naples 

3-9=5 

2.583 

I-1I5 

.0003 

.0002 

1.661 

i-333 

.00780 

!8, 233, 261 

Montpellier 

I 

o-5 

.250 

.0003 

.716 

.00942 

231,262 

Croton,  New  Aqueduct. . . 

13.600 

13.58 

9.200 

5.000 

.000133 

2.099 

•00357 

302  500,000 

From  data  of  flow*  in  the  Sudbury  Conduit  of  the  Boston 
water  works  (Fig.  83,  p.  431)  the  following  table  of  values  of 
m for  a series  of  r has  been  computed,  in  which 

m—(2gri)-^-v2  — 2g~0'\  and  C=  V2g-^m. 


TABLE  No.  91a. 


r 

0. 1 

0.2 

°-3  | 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

I . I 

1.2 

i-3 

i-4 

m 

00690 

.00587 

.00533 

.00497 

.00471 

.00451 

■00435 

.00421 

.00416 

.00399 

.00392 

.OO382 

■00375 

.00363 

C 

96.3 

104.7 

109.9! 

113.8 

116.9 

119.4 

121.7 

123.6 

125. 4i 

127.0 

128.5 

129.8 

131 . 1 

132.* 

r 

i-5 

1.6 

T-7  I 

1 8 

1 -9 

2.0 

2.1 

2.2 

2.3  1 

2.4 

2.5 

2.6 

2.7 

3.8 

m 

.00362 

00357 

.00352 

00347 

. 00342 

.00339 

•00336 

.00332 

00330 

.00328 

.00327 

.OO326 

.00325 

.00324 

C 

133-3 

*34-4 

I35-3I 

136.2 

i37-i 

137-8 

138-5 

139-i 

139-61 

140.0 

140.4 

I4O.6 

140.8 

141 .0 

These  coefficients  for  the  given  values  of  r may  be  used 

in  the  formulas  for  velocity,  v=\J~'^  x V ri,  and  V—C  V ri. 

Resident  engineer  Fteley  found  v = 127  r,62I*  to  repre- 
sent well  the  results  of  experiments  up  to  the  value  1.6 
for  r.  He  found  also  that  a liquid  cement  wash  on  the 
interior  of  the  brick  conduit  increased  the  flow  about  two 
per  cent.,  while  in  the  unlined  rock  tunnel  of  similar  section 
the  flow  decreased  about  forty  per  cent. 

The  low  values  of  m are  an  indication  that  the  short 
section  of  conduit  in  which  the  experiments  were  conducted 
was  very  smooth. 


* Descriptive  Report  of  Additional  Supply  of  Water  to  Boston,  from  Sud- 
bury River,  by  Alphonse  Fteley,  resident  Engineer. — Boston,  1882. 


CHAPTER  XXI. 


MAINS  AND  DISTRIBUTION  PIPES. 


445.  Static  Pressures  in  Pipes. — Passing  from  the 
consideration  of  masonry  conduits  to  that  of  pipes  with 
tough  metal  shells,  the  pressure  strains  and  the  capabilities 
of  resistance  of  the  pipe  metals  to  these  strains,  first  de- 
mands our  attention. 

The  theoretical  relations  of  thickness  to  pressure  are  so 
simple  that  we  may  easily  adapt  any  tough  metal  pipe  to 
withstand  any  practical  static  head  pressure,  however  great. 

By  the  term  static  pressure,  we  indicate  the  full  pressure 
due  to  the  head  of  water,  while  standing  at  rest. 

The  unit  of  pressure  area  is  commonly  taken  as  one 


Fig.  95. 


square  inch,  and  this  is  the  area  used 
herein  for  the  unit. 


6 


z 


J k 


The  pressure  p upon  the  unit  of 
area  al  of  a conduit  or  water-pipe,  is 
equal  to  the  product  of  the  given  area 
into  the  vertical  height  It  of  the  surface 
of  water  above  the  centre  of  gravity  of 
the  given  area,  into  the  weight  w of 
one  cubic  foot  of  water  (=  62.5  lbs.' 
divided  by  144. 


(1) 


Let  abcef,  Fig.  95,  be  the  internal  circumference  of  a 


Fig.  96«. 


FORMS  OF  PIPE  SOCKETS. 


THICKNESS  OF  SHELL. 


447 


water-pipe,  of  diameter  d,  in  inches  ; then  the  total  pressure 
P of  water  upon  the  circumference  is 

P = 3.1416tf  x .434A.  (2) 

The  maximum  pressure  acts  upon  each  point  of  the  cir- 
cumference radially  outward,  tending  to  tear  the  shell 
asunder. 

The  resultant  of  the  maximum  pressure  upon  any  given 
portion  of  the  circumference  ab,  acts  in  a radial  direction 
ox,  through  the  centre  of  gravity  of  the  surface  ab , and  is 
equal  to  the  product  of  pressure  into  the  projection  or  trace 
of  the  surface  ij , at  right-angles  to  radius, 

= { (area  ij)  x p\. 

Also  the  resultant  of  the  maximum  pressure  upon  the 
semi-circumference  cbaf  is  equal  to  the  product  of  pressure 
into  its  trace  gTc,  at  right-angles  to  the  radial  line  cutting  its 
centre  of  gravity, 

= { (area  gTc)  x p\. 

The  trace  of  the  semi-circumference  is  also  equal  to  the 
diameter  d , and  its  resultant  equals  the  product  dp. 

Opposed  to  the  resultant  ox  is  an  equal  resultant  of  the 
pressure  upon  the  semi-circumference  fee. 

These  two  resultants  exert  their  maximum  tensile  strain 
upon  the  pipe-shell  at  the  points  c and /. 

446.  Thickness  of  Shell  resisting  Static  Pressure. 
— Let  8 he  the  cohesive  strength  or  ultimate  tenaci  ty  per 
sq.  in.  of  the  metal  of  the  shell,  and  t he  the  thickness  ccx  and 
ffx  in  inches  of  the  shell,  then  we  have  for  equation  of  resist- 
ance of  shell  that  willy ust  balance  the  steady  static  pressure,, 

2 tS  = dp.  (3) 

from  which  we  deduce  the  required  thickness  of  shell : 


448 


MAINS  AND  DISTRIBUTION  PIPES. 


, _ dp  _ rp 
2S~  ~S’ 

in  wliich  r equals  radius  in  inches,  = 


d 

2 


(4) 


It  is  not  enough  that  the  shell  be  able  to  just  sustain  the 
steady  static  pressure,  since  this  pressure  may  be  increased 
by  “ water-rams ,”  incident  to  ordinary  or  extraordinary 
use  of  the  pipe,  or  the  metal  may  have  unseen  weaknesses, 
or  deteriorate  by  use. 

The  thickness  t should  therefore  be  multiplied  by  a 
coefficient,  for  safety,  equal  to  4,  6,  8,  or  10  ; or  the  pressure 
be  assumed  to  be  increased  4,  6,  8,  or  10  times,  or  the 
tenacity  of  the  metal  be  taken  at  .1,  .2,  .3,  or  .4  of  its  test 
value ; in  which  case  the  equation  of  t may  take  the  form, 


, _ 10 pr  # 


or 


/ _ pr 
.IS 


(5) 


If  F is  the  factor  of  safety,  then 


t = x F and  F = (6) 

S pr 

This  factor  will  vary  with  the  conditions  of  use  and 
materials,  as  in  water  pipes,  inclosed,  stand-pipes,  vented 
penstocks,  or  boilers,  and  must  include  weaknesses  due  to 
manufacture,  as  in  riveted  joints,  etc.  Tide  rivets , Chap. 
XXY. 

The  pressure  due  to  a given  head  II  of  water  is  greater 
within  a pipe  when  the  water  is  at  rest,  than  when  the  cur- 
rent is  flowing  through  the  pipe  at  a steady  rate,  for  when 
the  current  is  moving,  a portion  of  the  force  of  gravity  is 
consumed  in  producing  that  motion,  and  in  balancing  fric- 
tions. 

When  a pipe  has  a stop-valve  at  its  outflow,  or  in  its 
line,  the  pressure  p , used  in  its  formula  of  thickness  t,  for 


WATER-RAM. 


449 


any  point  above  the  valve,  should  be  the  static  pressure  of 
the  water  at  rest. 

447.  Water-ram. — If  any  valve  in  a line  or  system  of 
water-pipes  can  be  suddenly  closed  while  the  water  is  flow- 
ing freely  under  pressure,  such  sudden  closing  of  the  valve 
will  produce  a strain  upon  the  pipes  far  greater  thau  that 
due  to  the  static  head  of  water,  and  in  addition  thereto. 

For  illustration,  let  the  diameter,  dx  — 1 ft.,  length,  l = 
5280  ft.,  and  velocity  of  flow,  n ■—  5 ft.  per  second.  Then 
the  accumulated  energy,  M,  in  the  column  of  water,  due  to 
its  weight,  wx  {—  62.5  lbs.),  and  velocity,  is 

M — (.7854  x wx  x l)  x ~ = 100614.45  ft.  lbs. 

2g  2 g 

W=  259182  lbs.,  and  the  equivalent  head  Ti  — .3882  foot. 
IT  is  the  equivalent  of  a force  F acting  one  second  at  a 


R + t=  F+t  = - 


Wv 

rate  equal  to  one-lialf  «,  hence  IT  = F x i-v,  and  F = — 

9 

To  check  the  projectile  energy  of:  the  column  in  any  given 
time,  a resistance,  i?,  must  be  opposed  equal  to  F,  and 
Wo 

gt ' 

The  energy  IT  and  force  F are  above  expressed  in  foot- 
pounds.. If  the  column  is  checked  by  a closing  valve  or  a 
pressing  resistance,  its  energy  will  be  changed  into  press- 
ure, p1  per  unit  of  area,  and,  to  compute  it  in  inch  pounds, 

Wo^gt 


Pi  = 


.7854ff  x 144 


(Da) 


The  equivalent  static  head  = p ~ .433. 

Accumulations  of  air  in  the  pipe  summits  will  help  to 
cushion  the  force  of  ram  and  modify  the  strain  behind  them. 

No  system  of  distribution-pipes  should  be  fitted  with 
stop-valves  of  rapid  action,  lest  the  pipes  be  constantly 
in  danger  of  destruction  by  “ water-r ams.’’ ’ 

Genieys  made  allowance,  in  the  old  water-pipes  of  Paris, 
for  water-rams,  of  force  equal  to  static  heads  of  500  feet, 


450 


MAINS  AND  DISTRIBUTION-PIPES. 


but  he  used  on  his  smaller  mains  plug-valves  that  might  be 
very  rapidly  closed. 

With  proper  stop  and  hydrant  valves,  it  is  not  probable 
that  the  momentum  strain  will  exceed  that  due  to  a steady 
static  head  of  200  or  225  feet,  but  it  is  liable  to  be  great  in 
pipes  under  low  static  heads  as  well  as  in  pipes  under  great 
heads,  and  it  is  in  either  case  in  addition  to  the  static  head. 
The  momentum  strain  must  be  fully  allowed  for,  whether 
the  head  be  ten  feet  or  three  hundred  feet. 

448.  Formulas  of  Thickness  for  Ductile  Pipes. — 
Ordinarily,  for  ductile  pipes,  such  as  lead,  brass,  welded 
iron,  etc.,  an  allowance  of  from  200  to  300  feet  head  is  made 
for  the  momentum  strain,  and  the  tenacity  of  the  material 
is  taken  at  .25  or  .3  of  its  ultimate  resistance  S,  in  which 
case  the  formula  for  thickness  of  ductile  pipes , subject  to 
water-ram,  may  take  the  form, 

_ (4  + 230  ft.)  rw  _ (4  + 230 )dw  _ (4  + 230 )dio  „ 
1 ~ (.25 8)  x 144  ” 1.5  8)  x 144  ~ 728)  ’ ^ 

in  which  7i  is  the  head  of  water,  in  feet. 

w “ “ weight  of  one  cubic  foot  of  water,  in  lbs. 
r “ “ radius  of  the  pipe,  in  inches. 
d “ “ diameter  of  the  pipe,  in  inches. 
t “ “ thickness  of  the  pipe-sbell,  in  inches. 

8 “ “ tenacity  of  the  metal,  per  square  inch. 

If  we  substitute  a term  of  pressure  per  square  inch,  p 
(=  .4344),  for  in  the  equation  for  thickness  of  ductile 
pipes , it  becomes 

(p  + 100  pounds)  r _ (p  + 100)^  ^ 

.25  S ~ TS  ' 

If  the  pipes  have  merely  a steady  static  pressure  to  sus- 


MOULDING  OF  PIPES. 


451 


tain,  then  the  term  + 100  may  be  omitted,  and  the  equation, 
with  factor  of  safety  equal  to  4,  takes  the  simple  form, 


pr  _ pd 

~ 725S  ~ JiS’ 


(9) 


with  factor  of  safety  equal  to  6, 

pr  _ pd 
1 ~ . 1066X8'  “ .33333£* 


(10) 


449.  Strengths  of  Wrought  Pipe  Metals. — The  fol- 
lowing values  of  S give  the  tenacities  of  the  respective  ma- 
terials named,  in  pounds  per  square  inch  of  section  of 
metal , when  the  metal  is  of  good  quality  for  pipes : 


TAB  LE  No.  92. 
Tenacities  of  Wrought  Pipe  Metals. 


Weight 
per  Cu- 
bic Inch. 

COEF. 
6 (Jr). 

COEF. 
4 Kpr). 

COEF. 
6 (pd ). 

COEF. 

4 Jd). 

Pounds. 

6*.  in  lbs. 

.166676*. 

.256*. 

•33333-S'- 

•5-S 

Lead 

Block  tin 

Glass ,. .. 

Brass 

Copper 

Wrought-iron,  single  riveted 

“ “ double  44  

.4119 
.2637 
. 1046 
.3000 
.3146 
.2607 
.2607 

2,000 

4,600 

9,400 

28.000 

30.000 

35.000 

40.000 

333-33 

766.66 

1566.66 

4666.66 
5000 

5833-33 

6666.66 

500 
1150 
2350 
7000 
7500  1 

875O 
I OOOO 

666.67 
1533-33 
3*33-33 
9333-33 
10000 
11 666.66 
*3333-33 

IOOO 
2300 
4700 
14000 
1 500c 
17500 
20000 

CAST-IRON  PIPES. 

450.  Moulding  of  Pipes. — The  successful  founding 
of  good  cast-iron  pipes  requires  no  inconsiderable  amount 
of  skill,  such  as  is  acquired  only  by  long  practical  experi- 
ence, and  keen,  watchful  observation. 

The  loam  and  sand  of  the  moulds  and  cores  must  be 
carefully  selected  for  the  best  characteristics  of  grain,  and 


452 


MAINS  AND  DISTRIBUTION-PIPES. 


proportioned,  combined,  and  moistened,  so  that  the  mix- 
ture shall  be  of  the  right  consistency  to  form  smooth  and 
substantial  moulds  and  cores,  and  be  at  the  same  time  suf- 
ficiently porous  to  permit  the  free  exit  of  moisture  and 
steam  during  the  process  of  drying.  The  moulds  must  be 
filled  and  rammed  with  a care  that  insures  their  stability 
during  the  inflow  of  the  molten  metal,  and  must  be  dried 
so  there  will  be  no  further  generation  of  steam  dm'ing  the 
inflow ; and  yet  not  be  overdried  so  as  to  destroy  the  ad- 
hesion among  their  particles,  lest  the  grains  of  sand  be 
detached  and  scattered  through  the  casting.  The  core  roil- 
ing of  straw  must  be  judiciously  proportioned  in  thickness 
for  the  respective  diameters  of  their  finished  cores,  and  must 
be  twisted  to  a firmness  that  will  resist  the  pressure  of  the 
molten  metal,  so  that  the  pipe  will  be  free  from  swells  and 
the  proper  and  uniform  thickness  of  metal  will  be  secured. 
The  mixture  of  the  metals  and  fuel  in  the  cupola  must 
be  guided  by  that  experience  by  which  is  acquired  a fore- 
knowledge of  the  degre.  f tenacity,  elasticity,  and  general 
characteristics  of  the  finish^  castings.  A superior  class  of 
pipe  is  produced  only  wlier.  excellent  materials  are  used, 
and  when  superior  workmanship  and  mechanical  appli- 
ances give  to  them  accuracy  of  form  and  excellence  of 
texture. 

451.  Casting'  of  Pipes. — A certain  thickness  of  shell, 
of  twelve-foot  pipes,  cast  vertically,  is  required  for  each 
diameter  of  pipe,  to  insure  a perfect  filling  of  the  mould 
before  the  metal  chills,  or  cools,  and  also  to  enable  the 
pipes  to  be  safely  handled,  transported,  laid,  and  tapped. 

In  the  smaller  pipes  this  thickness  is  greater  than  that 
ordinarily  required  to  sustain  the  static  pressure  of  the 
water. 

The  necessary  additional  thickness,  beyond  that  re- 


THICKNESS  OF  CAST-IRON  PIPES. 


453 


quired  to  resist  the  water  pressure,  decreases  as  the  diam- 
eter of  the  pipe  increases. 

There  must,  therefore,  he  affixed  to  the  formula  of  thick- 
ness of  cast-iron  pipes,  a term  expressing  the  additional 
thickness  required  to  he  given  to  the  pipes  "beyond  that  re- 
quired to  resist  the  pressure  of  the  water,  and  this  term 
must  decrease  in  value  as  the  diameter  increases  in  value. 

452.  Formulas  of  Thickness  of  Cast-iron  Pipes. 
— The  ultimate  tenacity  of  good  iron-pipe  castings  ranges 
from  16,000  to  29,000  pounds  per  square  inch  of  section  of 
metal.  Their  value  of  8,  the  symbol  of  tensile  strength 
per  square  inch,  is  usually  taken  at  18,000  pounds,  and  the 
coefficient  of  safety  equal  to  10,  or  the  term  of  tensile  resist- 
ance is  taken  equal  to  .1 8,  or  if  an  independent  term  is 
introduced  in  the  formula  for  the  effect  of  water-ram,  the 
coefficient  of  S may  he  increased  to,  say  .2. 

Assuming  that  the  probable  or  possible  water-ram  will 
not  produce  an  additional  effect  greater  than  that  due  to  a 
static  pressure  of  100  pounds  per  square  inch,  or  head  of 
230  feet,  then  the  formula  for  thickness  of  cast-iron  pipes 
may  take  the  form, 


+ (h  + 230 )rw  , QOo  { 

1 (,2£)xl44  +-ddol 

i-A) 

100/ 

(h  + 230 )dw 
" (A8)x  144  + 

.333  (l 

d \ 
~ loo/' 

(11) 

in  which  h is  the  head  of  water,  in  feet. 

w “ weight  of  one  cubic  foot  of  water,  in  lbs. 
r “ internal  radius  of  the  pipe,  in  inches. 
d “ internal  diameter  of  the  pipe,  in  inches. 
t “ thickness  of  the  pipe  shell,  in  inches. 

S “ tenacity  of  the  metal,  in  pounds  per  sq.  in 

If  we  substitute  a term  of  pressure  per  square  inch 


454 


MAINS  AND  DISTRIBUTION  PIPES 


p (—  .434+  for  in  the  above  equations  for  thickness 
of  cast-iron  pipes,  they  become, 


t 


(p  + 100)r 


.28 


+ -933(1-m)={2±wM+ 


.333 


(l-— )■ 

V loo/ 


(12, 


453.  Thicknesses  found  Graphically. — Since  with  a 
constant  head,  pressure,  or  assumed  static  strain,  the  in- 
crease of  tensile  strain  upon  the  shell  is  proportional  with 
the  increase  of  diameter,  and  also  since  the  decrease  of 
additional  thickness  is  proportional  with  the  increase  of 
diameter,  it  is  evident  that  if  we  compute  the  thickness  of  a 
series  of  pipes,  say  from  4-inch  to  48-inch  diameters,  for  a 
given  pressure,  by  a theoretically  correct  formula,  and  then 
plot  to  scale  the  results,  with  diameters  as  abscissas  and 
thicknesses  as  ordinates,  the  extremes  of  all  the  ordinates 
will  lie  in  one  straight  line  ; and  also,  that  if  the  thicknesses 
for  the  minimum  and  maximum  diameters  of  the  senes  be 
computed  and  plotted  as  ordinates,  in  the  same  manner, 
and  their  extremities  be  connected  by  a straight  line,  the 
intermediate  ordinates,  or  thicknesses  for  given  diameters 
as  abscissas,  will  be  given  to  scale.  This  method  greatly 
facilitates  the  calculation  of  thicknesses  of  a series  of 
“classes”  of  pipes,  and  if  the  ordinates  are  plotted  to  large 
scale,  gives  a close  approximation  to  accuracy. 

454.  Table  of  Thicknesses  of  Cast-iron  Pipes.— 
The  following  table  gives  thicknesses  of  good,  tough,  and 
elastic  cast-iron,  with  S = 18,000  lbs.,  for  three  classes  of 
cast-iron  pipes,  covering  the  ordinary  range  of  static  pres- 
sures of  public  water  supplies,  in  which 


t = 


(p  + ioo)(7 

AS 


+ .333(1  - 


d_ 

100. 


t = .0000603(7i  + 230 )d  +(.333  - .00333(7.) 


THICKNESSES  OF  CAST-IRON  PIPES. 


455 


TABLE  No.  93. 
Thicknesses  of  Cast-iron  Pipes. 

(When  = 18000  lbs.) 


CLASS 

A. 

CLASS 

B. 

CLASS 

C. 

Diameter. 

Pressure.  50  lbs.  per 
square  inch,  or  less. 
Head,  116  feet. 

Pressure,  100  lbs.  per 
square  inch. 
Head,  230  feet. 

Pressure,  130  lbs.  per 
square  inch. 
Head,  300  feet. 

Thicknesses. 

Thicknesses. 

Thicknesses. 

Inches . 

3 

Inches . 

•3858 

Ap- 
prox, 
in. 
13 
3 2 

Inches. 

.4066 

Ap- 

prox. 

in. 

13 

T2 

Inches ■ 

.4191 

Ap- 

prox. 

in. 

7 

TF 

4 

•4033 

1 3 
3 2 

•43 11 

7 

TF 

•4477 

is 

6 

•4383 

7 

TF 

.4800 

1 

2 

•5050 

8 

•4734 

1 

2 

.5289 

I 7 
F2 

.5622 

Tv 

10 

■5o83 

1 

2 

•5777 

19 

F2 

.6194 

5 

F 

12 

•5433 

9 

TF 

.6266 

5 

F 

.6766 

tI 

14 

•5783 

19 

32 

•6755 

1 1 

TF 

•7338 

3 

T 

16 

•6133 

5 

F 

.7244 

3 

T 

•7944 

1 3 
TF 

18 

.6483 

2.1 
3 2 

•7733 

25 

T2 

.8483 

2 7 
T2 

20 

•6833 

1 1 
TF 

.8222 

2 7 
FT 

•9055 

29 

T2 

22 

•7i83 

2 3 

3 2 

.8711 

7 

F 

.9628 

3 I 
T2 

24 

•7533 

3 

¥ 

.9200 

I 5 
T6 

1.0200 

I 

27 

.8058 

13 

TF 

•9933 

1 

1.1058 

T 3 

1 3 2 

3° 

•8583 

7 

F 1 

1.0666 

1* 

1.1916 

T 3 

*TF 

33 

.9108 

1 5 
TF 

1. 1 400 

T 5 

1 -2  775 

T 9 
I3F 

36 

-9633» 

3 1 
T2 

1-2133 

T 7 
1 3 2 

1-3633 

T 3 

IF 

40 

i-°333 

T_I_ 

1 3 2 

I-3111 

T 5 

XTF 

00 

'I" 

M 

,15 

44 

1-1033 

1.4088 

1.592! 

.19 

48 

I-I733 

irV 

1.5066 

1.7066 

T1  I 
lT* 

In  the  following  table  are  given  the  thicknesses  of  cast 
iron  pipes,  as  used  by  various  water  departments. 


456 


MAINS  AND  DISTRIBUTION  PIPES. 


TABLE  No-  93  a. 


Thicknesses  of  Cast-iron  Pipes,  as  Used  in  Several  Cities. 


455.  Table  of  Equivalent  Fractional  Expressions. 

— The  following  tables  of  equivalent  expressions  for  fractions 
of  an  inch  and  of  a foot,  may  facilitate  pipe  calculations : 


CAST-IRON  PIPE  JOINTS. 


457 


TABLE  No.  94. 


Parts  of  an  Inch  and  a Foot,  expressed  Decimally. 


Inches. 

Equivalent 
Dec.  part  of 
an  inch. 

Equivalent 
Dec.  part  of 
a foot. 

1-32 

.03125 

. 002604 

1-16 

.06250 

.005208 

3-32 

•09375 

.007812 

1-8 

. 12500 

.010416 

5-32 

.15625 

.010420 

3-16 

.18750 

.015625 

7-32 

.21875 

.018229 

1-4 

.25000 

.020833 

9-32 

.28125 

.023437 

5-16 

.31250 

.026041 

n-32 

•34375 

.028645 

3-8 

.37500 

.031250 

13-32 

.40625 

.033854 

7-16 

•43750 

.036458 

15-32 

.46875 

.039062 

1-2 

. 50000 

.041666 

17-32 

•53125 

.044270 

9-16 

. 56250 

.046875 

19-32 

•59375 

.049479 

5-8 

.62500 

.052083 

21-32 

.65625 

.054607 

Ii-i6 

.68750 

.057291 

23-32 

•71875 

•059895 

3-4 

.75000 

.062500 

25-32 

.78125 

.065104 

13-16 

.81250 

.067708 

27-32 

•84375 

.070312 

7-8 

.87500 

.072916 

29-32 

.90625 

.075520 

15-16 

•93750 

.078125 

31-32 

.96875 

.080729 

I 

I . 

•083333 

Inches. 

Equivalent 

Dec.  parts 
of  a foot. 

Equiv. inches 

Dec.  parts  of 

and  32d  pts.. 

a loot. 

nearlj-. 

I 

•0833 

.1 

!fV 

2 

. 1667 

.2 

2| 

3 

.2500 

• 3 

?1ri 

4 

•3333 

•4 

• 4ir! 

5 

.4167 

■ 5 

6 

6 

.5000 

.6 

7fV 

7 

•5833 

•7 

8| 

8 

.6667 

.8 

9r! 

9 

.7500 

•9 

I0tf 

IO 

•8333 

I .O 

12 

II 

.9167 

12 

I .OOOO 

456.  Cast-Iron  Pipe  Joints. — According  to  Cresy,* 
castiron  pipes  were  first  generally  adopted  in  London  very 
near  the  close  of  the  last  century.  The  great  fire  destroyed 
many  of  the  lead  mains  in  that  city.  These  were  in  part 
replaced  by  wood  pipes,  but  when  water-closets  were  intro- 
duced and  more  pressure  was  demanded,  the  renewals  were 
afterward  wholly  of  iron. 


* Encyclopedia  of  Civil  Engineering,  p.  549.  London,  1865. 


458 


MAINS  AND  DiSTRlBUTION-FIPES. 


The  earliest  pipes  had  flanged  joints  with  a packing  ring 
of  leather,  and  were  bolted  together.  These  were  two  and 
one-half  feet  in  length.  Those  first  generally  used  by  the 
New  River  Company  were  somewhat  longer,  and  were 
screwed  rigidly  together  at  the  joiuts.  This  prevented 
their  free  expansion*  and  contraction,  with  varying  temper- 
atures of  water  and  earth,  rendering  them  troublesome  in 
winter,  when  they  were  frequently  ruptured.  Cylindrical 
socket-joints  were  then  substituted.  These  were  accurately 
turned  in  a lathe,  to  a slightly  conical  form.  and.  being 
luted  with  a little  whiting  and  tallow,  were  driven  together. 

The  length  of  the  pipes  was  subsequently  increased  to 
nine  feet,  and  a hub  and  spigot-joint  formed,  adapted  first 
to  a joint  packing  of  deal  wedges,  and  afterward  to  a pack- 
ing of  lead. 

The  hub  and  spigot-joint,  with  various  slight  modifica- 
tions, has  been  generally  adopted  in  the  British  and  con- 
tinental pipe  systems,  for  both  water  and  gas  pipes ; but 
the  turned  joint  has  by  no  means  been  entirely  superseded 
in  European  practice. 

A variety  of  the  forms  given  to  the  turned  joint  are  illus- 
trated and  commented  upon  in  a paper  f recently  read  by 
Mr.  Downie  in  Edinburgh.  The  illustrations  include  turned 
joints  used  in  Glasgow,  Launceston,  Dundee,  Flyde,  Liver- 
pool, Trieste,  Sydney,  Hobart  Town,  and  Hamilton  (Canada) 
water-works,  and  in  the  Buenos  Ayres  gas-works.  These 
joints  were  also  used  by  Mr.  George  H.  Norman,  the  well- 
known  American  contractor  for  water  and  gas  works,  in 
gas  works  constructed  by  him  in  Cuba. 


* M.  Girard  found  that  the  lineal  expansion  of  cast-iron  pipes,  when  free 
and  in  the  open  air  was  .C00036  of  an  inch  for  each  additional  degree  of  Fah- 
renheit. Rankine  gives  .0000733  inch  per  foot  per  degree, 
f Proceedings  Inst.  E.  S.,  vol.  vii,  p.  16. 


DIMENSIONS  OF  PIPE-JOINTS. 


459 


The  turned  joint  has  not  as  yet  been  adopted  in  the 
pipe  systems  in  the  United  States ; but  iu  the  new  water- 
work  of  Ottawa,  Canada,  completed  in  1875  under  the  direc- 
tion of  Thos.  C.  Keefer,  C.E.,  they  were  very  generally  used. 

The  depths  of  hub  and  of  lead  packing  in  the  early  Eng- 
lish and  Scotch  pipes,  and  in  fact  in  the  first  pipes  used  in 
connection  with  the  Fairmount,  Croton,  and  Washington 
aqueducts,  exceeded  greatly  the  depths  at  present  used. 

The  pine-log  water-pipes  of  Philadelphia  had  been  gen- 
erally replaced  by  cast-iron  pipes  as  early  as  about  1819, 
The  forms  of  hubs  and  spigots  then  used,  as  designed  bj 
Mr.  Graffe,  Sr.,  were  very  similar  to  those  now  used,  ex- 
cept that  the  hubs  had  somewhat  greater  depth.  The 
lengths  of  the  pipes  were  nine  feet,  and  other  dimensions  as 
in  the  following  table,  from  data  in  the  “Journal  of  the 
Franklin  Institute”  : 


Diameter  of  pipe,  in  inches.  3 I 4 

Thickness  of  shell f ! ^ 

Depth  of  hub \ 4 


6 

7 

T? 

4 


8 

1 

5 


10 

12 

16 

1 

9 

5 

¥ 

¥ 

5 

5i 

6 

It  is  observed  that  the  set,  by  which  the  lead  is  com- 
pacted in  the  joint,  acts  upon  the  lead,  ordinarily  only  to  a 
depth  of  from  one  to  one  and  one-quarter  inches.  The  lead 
beyond  the  action  of  the  set  is  of  but  little  practical  value, 
and  there  is  no  advantage  in  giving  the  hemp  packing  an 
excessive  depth. 

Deep  joints  run  solid  with  lead  often  give  to  the  line  of 
pipes  such  rigidity  that  it  cannot  accommodate  itself  to  the 
unevenness  of  its  bearings  and  weight  of  backfilling,  espe- 
cially in  ledge  cuttings,  and  rupture  results. 

When  trenches  are  too  wet  to  admit  of  pouring  the  lead 
successfully,  small,  soft  lead  pipe  may  be  pressed  into  the 
joint  and  faithfully  set  up  with  good  effect. 

457.  Dimensions  of  Pipe-joints.— Fig.  96  is  a re- 


460 


MAINS  AND  DISTRIBUTION-PIPES. 


Fig.  96. 


duced  section  of  a bell  and  spigot  of  a 12-inch  diameter 
pipe.  Dimensions  of  cast-iron  pipe  socket-joints  for  diam- 
eters from  4-incli  to  48-inch,  corresponding  to  the  letters  in 
the  sketch,  are  given  in  the  following  table  (iso.  95),  and 
like  data  are  given  for  flange-joints  in  the  next  succeeding 
table,  No.  96. 

The  weight  of  flanged  pipes,  per  lineal  foot,  exclusive  of 
weight  of  flanges,  which  is  given  in  Table  No.  96,  may  be 
computed  by  the  following  formula  (vide  § 461) : 

w = 9.817  (d  + f)t.  (13) 

458.  Templets  for  Bolt  Holes. — A sheet-metal  tem- 
plet for  marking  centres  of  bolt  holes  on  flanges  should  be 
laid  out  and  pricked  with  the  nicest  accuracy,  and  have  its 
face  side  and  one  space  conspicuously  marked. 

On  special  castings  intended  for  fixed  positions  the 
templet  should  be  placed  upon  the  flange  so  that  the  cen- 
tre of  the  marked  space  shall  be  placed  exactly  over  the 
centre  of  the  bore  of  the  pipe  when  the  pipe  shall  be 
placed  in  position ; then  the  bolt  holes  of  abutting  flanges 
will  match  with  uniformity. 


DIMENSIONS  OF  PIPES. 


461 


TABLE  No.  9 5 . 

Dimensions  of  Cast-iron  Water-pipes.  (Fig.  96.) 


(Thickness  of  shell  is  herein  proportioned  for  ioo  lbs.  static  pressure.) 


0 

<D 

s 

a 

Length  over  all. 

Thickness 

of  shell. 

Depth  of 
hub. 

Joint  room. 

6 

ab 

bq 

be 

cd 

dA 

ce 

eg 

ef 

fp 

kl 

km 

mn 

ho 

27 

in. 

4 

/ // 

12-3 

// 

7 

T¥ 

tr 

3 

// 

T¥ 

// 

4 

// 

i} 

rr 

if 

tr 

1 

¥ 

ft 

3 

l¥ 

tr 

5 

¥ 

ft 

1 

¥ 

tr 

5 

l¥ 

rr 

5 

¥ 

rr 

7 

¥ 

tr 

2 

6 

12-3 

i 

3 

5 

T¥ 

I¥ 

if 

if 

1 

¥ 

3 

1 ¥ 

¥ 

1 

¥ 

5 

l¥ 

5 

¥ 

I 

2 

8 

12-3 

1 7 

32 

3 

5 

T¥ 

if 

if 

if 

1 

¥ 

3 

T¥ 

5 

¥ 

1 

¥ 

A 

5 

¥ 

if 

2f 

IO 

12-3 

1 9 
¥¥ 

3 

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If 

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462 


MAINS  AND  DISTRIBUTION-PIPES. 


TABLE  No.  9 6. 


Flange  Data  of  Flanged  Cast-iron  Pipes.* 


Diam. 

Thick- 

Radius 

Diam. 

Thick. 

Width 

Diam.  of 

No.  of 
Bolts. 

Diam. 

Length 

ness  of 

of 

of 

of 

of 

Bolt 

of 

of 

of  Bore. 

Pipe. 

Fillet. 

Flange. 

Flange. 

Flange. 

Circle. 

Bolt. 

Bolt. 

Inches. 

Inches. 

Inches . 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

3 

.448 

1 

i\ 

i 

2± 

6 

4 

f 

2f 

4 

.468 

i 

9 

If 

2f 

7 1 

4 

f 

2f 

5 

•525 

i 

10 

i-l 

2l 

81 

8 

f 

f 

3 

6 

•563 

1 

1 1 

I 

2f 

9f 

8 

3 

7 

. 600 

i 

12I 

1 tV 

2f 

1 of 

8 

f 

3l 

8 

• 639 

i 

I3T 

Is 

2i 

nf 

8 

f 

3l 

9 

.678 

yV 

i5 

4 

2* 

13 

12 

f 

3! 

10 

•7i3 

ttt 

l6 

3 

I4l 

12 

7 

■g 

3l 

3f 

12 

.790 

tV 

19 

ii 

3l 

16I 

12 

7 

¥ 

14 

.864 

tV 

21 

if 

3l 

i8f 

12 

1 

4i 

15 

• 9°4 

tV 

22I 

if 

3t 

20 

16 

I 

4f 

16 

.946 

tV 

2 3I 

jtV 

3i 

21I 

16 

1 

4l 

18 

I . 02 

3 

25 

T 9 

IT¥ 

3l 

22§ 

16 

if 

4f 

20 

1 .09 

3 

TT 

27I 

ill 

3-1 

25 

20 

4 

5 

22 

1. 18 

X 

4 

294 

1 If 

3f 

27l 

20 

X 

51 

24 

I-2S 

i 

32 

if 

4 

29I 

20 

X 

5i 

26 

1.3° 

1 

344 

2 

4s 

3if 

24 

X 

sf 

28 

1.38 

1 

¥ 

3«i 

2tV 

4l 

34 

28 

X 

6 

3° 

1 . 48 

1 

381 

2s 

4f  ' 

36 

28 

if 

61 

36 

1 .71 

1 

45f 

2f 

4l 

42I 

32 

4 

61 

42 

1.87 

1 

T 

52! 

2f 

5s 

49l 

36 

a- 

7l 

48 

2.17 

X 

4 

59t 

2f 

St 

56 

44 

i-l 

7f 

* Fot  pressures  of  200  lbs.  to  the  square  inch. 

Adopted  July  18,  1894,  at  a conference  of  committees  of  the  Am.  Soc.  of 
Mechanical  Engrs.  and  the  Master  Steam  and  Hot  Water  Fitters’  Assn. 


I 


FLEXIBLE  PIPE-JOIXT. 


463 


If  an  even  number  of  bolts  are  used,  then  there  will  be 
a space  vertically  over  and  under  the  centre  of  the  bore 
of  the  pipe. 

If  the  templet  is  not  very  exactly  spaced  the  face  side 
should  be  placed  against  one  flange  with  the  marked 
space  at  top,  and  the  back  against  the  other  abutting 
flange  with  same  space  at  top ; otherwise  the  bolt  holes 
may  not  exactly  match. 

459.  Flexible  Pipe- Joint. — It  is  sometimes  necessary 
to  take  a main  or  sub-main  across  a broad,  deep  stream  oi 


Fig.  97. 


estuary,  or  arm  of  a lake,  where  it  is  both  difficult  and 
expensive  to  coffer  a pipe  course  so  as  to  make  the  usual 
form  of  rigid  joint.  Different  forms  of  hall  and  sockei 


464 


MAINS  AND  DISTRIBUTION-PIPES. 


flexible  joints  have  been  adopted  for  such  cases,  which 
allow  the  pipes  to  be  joined  and  the  joints  completed  above 
the  water  surface,  and  the  pipe  then  to  be  lowered  into 
its  bed. 

Fig.  97  illustrates  the  form  of  joint  designed  by  the 
writer  for  a twenty-four  inch  pipe,  which  is  especially 
adapted  to  large-size  pipe-joints.  It  is  a modification  of  the 
Glasgow  “ universal  joint.” 

The  difficulty  of  making  the  back  part  of  the  lead-pack- 
ing of  the  joint  Ann  and  solid,  which  difficulty  has  here- 
tofore interfered  with  the  complete  success  of  the  larger 
flexible  pipes,  is  here  overcome  by  separating  the  bell  into 
two  parts,  so  as  to  permit  both  the  front  and  rear  parts  of 
the  packing  to  be  driven. 

In  putting  together  this  joint,  the  loose  ring  is  passed 
over  the  ball-spigot  and  slipped  some  distance  toward  the 


Fig.  98. 


centre  of  the  pipe  ; the  ball-socket  is  then  entered  into  the 
solid  part  of  the  bell  and  its  lead  joint  packing  poured  and 
snugly  driven  ; the  loose  ring  is  then  bolted  in  position,  and 
its  lead  joint  packing  is  poured  and  firmly  driven,  also. 
This  secures  a solid  packing  at  both  front  and  rear  of  the 


WEIGHTS  OF  CAST-IRON  PIPES. 


465 


joint,  capable  of  withstanding  the  strain  that  comes  upon  it 
as  the  pipe  is  lowered  into  position,  and  ensures  a tight 
joint.  The  ball-spigot  is  turned  smooth  in  a lathe  to  true 
spherical  form. 

Fig.  98  illustrates  J.  B.  Ward’s  patent  flexible  joint. 

460.  Thickness  Formulas  Compared. — The  result? 
given  by  some  of  the  well-known  formulas  for  thicknesses 
of  cast-iron  pipes,  may  be  compared  in  Table  No.  97. 

461.  Formulas  for  Weights  of  Cast-iron  Pipes.— 
The  mean  weight  of  cast-iron  is  about  450  pounds  per  cubic 
foot,  or  .2604  pounds  per  cubic  inch. 

Let  d be  the  diameter  of  a cast-iron  pipe,  in  inches ; 
t,  the  thickness  of  the  pipe-shell,  in  inches  ; and  n the  ratio 
of  circumference  to  diameter  (=  3.1416) ; then  the  cubical 
volume  Vx , in  inches,  of  a pipe-shell  (neglecting  the  weight 
of  hub),  is,  for  each  foot  in  length, 

Vx  = (d  + t)  x t x 7T  x 12.  (14) 

When  the  length  of  a pipe  is  mentioned,  it  is  commonly 
the  length  between  the  bottom  of  the  hub  and  the  end  of 
the  spigot  that  is  referred  to  ; that  is,  the  net  length  of  the 
pipe  laid,  or  which  it  will  lay. 

The  average  weight  of  a pipe  per  foot  includes  the 
weight  of  the  hub,  which,  as  thus  spoken  of,  is  assumed  to 
be  distributed  along  the  pipe. 

The  weights  of  the  hubs,  of  general  form  shown  in 
Fig.  96,  and  whose  dimensions  are  given  in  Table  No.  95 
(p.  461),  increase  the  average  weight  per  foot  of  the  twelve- 
foot  light  pipes,  approximately,  eight  per  cent. ; of  the 
medium  pipes,  seven  and  one-half  per  cent. ; and  of  heavier 
pipes,  seven  per  cent. 

The  equation  for  cubical  volume  of  pipe-metal,  includ- 
ing hub,  is 


30 


466 


MAINS  AND  DISTRIBUTION-PIPES. 


TABLE  No.  97. 

Formulas  for  Thickness  of  Cast-iron  Pipes  Compared. 

Assumed  static  pressure,  75  lbs.  per  square  inch.  Assumed  tenacity  of  mewl,  18,000  lbs.  pel 

square  inch. 


Authority. 


Equations. 


Diameters. 


4 in. 

12  in. 

24  in. 

48  in. 

Thick- 

ness 

Thick- 

ness. 

Thick- 

ness. 

Thick- 

ness. 

Inches. 

.4172 

Inches. 

.5850 

Inches. 

.8367 

Inches. 

I*34°° 

.4055 

.5766 

•8333 

1.3466 

•4550 

•575° 

•7550 

1. 1150 

•3899 

.4897 

.6394 

.9389 

•4534 

.6002 

.8204 

1.2608 

•3776 

•5794 

.8069 

1. 1750 

.4074 

.6121 

■7242 

1.0684 

.2887 

.5000 

.7071 

1. 0000 

■4175 

.6126 

•9°53 

1.4902 

.3600 

•6235 

.8818 

1.2470 

•3334 

.5002 

•7504 

1.2508 

.4129 

.6148 

.9176 

1.5232 

.4900 

.6699 

•9397 

I-479S 

■3542 

•5625 

.8750 

1.500a 

•4554 

.646I 

.9322 

1.500a 

•4384 

•7I52 

1. 1304 

1.9608 

.4496 

.6488 

.9476 

1.5453 

Equation  (12),  § 452. 

M.  Dupuit 

J.  F.  D’Aubuisson.. 

Julius  Weisbach 

Dionysius  Lardner. 


Thomas  Box 

G.  L.  Molesworth.. 
ffm.  J.  M.  Rankine 

John  Neville  ...  . 
Thos.  Hawksley  . 
Baldwin  Latham  . 
James  B.  Francis. 
Thos.  J.  Whitman 

M.  C.  Meigs 

J.  II.  Shedd  

J.  F.  Ward 

Jos.  P.  Davis 


(p  + ioo)d  , / d ^ 

' = ~ + -333  (‘--j 


■4-S- 


t = (.0016  nd)  + .013*/  + .32 

C 

t = (.015  d)  + .395 

t = (.00238  nd)  + .34 

t = (.oo7»r)  + .38 

, ji  Vd  l hd 

t=  f—  + .15  \ + 

( 10  ) 25000 

( .37  for  4"  to  12"  ) 
t = (.000054/**/)  + ■<  .50  12  u 30  > 

( .62  “ 30  “ 50  ) 

-\fl 

/ = [.0016  (n  + 10)  d]  + .32 

t = .18  Vd 

TV  fid 


t = (.000058/**/)  + .0152 d + .312  . 
t = (.0045  nd)  + .4  — .0011*/. . . . , 

t = (.0260416*/)  + .25 

t = (.0000 8kd)  4-  .oid  + .36..... 

/ = (.0002 fid)  + .30 . 

t = (.00475  nd)  + .35 


In  which 


t = thickness  of  pipe  wall,  in  inches. 
d = interior  diameter  of  pipe,  in  inches. 
h — head  of  water,  in  feet 
w = weight  of  a cubic  foot  of  water,  = 62.5  lbs. 

K = number  of  atmospheres  of  pressure,  at  33  feet  each. 
p = pressure  of  water,  in  pounds  per  square  inch. 

£ m ultimate  tenacity  of  cast-iron,  in  pounds  per  square  inch. 


WEIGHTS  OF  CAST-IRON  PIPES. 


467 


V = (d  + t)  x 1.08£  x n x 12.  (15) 

Let  Wi  be  the  weight  per  cubic  inch  of  the  metal 
(=.2604  lbs.),  and  w the  average  weight  per  foot  of  the  pipe, 
then  we  have  for  equation  of  average  weight  per  foot,  of 
twelve-foot  pipes, 

w — 12  (^  + t)  x 1.08£  x 7i701#  (16) 

To  compute  the  average  weight  per  lineal  foot  of  an 
18-incli  diameter  pipe,  twelve  feet  long,  and  f J inch  thick  in 
the  shell,  assign  the  numerical  value  to  the  symbols,  and 
the  equation  is : 

w = 12(18  + .65625)  x (1.08  x .65625)  x 3.1416  x .2604 
= 129.80  pounds. 

In  the  equation,  12,  tt,  and  Wi  are  constants,  and  may  be 
united,  and  their  product  (=  9.81687)  supply  their  place  in 
the  equation,  when  the  equation  for  average  weight  per 
foot  is, 

w = 9.82  (d  + t)  x 1.08£  (17) 

and  for  the  total  weight  of  a 12-foot  pipe  : 

W = 117.84  (cl  + t)  x 1.08£  (18) 

462.  Table  of  Weights  of  Cast-iron  Pipes. — The 

following  table  gives  minimum  weights  of  three  classes  of 
cast-iron  pipes,  of  good,  tough,  and  elastic  cast-iron  (with 
8 = 18,000  lbs.),  for  heads  up  to  300  ft. ; also,  approximate 
weights  of  lead  required  per  joint  for  the  respective  diam- 
eters, from  4 to  48  inches,  inclusive. 


408 


MAINS  AND  DISTRIBUTION-PIPES. 


TABLE  No.  9 8. 

Minimum  Weights  of  Cast-iron  Pipes. 


Diameter. 

CLASS  A. 

Head,  116  feet. 
Pressure,  50  lbs. 

CLASS  B. 

Head,  230  feet. 
Pressure,  100  lbs. 

CLASS  C. 

Head,  300  feet. 
Pressure,  130  lbs. 

| Depth  of  lead  in  socket. 

Weights  of  lead  per  joint. 

Thickness.* 

i i 

5 x 

tbO  O Q 
+ 

4)  8 x 

bfi  c ‘ 

£ O' 

< 1 

Total  weight  of  a 
12-foot  pipe. 

Thickness. 

QJ  IQ 
Cu  0 

£ *1  z 

.bp  0 jQ 
’5  <2  ^ 
> — + 

be  c N 
«i=oo 
V O' 

5 11 

^ s 

Total  weight  of  a 
12-foot  pipe. 

Thickness. 

O N 

— °. 

_fcj)Orv 

+ 

t£  C W 

rt  j=  *» 

Jr  O' 

> II 
< s 

Total  weight  of  a 
12-foot  pipe. 

in. 

in. 

lbs. 

lbs. 

in. 

lbs. 

lbs. 

in. 

lbs. 

lbs. 

lbs. 

4 

•4033 

18.85 

226.20 

• 43 11 

20.16 

241.92 

•4477 

20.92 

250.06 

4.25 

6 

•4383 

30.07 

360.84 

.4800 

32.83 

393-96 

.5050 

34.52 

414.19 

u. 

6.25 

8 

•4734 

42.4I 

508 . 92 

•5289 

47-57 

570-84 

.5622 

50.58 

606. qq 

lJ-8 

8.25 

IO 

■5083 

56.64 

679.68 

•5777 

64.50 

774.00 

.6194 

69.  II 

829.37 

1% 

10.25 

12 

•5433 

72.30 

867.60 

.6266 

83-53 

1002.00 

.6766 

90.  12 

1081.46 

2 

13.00 

14 

• 5783 

89.4O 

1072.80 

•6755 

104.62 

1255-44 

•7338 

II3.60 

1363.22 

2 

15.00 

16 

.6166 

I08.65 

1303.80 

.7277 

I28.46 

I54I-52 

-7944 

I40. l8 

1682. 16 

2 l; 

24-25 

18 

.6483 

128.20 

r538 . 40 

•7733 

i53-»9 

1838.28 

.8483 

168.OO 

2016.00 

2', 

27.25 

20 

•6833 

149  81 

I797.72 

.8222 

l80.7I 

2168.42 

•9955 

I98.I4 

2377.68 

2% 

3°-75 

22 

.7183 

172.97 

2075.64 

.8711 

210.21 

2522.52 

.9628 

232.25 

2787.02 

= l4 

35-25 

24 

•7533 

197-65 

2371.80 

.9200 

242.OI 

2904. 12 

1 .0200 

268. 15 

3217.84 

21., 

38.25 

2 7 

.8058 

237-55 

2850.60 

•9933 

293- 31 

35I9-72 

1 . 1058 

326. 56 

3918.77 

23« 

51.25 

30 

.8583 

280.75 

3367.80 

1.0666 

349.61 

/I95.32 

1 . 1916 

39° -53 

4686.41 

2?8 

56.25 

33 

.9108 

307-53 

3690.36 

1 . 1400 

4^.67 

4928.04 

1-2775 

460.11 

5521.26 

238 

62.25 

36 

•9633 

373.88 

4486.56 

1.2183 

478.42 

5741-04 

1-3633 

535-19 

6422.28 

2& 

79-5° 

40 

1 • °333 

449.44 

5393-28 

1.3x11 

571-74 

6860.88 

1.4778 

043.96 

7727.47 

2 Vi 

88.75 

44 

1 • 1033 

527.48 

6329.76 

1 . 4088 

675.29 

8103.48 

1. 5921 

762.69 

9152.26 

25s 

107.75 

48 

1 -1733 

6ll .8l 

7321 . l8 

1 . 5066 

787.08 

9444 ■ 96 

1 .7066 

891.30 

10695.62 

2% 

III .OO 

Weight  of  Water  and  Gas  Pipes  of  Cast-iron. 

So-called  Manufacturers’  Standards. 

Water  Pipes.  (For  100  lbs.  per  sq.  in.  Pressure.) 


Diameter  in  inches. 

4 

6 

8 

10 

12 

*4 

16 

18 

20 

24 

30 

36 

48 

Thickness,  inches 

Weight  per  foot 

Weight  per  12  feet 

i 

22 

264 

i 

33 

396 

f 

45 

540 

15 

60 

720 

9 

15 

75 

900 

f 

117 

1400 

* 

125 

1500 

167 

2000 

H 

200 

24OO 

I 

25O 

3000 

*£ 

350 

4200 

if 

475 

5700 

•I 

775 

9300 

Gas  Pipes. 


Thickness,  inches  

4 

t75 

T5 

: ! 

I95 

IS 

u 

a | i 

* j i ! >1 

Weight  per  foot  

17 

30 

40 

50  70 

84 

IOO 

x34 

130;  i S4 

250  350  542 

Weight  per  12  feet 

204 

360 

480 

600  840 

IOOO 

1200 

1600 

iSooj  2200 

3OOO  4 2 CO  65OO 

Minimum  weight  per  foot 

16 

26 

35 

44  63 

75 

90 

124 

I38I  169 

232j  33° | 52o 

INTERCHANGEABLE  JOINTS. 


469 


TAB  L E No.  98«7. 

Weights  of  Cast-iron  Pipes,  as  used  in  Several  Cities  for 
their  Maximum  Pressures,  in  1876. 


14 

16 

20 

24 

3° 

36 

48 


Maximum  Head,  in  feet. 


R. 

R. 

R. 

R. 

R. 

R. 

S.-P. 

R. 

R.  S.-P. 

S.-P. 

R.  <* 
D.-t 

D.-P. 

R. 

R.  & 

S. -P. 

250 

100 

180 

218 

I98 

170 

125 

1801 

200 1 260 

175 

200 

250 

237 

200 

Average  Weights,  per  lineal  foot,  in  pounds. 


15 

Hi 

12 

19 

24 

20 

i8i 

18 

24l 

31 

36 

32 

28.y 

395 

35 

36^ 

42 

46 

40 

55 

50 

53 

56 

71 

8b 

81 

85 

90 

85 

835 

105 

I24 

130 

125 

151 

170 

174 

200 

208 

183 

3°7 

235 

23I 

250 

330 

340 

337 

35° 

407^ 

325 

422 

405 

458 

400 

438 

450 

585 

696 

606 

692 

335 

49 

643 

85 

103 

128 

1785 

239 

338 

472 


1293 

l82 

241  3 

350 

412 


24 

43 

69 

87 

123 


1975 

239 

257 


235 

34 


134 

194 

265 

358 


32 

45 

535 

75 


n3 

165 

265 

334 


46 

"86 

*125 


2C2 

257 


35 

5° 

87 


i2gj 
194 
2^6  i 
557' 


The  initials  in  the  horizontal  column  of  heads  indicate  the  systems  of  pressure,  viz.,  R.,  res- 
ervoir ; S.-P.,  stand-pipe  ; and  D.-P.,  direct  pressure. 


463.  Interchangeable  Joints. — When  several  classes 
of  pipes,  varying  in  weight  for  similar  diameters,  enter  into 
the  same  system  of  distribution,  as,  for  instance,  in  an  un- 
dulating town,  with  considerable  differences  in  levels,  there 
is  an  advantage  in  making  the  exterior  diameters  the  con- 
stants, instead  of  the  interiors,  for  then  the  spigots  and  bells 
of  both  plain  and  special  castings,  and  of  valves  and 
hydrants,  have  uniformity,  and  are  interchangeable,  as  occa- 
sion requires,  and  the  different  classes  join  each  other  with- 
out special  fittings. 

* The  Ottawa  pipe  weights  classed  as  of  4 and  14  inch  diameter#  are 
fact  5 and  15  inch  diameters  respectively. 


470- 


MAINS  AND  DISTRIBUTION-PIPES. 


If  it  is  objectionable  to  increase  and  decrease  the  interior 
diameters  of  the  light  and  heavy  classes,  then  the  object 
may  be  attained  by  increasing  the  thickness  of  the  ends  of 
the  light  and  medium  classes,  so  far  as  they  enter  the  hubs, 
464.  Characteristics  of  Pipe-Metals. — The  metal 
of  pipes  should  be  tough  and  elastic,  and  have  great 
tenacity.  In  proportion  as  these  qualities  are  lacking,  bulk 
of  metal,  increased  in  a geometrical  ratio,  must  be  sub- 
stituted to  produce  their  equivalents.  In  our  formula  given 
above  (§  452)  for  thickness  of  cast-iron,  it  will  be  re- 
membered that  we  were  obliged  to  add  a term  of  thickness 


If  the  metal  is  given  great  degrees  of  toughness  and  elas- 
ticity, we  may  omit,  for  the  larger  pipes,  this  last  member 
of  the  formula  ; but  now  we  add  to  each  twelve-foot  piece 
of  pipe,  of  20-incli  diameter,  five  or  six  hundred  pounds ; 
36-incli  diameter,  six  or  eight  hundred  pounds,  etc.,  that 
would  not  be  required  with  a superior  metal. 

It  is  expensive  to  freight  this  extra  metal  a hundred  or 
more  miles,  and  then  to  haul  it  to  the  trenches  and  swing  it 
into  place,  and  at  the  same  time  to  submit  to  the  breakage 
of  from  three  to  five  per  cent,  of  the  castings  because  of  the 
brittleness  of  the  inferior  metal. 

It  is  well  known  that  the  same  qualities  of  iron  stone,  and 
of  fuel,  may  produce  from  the  same  furnace  very  different 
qualities  of  pigs,  and  it  is  the  smelter  s business  to  know, 
and  he  generally  does  know,  whether  he  has  so  proportioned 
his  materials  and  controlled  his  blast,  as  to  produce  pigs 
that  when  remelted  will  flow  freely  into  the  mould,  take 
sharply  its  form,  and  become  tough  and  elastic  castings. 
The  founders  will  supply  a refined  and  homogeneous  iron, 
if  such  quality  is  clearly  specified,  and  it  is  well  worthy  of 


enable  the  pipes  to  be  safely  handled. 


CHARACTERISTICS  OP  PIPE  METALS. 


471 


consideration  in  the  majority  of  cases  wli ether  such  iron 
will  not  be  in  fact  the  most  economical,  at  its  fair  additional 
cost,  if  extra  weight,  extra  freight  and  haulage,  and  extra 
breakage,  are  duly  considered. 

Expert  inspectors  cannot  with  confidence  pronounce 
upon  the  quality  of  the  cast  metal  from  an  examination 
of  its  exterior  appearance,  nor  infallibly  from  the  appear- 
ance of  its  fracture.  Wilkie  says*  of  the  fracture  of  good 
No.  1 cast-iron,  that  it  shows  a dark  gray  color  with  high 
metallic  lustre  ; the  crystals  are  large,  many  of  them  shining 
like  particles  of  freshly-cut  lead ; and  that  however  thin 
the  metal  may  be  cast,  it  retains  its  dark  gray  color.  It 
contains  from  three  to  five  per  cent,  of  carbon.  This  is 
the  most  fusible  pig  iron  and  most  fluid  when  melted,  and 
superior  castings  may  be  produced  from  it. 

No.  3 has  smaller  and  closer  crystals,  which  diminish  in 
size  and  brightness  from  the  centre  of  the  casting  toward 
the  edge.  Its  color  is  a lighter  gray  than  No.  1,  with  less 
lustre.  No.  2 is  intermediate  in  appearance  and  quality 
between  Nos.  1 and  3. 

The  “ bright ,”  “mottled”  and  “ white ” irons  have  still 
lighter  colored  fractures,  with  a white  “list”  at  the  edges, 
are  less  fusible,  and  are  more  crude,  hard,  and  brittle. 

The  mottled  and  white  irons  are  sometimes  produced  by 
the  furnace  working  badly,  or  result  from  using  a minimum 
of  fuel  with  the  ore  and  flux. 

The  crystals  of  the  coarser  kinds  of  cast-irons  were  found 
by  Dr.  Schott,  in  his  microscopical  examinations  of  frac- 
tures, to  be  nearly  cubical,  and  to  become  flatter  as  the 
proportion  of  carbon  decreased  and  the  grain  became  more 
uniform. 


* “The  manufacture  of  Iron  in  Great  Britain.”  London,  1857. 


472 


MAINS  AND  DISTRIBUTION  PIPES. 


In  wrought  iron,  the  double  pyramidal  form  of  the  cast 
crystal  is  almost  lost,  and  has  become  flattened  down  to 
parallel  leaves,  forming  what  is  termed  the  fibre  of  the  iron 

In  steel  the  crystals  have  become  quite  parallel  and 
fibrous. 

465.  Tests  of  Pipe  Metals. — The  toughness  and  elas- 
ticity of  pipe  metal  may  be  tested  by  taking  sample  rings 
of,  say,  24-inch  diameter,  1-inch  width,  and  f-incli  thickness, 
hanging  them  upon  a blunt  knife-edge,  and  then  suspending 
weights  from  them,  at  a point  opposite  to  their  support, 
noting  their  deflections  down  to  the  breaking  point ; also,  by 
letting  similar  rings  fall  from  known  heights  upon  solid  an- 
vils. The  iron  may  also  be  submitted  to  what  is  termed  the 
“beam  test,”  generally  adopted  to  measure  the  transverse 
strength  and  elasticity  of  castings  for  building  purposes. 

In  such  case  the  standard  bar,  Fig.  99,  is  2 ft.  2 in.  long, 

1 in.  deep,  and  2 in.  broad,  and 
is  placed  on  bearings  2 ft.  apart, 
and  is  loaded  in  the  middle  till 
broken. 

Iron  that  lias  been  first  skill- 
fully made  into  pigs,  from  good 
ore  and  with  good  fuel,  and  has 
then  been  remelted,  should  sustain  in  the  above  described 
1 1 dam  test,  from  1,800  to  2,200  pounds,  and  submit  to  a 
deflection  of  from  T3o  to  tV  inch. 

The  tenacity  of  the  iron  is  usually  measured  by  submit- 
ting it  to  direct  tensile  strain  in  a testing  machine,  fitted  for 
the  purpose.  Its  tenacity  should  reach  an  ultimate  limit 
of  23,000  pounds  per  square  inch  of  breaking  section,  while 
still  remaining  tough  and  elastic.  Hard  and  brittle  irons 
may  show  a much  greater  tenacity,  though  making  less 
valuable  pipes. 


Fig.  99. 


THE  PRESERVATION  OF  PIPE  SURFACES. 


473 


466.  The  Preservation  of  Pipe  Surfaces.— The 

uncoated  iron  mains  lirst  laid  down  in  London,  by  the  New 
River  Company,  were  supposed  to  impart  a chalybeate 
quality  to  the  water,  and  a wash  of  lime-water  was  applied 
to  the  interiors  of  the  pipes  before  laying  to  remedy  this  evil. 

Before  iron  pipes  had  been  long  in  use,  in  the  early  part 
of  the  present  century,  in  those  European  towns  and  cities 
supplied  with  soft  water,  it  was  discovered  that  tuberculous 
accretions  had  formed  so  freely  upon  their  interiors  as  to 
seriously  diminish  the  volume  of  flow  through  the  pipes  of 
three,  four,  and  six-incli  diameters. 

This  difficulty,  which  was  so  serious  as  to  necessitate  the 
laying  of  larger  distribution  pipes  than  would  otherwise 
have  been  necessary,  engaged  the  attention  of  British  and 
continental  engineers  and  chemists  from  time  to  time.  Many 
experimental  coatings  were  applied,  of  silicates  and  oxides, 
and  the  pipes  were  subjected  to  baths  of  hot  oil  under 
pressure,  with  the  hope  of  fully  remedying  the  difficulty. 
A committee  of  the  British  Association  also  inquired  into 
the  matter  in  connection  with  the  subject  of  the  preservation 
of  iron  ships,  and  instituted  valuable  experiments,  which 
are  described  in  two  reports  of  Robert  Mallet  to  the  Asso- 
ciation. 

A similar  difficulty  was  experienced  with  the  uncoated 
iron  pipes  first  laid  in  Philadelphia  and  New  York. 

In  the  report  of  the  city  engineer  of  Boston,  January, 
1852,  mention  is  made  of  some  pipes  taken  up  at  the  South 
Boston  drawbridge,  which  had  been  exposed  to  the  flow 
of  Cochituate  water  nine  years. 

He  remarks  that  “ some  of  the  pipes  were  covered  inter- 
nally with  tubercles  which  measured  about  two  inches  in 
area  on  their  surfaces,  by  about  three-quarters  of  an  inch 
in  height,  while  others  had  scarcely  a lump  raised  in  them. 


474 


MAINS  AND  DISTRIBUTION-PIPES. 


Those  which  were  covered  with  the  tubercles  were  corroded 
to  a depth  of  about  one-sixteentli  of  an  inch ; the  iron  tc 
that  depth  cutting  with  the  knife  very  much  like  plumbago.’ 
Mr.  Slade,  the  engineer,  expressed  the  opinion,  after  com- 
paring the  condition  of  these  pipes  with  that  of  pipes  exam- 
ined in  1852,  that  the  corrosion  is  very  energetic  at  first, 
but  that  it  gradually  decreases  in  energy  year  by  year. 

The  process  used  by  Mons.  Le  Beuffe,  civil  engineer  of 
Vesoul,  France,  for  the  defence  of  pipes,  as  communicated* 
by  him  to  Mr.  Kirkwood,  chief  engineer  of  the  Brooklyn 
Water- works,  “consists  of  a mixture  of  linseed  oil  and 
beeswax,  applied  at  a high  temperature,  the  pipe  being 
heated  and  dipped  into  the  hot  mixture. 

The  varnish  of  M.  Crouziere,  tested  on  iron  immersed  in 
sea-water  at  Toulon,  by  the  French  navy,  consisted  of  a 
mixture  of  sulphur,  rosin,  tar,  gutta-percha,  minum,  blanch 
de  ceruse,  and  turpentine.  This  protected  a plate  of 
wrought  iron  perfectly  during  the  year  it  was  immersed. 

A process  that  has  proved  very  successful  for  the  preser- 
vation of  iron  pipes  used  to  convey  acidulated  waters  from 
German  mines,  is  as  follows  :f  “The  pipes  to  be  coated 
are  first  exposed  for  three  hours  in  a bath  of  diluted  sul- 
phuric or  hydrochloric  acid,  and  afterward  brushed  with 
water  ; they  then  receive  an  under-coating  composed  of 
34  parts  of  silica,  15  of  borax,  and  2 of  soda,  and  are  ex- 
posed for  ten  minutes  in  a retort  to  a dull  red  heat.  After 
that  the  upper  coating,  consisting  of  a mixture  of  34  parts 
of  feldspar,  19  of  silica,  24  of  borax,  16  of  oxide  of  tin,  4 of 
fluorspar,  9 of  soda,  and  3 of  saltpetre,  is  laid  over  the  inte- 
rior surface,  and  the  pipes  are  exposed  to  a white  heat  for 
twenty  minutes  in  a retort,  when  the  enamel  perfectly  unites 


* Vide  Descriptive  Memoir  of  the  Brooklyn  Water-works,  p.  43.  N I . , 1867. 
+ Vide  “Engineering.”  London,  Jan.,  1872,  p.  45. 


PRESERVATION  OF  PIPE  SURFACES 


475 


with  the  cast-iron.  Before  the  pipes  are  quite  cooled  down, 
their  outside  is  painted  with  coal-tar.  The  above  ingre- 
dients of  the  upper  coating  are  melted  to  a mass  in  a cru- 
cible, and  afterwards  until  little  water  ground  to  a fine 
paste.” 

Prof.  Barff,  M.A.,  proposes  to  preserve  iron  (including 
iron  water-pipes)  by  converting  its  surfaces  into  the  mag- 
netic or  black  oxide  of  iron,  which  undergoes  no  change 
whatever  in  the  presence  of  moisture  and  atmospheric 
oxygen 

He  says,  “ The  method  which  long  experience  has  taught 
us  is  the  best  for  carrying  out  this  process  for  the  protection 
of  iron  articles,  of  common  use,  is  to  raise  the  temperature 
of  those  articles,  in  a suitable  chamber,  say  to  500°  F.,  and 
then  pass  steam  from  a suitable  generator  into  this  cham- 
ber, keeping  these  articles  for  five,  six,  or  seven  hours,  a? 
the  case  may  be,  at  that  temperature  in  an  atmosphere  oi 
superheated  steam. 

“ At  a temperature  of  1200°  F.,  and  under  an  exposure 
to  superheated  steam  for  six  or  seven  hours,  the  iron  surface 
becomes  so  changed  that  it  will  stand  the  action  of  water 
for  any  length  of  time,  even  if  that  water  be  impregnated 
with  the  acid  fumes  of  the  laboratory.” 

The  first  coated  pipes  used  in  the  United  States,  were 
imported  from  a Glasgow  foundry  in  1858.  These  were 
coated  by  Dr.  Angus  Smith’s  patent  process,  which  had 
been  introduced  in  England  about  eight  years  eariier. 
Dr.  Smith’s  Coal  Pitch  Varnish  is  distilled  from  coal-tar 
until  the  naphtha  is  entirely  removed  and  the  material 
deodorized,  and  Dr.  Smith  recommends  the  addition  of  five 
or  six  per  cent,  of  linseed  oil. 

The  pitch  is  carefully  heated  in  a tank  that  is  suitable 
to  receive  the  pipes  to  be  coated,  to  a temperature  of  about 


476 


MAINS  AND  DISTRIBUTION-PIPES. 


300  degrees,  when  the  pipes  are  immersed  in  it  and  allowed 
to  remain  until  they  attain  a temperature  of  300°  Fall. 

A more  satisfactory  treatment  is  to  heat  the  pipes  in  a 
retort  or  oven  to  a temperature  of  about  310°  Fall.,  and 
then  immerse  them  in  the  bath  of  pitch,  which  is  maintained 
at  a temperature  of  not  less  than  210°. 

When  linseed  oil  is  mixed  with  the  pitch,  it  has  a ten- 
dency at  high  temperature  to  separate  and  float  upon  the 
pitch.  An  oil  derived  by  distillation  from  coal-tar  is  more 
frequently  substituted  for  the  linseed  oil,  in  practice. 

The  pipes  should  be  free  from  rust  and  strictly  clean 
when  they  are  immersed  in  the  pitch-batli. 

467.  Varnishes  for  Pipes  and  Iron-work. — A good 
tar  varnish , for  covering  the  exteriors  of  pipes  where  they 
are  exposed,  as  in  pump  and  gate  houses,  and  for  exposed 
iron  work  generally,  is  mentioned*  by  Ewing  Matheson, 
and  is  composed  as  follows : 30  gallons  of  coal-tar  fresh, 
with  all  its  naphtha  retained  ; 6 lbs.  tallow ; 1^  lbs.  resin ; 
3 lbs.  lampblack ; 30  lbs.  fresh  slacked  lime,  flnely  sifted. 
These  ingredients  are  to  be  intimately  mixed  and  applied 
hot.  This  varnish  may  be  covered  with  the  ordinary  lin- 
seed-oil paints  as  occasion  requires. 

A black  varnish , that  has  been  recommended  for  out- 
door iron  work,  is  composed  as  follows : 20  lbs.  tar-oil ; 
5 lbs.  asphaltum  ; 5 lbs.  powdered  rosin.  These  are  to  be 
mixed  hot  in  an  iron  kettle,  with  care  to  prevent  ignition. 
The  vamish  may  be  applied  cold. 

46S.  Hydraulic  Proof  of  Pipes. — When  the  cast- 
iron  pipes  have  received  their  preservative  coating,  they 
should  be  placed  in  an  hydraulic  proving-press,  and  tested 
by  water  pressure,  to  300  lbs.  per  sq.  in.  ; and  while  under 


“Works  in  Iron,”  p.  281.  London,  1873. 


HYDRAULIC  PROOF  OF  PIPES. 


477 


the  pressure  be  smartly  rung  with  a hammer,  to  test  them 
for  minor  defects  in  casting,  and  for  undue  internal  strains. 

Fig.  100  is  one  of  the  most  simple  forms  of  hydraulic 
proving-presses.  The  cast-iron  head  upon  the  left  is  fixed 
stationary,  while  toward  the  right  is  a strong  head  that  is 
movable,  and  that  advances  and  retreats  by  the  action  cf 


Fig.  100. 


the  screw  working  in  the  nut  of  the  fixed  head  at  the  right. 
When  the  pipe  is  rolled  into  position  for  a test,  suitable 
gaskets  are  placed  upon  its  ends,  or  against  the  two  heads, 
and  then  by  a few  turns  of  the  hand-wheel  of  the  screw,  the 
movable  head  is  set  up  so  as  to  press  the  pipe  between  the 
two  heads.  Levers  are  then  applied  to  the  screw,  and  the 
pressure  increased  till  there  will  be  no  leakage  of  water  at 
the  ends  past  the  gaskets.  The  air-cock  at  the  right  is  then 
opened  to  permit  escape  of  the  air,  and  the  water-valve  at 
the  left  opened  to  fill  the  pipe  with  water.  The  hydraulic 
pump  and  the  water-pressure  gauge,  which  are  attached  at 
the  left,  are  not  shown  in  the  engraving.  When  the  pipe  is 
filled  with  water,  and  the  valves  closed,  the  requisite  pres- 
sure is  then  applied  by  means  of  the  pump.  Care  must  be 
taken  that  all  the  air  is  expelled,  before  pressure  is  applied, 
lest  in  case  of  a split,  the  compressed  air  may  scatter  the 
pieces  of  iron  with  disastrous  results. 


Fig.  101 


Fig.  102. 


Fig.  100. 


CEMENT-LINED  AND  COATED  PIPES. 


479 


409.  Special  Pipes. — Fig.  101  is  a section  through  a 
single  Branch,  with  side  views  of  lugs  for  securing  a cap  or 
hydrant  branch. 

Fig.  102  is  a section  through  a Reducer. 

Fig.  103  is  a section  through  a Bend. 

Fig.  104.  Fig.  105. 


Fig.  104  is  a section  through  a Sleeve,  the  upper  half 
being  the  form  for  covering  cut  ends  of  pipes,  and  the  lower 
half  the  form  for  uncut  spigot  ends. 

Fig.  105  is  a part  section  and  plan  of  a clamp  Sleeve. 


WROUG  HT-IRON  PIPES 

470.  Cement-Lined  and  Coated  Pipes. — Sheet-iron 
water-pipes,  lined  and  coated  with  hydraulic  cement  mor- 
tar, by  a process  invented  by  Jonathan  Ball,  were  laid  in 
Saratoga,  IN’.  Y.,  to  conduct  a supply  of  water  for  domestic 
purposes  to  some  of  the  citizens,  as  early  as  1845. 

The  inventor,  who  was  aware  of  the  ready  corrosion  of 
wrought-iron  when  exposed  to  a flow  of  water  and  to  tha 
dampness  and  acids  of  the  earth,  had  observed  the  pre* 
servative  influence  of  lime  and  cement  when  applied  to  iron, 
and  saw  that  with  its  aid,  the  high  tensile  strength  of 


180 


MAINS  AND  DISTRIBUTION-PIPES. 


wrought  or  rolled  iron,  could  be  utilized  in  water-pipes  to 
sustain  considerable  pressures  of  water,  and  the  weight  of 
the  iron  required,  thus  be  materially  reduced. 

The  reduction  in  the  weight  of  the  iron  reduced  also  the 
total  cost  of  the  complete  pipe  in  the  trench. 

The  favorable  qualities  of  hydraulic  cement  as  a conduc- 
tor of  potable  waters  had  long  been  well-known,  for  the 
Romans  invariably  lined  their  aqueducts  and  conduits 
with  it. 

Twenty-five  or  thirty  towns  and  villages,  and  a number 
of  corporate  water  companies  had  already  adopted  the 
wrouglit-iron  cement  lined  water  pipes  in  their  systems,  and 
still  others  were  experimenting  with  it  at  the  breaking  out 
of  the  civil  war  in  1861. 

As  one  result  of  the  war,  the  price  of  iron  * rose  to  more 
than  double  its  former  value,  and  the  difference  in  cost  be- 
tween cast  and  wrought  iron  pipes  became  conspicuous,  and 
the  cost  of  all  pipes  rose  to  so  great  total  sums  that  the  pipe 
of  least  first  cost  must  of  necessity  be  adopted  in  most 
instances,  almost  regardless  of  comparative  merits.  So 
long  as  the  high  prices  of  iron  and  of  labor  remained  firm, 
the  contractors  for  the  wrouglit-iron  were  enabled  to  lay  it 
at  a reduction  of  forty  per  cent,  from  the  cost  of  the  cast- 
iron  pipe. 

Increased  attention  to  sanitary  improvements  led  many 
towns  to  complete  their  water  supplies  even  at  the  high 
rates,  and  many  hundred  miles  of  the  cement-lined  pipes 
came  into  use. 

471.  Methods  of  Lining. — Its  manufacture  is  simple. 
The  sheet-iron  is  formed  and  closely  riveted  into  cylinders 

* New  York  and  Philadelphia  prices  current  record  the  nearly  regular 
average  monthly  increase  in  the  price  of  Anthracite  Pig  Iron  No.  1,  from  18f 
dollars  per  ton  of  2240  pounds  in  August,  1861,  to  73f  dollars  per  ton  in 
August,  1864. 


COVERING. 


481 


of  seven  or  eight  feet  in  length,  and  of  diameter  from  one 
to  one  and  one-lialf  inches  greater  than  the  clear  bore  of  the 
lining  is  to  be  finished.  The  pipe  is  then  set  upright  and  a 
short  cylinder,  of  diameter  equal  to  the  desired  bore  of  the 
pipe,  is  lowered  to  the  bottom  of  the  pipe.  Some  freshly 
mixed  hydraulic  cement  mortar  is  then  thrown  into  the  pipe 
and  the  cylinder,  which  has  a cone-shaped  front ; and  guid- 
ing spurs  to  maintain  its  central  position  in  the  shell,  is 
drawn  up  through  the  mortar.  A uniform  lining  of  the 
mortar  is  thus  compressed  within  the  wrought-iron  shell. 
The  ends  are  then  dressed  up  with  mortar  by  the  aid  of  a 
small  trowel  or  spatula,  and  the  pipes  carefully  placed  upon 
skids  to  remain  until  the  cement  is  set. 

The  interiors  of  the  pipe-linings  are  treated  to  a wash  of 
liquid  cement  while  they  are  still  fresh,  so  as  to  fill  their  pores. 

In  another  process  of  lining,  a smoothly-turned  cylin- 
drical mandril  of  iron,  equal  in  length  to  the  full  length  of 
the  pipe,  and  in  diameter  to  the  diameter  of  the  finished 
bore,  is  used  to  form  the  bore,  and  to  compress  the  lining 
within  the  shell.  A fortnight  or  three  weeks  is  required  for 
the  cement  to  set  so  as  safely  to  bear  transportation  or  haul- 
age to  the  trenches.  In  the  meantime  the  iron  is  or  should 
be  protected  from  storms  and  moisture,  and  also  from  the 
direct  rays  of  the  sun,  which  unduly  expands  the  iron,  and 
separates  it  from  a portion  of  the  cement  lining. 

47%.  Covering. — When  these  pipes  are  laid  in  the 
trench,  a bed  of  cement  mortar  is  prepared  to  receive  them, 
and  they  are  entirely  coated  with  about  one  inch  thickness 
of  cement  mortar,  as  is  shown  in  the  vertical  section  of  a 
six-inch  pipe,  Fig.  106. 

The  writer  has  used  upwards  of  one  hundred  miles  of 
this  kind  of  pipes,  and  the  smaller  sizes  have  proved  uni- 
formly successful. 

31 


482 


MAINS  AND  DISTRIBUTION-PIPES. 


Fig.  106. 


The  iron  is  relied  upon  wholly  to  sustain  the  pressure 
of  the  water  and  resist  the  effects  of  water-rams.  The 
cement  is  depended  upon  to  preserve  the  iron,  which  object 
it  has  accomplished  during  the  term  these  pipes  have  been 
in  use,  when  the  cement  was  good  and  workmanship  faith- 
ful, which,  unfortunately  for  this  class  of  pipe,  has  not 
always  been  the  case,  and  the  reputation  of  the  pipe  has 
suffered  in  consequence. 


473.  Cement- Joint. —A  sheet  -iron  sleeve,  about  eight 
inches  long,  as  shown  in  Fig.  107.  is  used  in  the  common 
form  of  joint  to  cover  the  abutting  ends  of  the  pipe  as  they 
are  laid  in  the  trench. 

The  diameter  of  the  sleeve  is  about  one  inch  greater  than 
the  diameter  of  the  wrought-iron  pipe  shell,  and  the  annular 
space  between  the  pipe  and  sleeve  is  tilled  with  cement.  The 
sleeve  and  pipe  are  then  covered  with  cement  mortar. 

In  a more  recently  patented  form  of  pipe,  the  shell  has  a 
taper  of  about  one  inch  in  a seven-foot  piece  of  pipe,  and 


Fig.  107. 


CAST  HUB-JOINTS. 


483 


the  small  end  of  one  piece  of  pipe  enters  about  four  inches 
into  the  large  end  of  the  adjoining  pipe,  thus  forming  a 
lap  without  a special  sleeve.  The  thickness  of  lining  in 
these  pipes  varies,  but  the  bore  is  made  uniform. 

474.  Cast  Hub- Joints. — The  writer  having  experienced 
some  difficulty  with  both  the  above  forms  of  cement-joints,  of 
the  larger  diameters,  and  desiring  to  substitute  lead  pack- 
ings for  the  cement,  in  a 20-inch  force  main,  to  be  subjected 
to  great  strains,  devised  the  form  of  joint  shown  in  Fig.  108. 


Fig.  108. 


In  this  case  the  wrought-iron  shells  were  riveted  up  as 
for  the  common  20-inch  pipe,  and  then  the  pipe  was  set 
upon  end  in  a foundry  near  at  hand,  a form  of  bell  moulded 
about  one  end,  and  molten  iron  poured  in,  completing  the 
bell  in  the  usual  form  of  cast-iron  bell.  A spigot  is  cast 
upon  the  opposite  end  in  a similar  manner.  The  lead  pack- 
ing is  then  poured  and  driven  up  with  a set,  as  the  pipes 
are  laid,  as  is  usual  with  cast-iron  pipes.  The  joint  is  as 
successful  in  every  respect  as  are  the  lead-joints  of  cast-iron 
pipes. 

The  force-main  in  question  has  been  in  use  upwards  of 
three  years,  and  water  was,  during  several  months  of  its 


484 


MAINS  AND  DISTRIBUTION-PIPES. 


earliest  use,  pumped  through  it  into  the  distribution  pipes, 
on  the  direct  pumping  system. 

For  lead  joints  on  wrouglit-iron  pipes  from  ten  to  sixteen 
inches  diameter  inclusive,  about  four  inches  width  of  the 
edge  of  the  spigot  end  sheet  may  be  rolled  thicker,  so  as  to 
bear  the  strain  of  caulking  the  lead,  as  a substitute  for  the 
cast  spigot. 

475.  Composite  Branches.  — The  wrought -iron 
branches  were  originally  joined  to  their  mains  by  the  appli- 
cation of  solder,  the  iron  being  lirst  tinned  near  and  at  the 
junction.  After  the  successful  pouring  of  the  bells,  the 
experiment  was  tried  of  uniting  the  parts  by  pouring  molten 
metal  into  a mould,  formed  about  them,  the  metal  being 


Fig.  109. 


cast  partly  outside  and  partly  inside  the  pipes,  as  in  the 
case  of  the  hub-joint.  The  parts  were  rigidly  and  veiy  sub- 
stantially united  by  the  process,  which  is  in  practical  effect 
equal  to  a weld. 

Fig.  109  shows  a section  of  a double  six-inch  branch  on 
a twelve-inch  sub-main. 


THICKNESS  OF  SHELLS  FOR  CEMENT  LININGS.  485 


Fig.  110  is  a section  of  a wrought-iron  angle  with  its 
parts  united  by  a cast  union. 

Several  holes,  similar  to  the  rivet  holes  of  the  pipe,  are 
punched  near  the  ends  to  be  united  at  different  points  in 
the  circumference,  so  that  the  metal  flows  through  them, 
as  shown  in  the  sketches. 


Fig.  110. 


The  writer  has  used  these  branches  and  angles  exclu- 
sively in  several  cities,  in  wrought-iron  portions  of  the 
distribution-pipes,  without  a single  failure. 

476.  Thickness  of  Shells  for  Cement  Linings. — 
When  computing  the  thickness  of  sheets  for  the  shells  of 
wrought-iron  cement-lined  pipes,  the  internal  diameter  of 
the  shell  itself,  and  not  of  finished  bore , is  to  be  taken. 
The  longitudinal  joints  of  the  shells  for  pipes  of  12-inch  and 
greater  diameters,  should  be  closely  double  riveted. 

The  tensile  strength  of  the  shells,  when  made  of  the  best 
plates,  may  be  assumed,  if  single  riveted,  36,000  pounds 
per  square  inch,  and  double  riveted  40,000  pounds  per 
square  inch. 

A formula  of  thickness,  given  above,  with  factor  of 
safety  = 4,  in  addition  to  allowance  for  water-ram,  may  be 
used  to  compute  the  thickness  of  plates,  viz.: 

t_(p  + 100  )d 
1 J5S  5 


(19) 


486 


MAINS  AND  DISTRIBUTION-PIPES. 


in  which  t is  the  thickness  of  rolled  plate,  in  inches. 
cl  “ diameter  of  the  shell,  in  inches. 
p “ static  pressure  due  to  the  head  in  lbs.  pei 
sq.  in.  = AMTi. 

S “ tenacity  of  riveted  shells,  in  lbs.  per.  sq.  in. 

The  following  table  gives  the  thickness  of  shells  foi 
cement  linings,  and  the  nearest  No.  of  Birmingham  gauge 
in  excess,  suitable  for  heads  of  from  100  to  300  feet,  by 
formula, 

/ _ (p  + ioov* 

.58  • 


TABLE  No.  9 9 

Thickness  of  Wrought  Iron  Pipe  Shells. 

(Diameters  4"  to  10"  single  riveted,  N = 36,ooolbs.  Diameters  12"  and  upward,  double  riveted, 

6*  = 40,000  lbs.) 


Head  ii 6 Feet. 

Head  175  Feet. 

Head  300  Feet. 

Diameter 
of  Bore. 

Diameter 
of  Shell. 

Thickness 

by 

Formula. 

Nearest 
No.  Birm. 
Gauge  in 
Excess. 

Thickness 

by 

Formula. 

Nearest 
No.  Birm. 
Gauge  in 
Excess. 

Thickness 

by 

Formula. 

Nearest 
No.  Birm. 
Gauge  in 
Excess. 

1 tic he  s. 

4 

Inches. 

5 

Inches . 

.0417 

T9 

Inches. 

.0486 

18 

Inches. 

.0639 

l6 

6 

7 

.0528 

17 

.0681 

IS 

.0894 

13 

8 

9-25 

.0771 

15 

.0899 

13 

.1182 

II 

10 

11.25 

•°937 

13 

.1094 

12 

• 1437 

9 

12 

T3-  25 

.0994 

12 

• 1 T59 

II 

• 1524 

8 

14 

15-25 

.1144 

12 

•1334 

IO 

• 1754 

7 

16 

17*5 

•1313 

10 

•I532 

8 

.2012 

6 

18 

19-5 

.1463 

9 

. 1706 

7 

.2242 

5 

20 

21-5 

.1613 

8 

.1881 

6 

.2472 

3 

22 

23-5 

•1763 

7 

.2056 

5 

.2702 

2 

24 

25-5 

• r9x3 

6 

•22  36 

4 

.2932 

1 

Shells  having  less  factors  of  safety  than  our  formula 
gives,  have  been  used  in  many  small  works.  A factor  not 
less  than  3,  beside  effect  of  water-ram,  should  always  be 


LINING  COVERING,  AND  JOINT  MORTAR. 


487 


taken,  and  this  may  be  found  directly  by  a formula  in  the 
following  form  for  double  riveted  steel  plate  conduits  : 


477.  Gauge  Thickness  and  Weights  of  Rolled 

Iron. — The  following  table  (No.  100)  gives  the  thicknesses 
and  weights  of  sheet-iron,  corresponding  to  Birmingham 
gauge  numbers ; also  thicknesses  and  weights  increasing 
by  sixteenths  of  an  inch. 

478.  Lining,  Covering,  and  Joint  Mortar. — The 

lining  mortar  and  covering  mortar  should  have  the  volume 
of  cement  somewhat  in  excess  of  the  volume  of  voids  in  the 
sand,  or,  for  linings,  equal  parts  of  the  best  hydraulic 
cement  and  fine-grained,  sharp,  silicious  sand ; and,  for 
coverings,  two-fifths  like  cement  and  three-fifths  like  sand. 

The  joint  mortar  should  be  of  clear  cement,  or  may  be 
of  four  parts  of  good  Portland  cement,  and  one  part  of 
hydraulic  lime,  with  just  enough  water  to  reduce  it  to  a 
stiff  paste. 

This  kind  of  pipe  demands  very  good  materials  for  all 
its  parts,  and  the  most  thorough  and  faithful  workmanship. 

A concrete  foundation  should  be  laid  for  it  in  quicksand, 
or  on  a soft  bottom,  and  a bed  of  gravel,  well  rammed, 
should  be  laid  for  it  in  rock  trench,  and  exceeding  care 
must  be  taken  in  replacing  the  trench  back-fillings.  Poor 
materials  or  slighted  workmanship  will  surely  lead  to  after 
annoyance. 

Some  of  the  cement-lined  pipes  are  given  a bath  in  hot 
asphaltum  before  their  linings  are  applied.  In  such  case,  a 
sprinkling  of  clean,  sharp  sand  over  their  surfaces  imme- 
diately after  the  bath,  while  the  coating  is  tacky,  assists  in 
forming  bond  between  the  cement  and  asphaltum. 


d X A34(h  + 230) 
40,000  lbs. 


X 1.5  = .000016275d(7i  + 230)  (20) 


-230  = 


230. 

d 


(20a) 


488 


MAINS  AND  DISTRIBUTION-PIPES. 


TABLE  No.  1 OO. 
Thicknesses  and  Weights  of  Plate-iron. 


Birming- 

ham 

gauge 

No. 

Thickness. 

Weight  of  a 
square  foot  ! 

Thickness, 

in 

sixteenths  ! 
of  an  inch. 

I 

Thickness, 
in  decimals  of 
an  inch. 

W eight  of 
a square  foot 

Inches . 

Pounds. 

Inches. 

Inches. 

Pounds. 

oooo 

• 454 

18.35 

I 

TJ 

•03125 

1.263 

ooo 

•425 

17.18 

I 

nr 

.06250 

2.526 

OO 

.38 

I5-36 

3 

A 2 

•09375 

3-789 

o 

•34 

13-74 

■S' 

.12500 

5-°52 

I 

•3 

12.13 

5 

AT 

•15625 

6.315 

2 

.284 

1 1.48 

3 

nr 

.18750 

7-578 

3 

• 259 

IO-47 

7 

m 

.21875 

8.841 

4 

.238 

9-6i9 

1 

* 

.25000 

IO.IO 

5 

.22 

8.892 

9 

XJ 

.28125 

H-37 

6 

.203 

8.205 

5 

nr 

•3I25° 

12.63 

7 

.18 

7-275 

1 1 

XI 

•34375 

13.89 

8 

.165 

6.669 

3 

¥ 

.375oo 

15.16 

9 

. 148 

5.981 

13 

II 

.40625 

16.42 

IO 

• 134 

5-4i6 

7 

n- 

.43750 

17.68 

ii 

.12 

4.850 

1 5 
T2 

.46875 

18.95 

12 

.109 

4-4°5 

1 

.50000 

20.21 

13 

•°95 

3.840 

9 

T<r 

.56250 

22.73 

14 

.083 

3-355 

5 

■S' 

.62500 

25.26 

15 

.072 

2.910 

1 1 
T6 

.68750 

27-79 

16 

.065 

2.627 

3 

.75000 

30-31 

17 

.058 

2-344 

13 

nr 

.81250 

32.84 

18 

.049 

1.980 

7 

"S' 

.87500 

35-37 

19 

.042 

1.697 

1 5 
nr 

.93750 

37-89 

20 

•°35 

I-4I5 

1 

1 

40.42 

21 

.032 

1.293 

IT5‘ 

1.06250 

42.94 

22 

.028 

1-132 

Ii 

1. 12500 

45-47 

23 

.025 

1. 010 

1.18750 

48.00 

24 

.022 

.8892 

if 

1.25000 

5°-52 

25 

.02 

.8083 

I1A' 

1-31250 

53-o5 

26 

.018 

.7225 

If 

1.37500 

55-57 

27 

.016 

.6467 

iff 

1.43750 

58.10 

28 

.014 

.5658 

If 

1.50000 

60.63 

29 

.013 

•5254 

T 9 

XT5 

1.56250 

03-I5 

30 

.012 

.4850 

T ^ 

1.62500 

65-6S 

3i 

.010 

.4042 

Iff 

1.68750 

68.20 

32 

.009 

•3638 

If 

1.75000 

7°-73 

33 

.008 

•3233 

iff 

1.81250 

73-26 

34 

.007 

.2829 

If 

1.87500 

75.78 

35 

.005 

.2021 

T I 5 

1-9375° 

7S.31 

36 

.004 

.1617 

2 

2 

So.S3_ 

ASPHALTUM-BATH  FOR  PIPES. 


489 


479.  Asphaltum-coated  Wrought-iron  Pipes. — 

Wrought-iron  pipes,  coated  with  asphaltum,  have  been 
used  almost  exclusively  in  California,  Nevada,  and  Oregon, 
some  of  those  of  the  San  Francisco  water  supply  being 
thirty  inches  in  diameter. 

Some  of  these  wrought-iron  pipes,  in  siphons,  are  sub- 
jected to  great  pressure,  as,  for  instance,  in  the  Virginia 
City,  Nevada,  supply  main,  leading  water  from  Marlette 
Lake. 

This  main  is  \l\  inches  diameter,  and  37,100  feet  in 
length,  and  crosses  a deep  valley  between  the  lake,  upon 
one  mountain  and  Virginia  City  upon  another.  The  inlet, 
where  the  pipe  receives  the  water  of  the  lake,  is  2,098  feet 
above  the  lowest  depression  of  the  pipe  in  the  valley,  where 
it  passes  under  the  Virginia  and  Truckee  Railroad,  and  the 
delivery  end  is  1528  feet  above  the  same  depression.  A 
portion  of  the  pipe  is  subjected  to  a steady  static  strain  of 
750  pounds  per  square  inch. 

The  thickness  of  this  pipe-shell  varies,  according  to  the 
pressure  upon  it,  as  follows  : 


( 

200  200 

33° 

430 

57° 

700 

950 

1050 

1250 

1400 

Head,  in  feet •< 

or  to 

to 

to 

to 

to 

to 

to 

to 

and 

1 

less.1  330 

43° 

570 

700 

950 

1050 

1250 

I4OO 

over. 

No.  of  iron,  Birmingham  gauge... 

1 6 i 15 

14 

12 

II 

9 

7 

5 

' 3 

0 

Thickness,  in  inches 

.065  .072 

b 

OO 

OJ 

.109 

.12 

.148 

.18 

.22 

•259 

•34 

The  joints  are  covered  with  a sleeve,  and  the  joint  pack- 
ing is  of  lead. 

480.  Asphaltum -Batli  for  Pipes. — A description  of 
the  asphaltum  coating,  as  prepared  for  these  pipes  by 
Herman  Schussler,  C.E.,  under  whose  direction  many  pipes 
have  been  laid,  is  given  in  the  January,  1874,  Report  of 
J.  Nelson  Tubbs,  Esq.,  Chief  Engineer  of  the  Rochester 
Water- works,  as  follows,  in  Mr.  Schussler’ s language  : 


490 


MAINS  AND  DISTRIBUTION-PIPES. 


“ The  purest  quality  of  asphaltum  (we  use  the  Santa 
Barbara)  is  selected  and  broken  into  pieces  of  lrom  the  size 
of  a hen’s  egg  to  that  of  a list.  With  this,  three  or  foni 
round  kettles  are  tilled  full,  then  the  interstices  are  tilled 
with  the  best  quality  of  coal  tar  (free  from  oily  substances), 
and  boiled  from  three  to  four  hours,  until  the  entire  kettle 
charge  is  one  semi-fluid  mass,  it  being  frequently  stirred  up. 

„ The  best  and  most  practical  test  then,  as  to  the  suitability 
of  the  mixture,  is  to  take  a piece  of  sheet  iron  of  the  thick- 
ness the  pipe  is  made  of,  say  six  inches  square,  it  being 
cold  and  freed  from  impurities,  and  dip  it  into  the  boiling 
mass,  and  keep  it  there  from  five  to  seven  minutes.  Imme- 
diately after  taking  it  out,  plunge  it  into  cold  water,  if 
possible  near  the  freezing-point,  and  if,  after  removal  from 
the  water,  the  coating  don’t  become  brittle,  so  as  to  jump 
off  the  iron  in  chips,  by  knocking  it  with  a hammer,  but 
firmly  adheres  (like  the  tin  coating  to  galvanized  iron),  the 
coat  is  good  and  will  last  for  ages.  If,  on  the  other  hand, 
it  is  brittle,  it  shows  that  there  is  either  too  much  oil  in  the 
tar  or  asphaltum,  or  the  mixture  was  boiled  too  hot,  or 
there  was  too  much  coal-tar  in  the  mixture  ; as  adding  coal- 
tar  makes  the  mixture  brittle,  while  by  adding  asphaltum 
it  becomes  tough  and  pliable.  The  pipes  are  immersed  in 
the  bath  as  thus  prepared.” 

Wrought-iron  pipes  of  this  description  are  extensively 
used  in  France,  in  diameters  up  to  48  inches. 

They  are  first  subjected  to  a bath  of  hot  asphaltum,  and 
then  the  exteriors  are  coated  -with  an  asphaltum  concrete, 
into  which  some  sand  is  introduced,  as  into  the  cement- 
covering above  described. 

481.  Wrought  Pipe  Plates.— The  shells  of  wrought 
iron  conduits  and  pipes  should  be  of  the  best  rolled  plates, 
of  tough  and  ductile  quality,  of  ultimate  strength  not  less 


WYCKOFF’S  PATENT  PIPE. 


491 


than  55,000  lbs.  per  square  inch,  and  that  will  elongate 
fifteen  per  cent,  and  reduce  in  sectional  area  twenty-five  per 
cent,  before  fracture. 

WOOD  PIPES. 

482.  Bored  Pipes.— The  wooden  pipes  used  to  replace 
the  leaden  pipes,  in  London,  that  were  destroyed  by  the 
great  fire,  three-quarters  of  a century  ago,  reached  a total 
length  exceeding  four  hundred  miles.  These  pipes  were 
bored  with  a peculiar  core-auger,  that  cut  them  out  in 
nests,  so  that  small  pipes  were  made  from  cores  of  larger 
pipes. 

The  earliest  water-mains  laid  in  America  were  chiefly  of 
bored  logs,  and  recent  excavations  in  the  older  towns  and 
cities  have  often  uncovered  the  old  cedar,  pitch-pine,  or 
chestnut  pipe-logs  that  had  many  years  before  been  laid  by 
a single,  or  a few  associated  citizens,  for  a neighborhood 
supply  of  water. 

Bored  pine  logs,  with  conical  faucet  and  spigot  ends, 
and  with  faucet  ends  strengthened  by  wrouglit-iron  bands, 
were  laid  in  Philadelphia  as  early  as  1797. 

Detroit  had  at  one  time  one  hundred  and  thirty  miles  of 
small  wood  water-pipes  in  her  streets. 

483.  Wyckoff’s  Patent  Pipe.— A patent  wood  pipe, 
manufactured  at  Bay  City,  Michigan,  has  recently  been 
laid  in  several  western  towns  and  cities,  and  has  developed 
an  unusual  strength  for  wood  pipes.  Its  chief  peculiarities 
are,  a spiral  banding  of  hoop-iron,  to  increase  its  resistance 
to  pressure  and  water-ram  ; a coating  of  asphaltum,  to 
preserve  the  exterior  of  the  shell ; and  a special  form  of 
thimble-joint. 

Fig.  Ill  is  a longitudinal  section  through  a joint  of  this 
wood  pipe,  showing  the  manner  of  inserting  the  thimble. 


492 


MAINS  AND  DISTRIBUTION-PIPES. 


Fig.  111. 


and  Fig.  112  is  an  exterior  view  of  the  pipe,  showing  the 
spiral  banding  of  hoop-iron,  and  the  asphaltum  covering. 

The  manufacturer’s  circular,  from  which  the  illustra- 
tions are  copied,  states  that  the  pipes  made  under  this 


Fig.  112. 


patent  are  from  white  pine  logs,  in  sections  eight  feet  long. 
The  size  of  the  pipes  is  limited  only  by  the  size  of  the  suit- 
able logs  procurable  for  their  manufacture. 

Judged  by  schedules  of  factory  prices,  these  pipes  do 
not  appear  to  be  cheaper  in  first  cost  than  wrought-iron 
pipes. 

A wood-stave  pipe  is  described  and  illustrated  in  §441, 
page  439,  and  in  the  Plate,  page  444a. 


Figs.  114,  115, 


flowers  stop-valve*- ^Flowers  Brothers,  Detroit.) 


coffin’s  stop-valve. --(Boston  Machine  Co.,  Boston.') 


CHAPTER  XXII. 

DISTRIBUTION  SYSTEMS,  AND  APPENDAGES, 

484.  Loss  of  Head  by  Friction.— In  the  chapter 
upon  flow  of  water  in  pipes  (XIII,  ante),  we  have  discussed 
at  length  the  question  of  the  maximum  discharging  ca- 
pacities of  pipes.  When  planning  a system  of  distribution 
pipes  for  a domestic  and  fire  service,  it  is  quite  as  import- 
ant to  know  how  much  of  the  available  head  rvill  be  con- 
sumed by,  or  will  remain  after,  the  passage  of  a given 
quantity  of  water  through  a given  pipe. 

For  a really  valuable  fire  service,  the  effective  head 
pressure  remaining  upon  the  pipes,  with  full  draught, 
should  be,  in  commercial  and  manufacturing  sections  of  a 
town,  not  less  than  one  hundred  and  fifty  feet , and  in 
suburban  sections,  not  less  than  one  hundred  feet . 

Water  at  such  elevations,  near  a town,  has  a large  com- 
mercial value,  whether  it  has  been  lifted  by  the  operations 
of  nature  and  retained  by  ingenuity  of  man,  or  has  been 
pumped  up  through  costly  engines  and  with  great  expend- 
iture of  fuel. 

When  sucli  head  pressures  are  secured  at  the  expense 
of  pumps  and  fuel,  they  are  too  costly  to  be  squandered  in 
friction  in  the  pipes.  Such  frictional  loss  entails  a corre- 
sponding daily  expense  of  fuel  so  long  as  the  works  exist. 
In  such  case,  the  pipes  may  be  economically  increased  in 
size  until  the  daily  frictional  expense  capitalized,  approxi- 
mates to  the  additional  capital  required  to  increase  the 
given  pipes  to  the  next  larger  diameters. 


494 


DISTRIBUTION  SYSTEMS,  AND  APPENDAGES. 


The  frictional  head  Ti"  in  pipes  under  pressure,  is  found 
by  the  formula, 

J'’=8!(4m)2 k'  (1) 

The  frictional  head  for  a given  diameter  is  as  the  square 
of  the  velocity,  nearly  (v2m)  and,  for  different  diameters, 
inversely  as  the  diameters. 

The  coefficient*  m decreases  in  value  as  the  velocity 
increases,  and  for  a given  velocity  decreases  as  the  diameter 
increases. 

485.  Table  of  Frictional  Heads  in  Pipes.— The 

following  table  (No.  101,  p.  495)  we  have  prepared  to  facili- 
tate frictional  head  calculations,  and  to  show  at  a glance  the 
frictional  effect  of  increase  of  velocity,  in  given  pipes  from 
4 to  36  inch  diameters.  The  second  and  last  columns  show 
also  the  theoretical  volume  of  delivery  through  clean,  smooth 
pipes  at  different  given  velocities.! 

The  fourth  column  gives  approximate  values  of  the 
coefficient  m for  given  diameters  and  velocities,  and  for 
clean  smooth  pipes  under  pressure. 

* Vide  Table  No.  62,  page  248,  of  coefficients  (m)  for  clean,  slightly  tuber- 
culated,  and  foul  pipes  ; also  § 274,  page  250,  for  formula  of  frictional  resist- 
ance to  flow. 

f There  will  be  a slight  reduction  of  volume  and  velocity,  and  increase  of 
coefficient  and  friction,  for  each  valve  and  branch,  and  material  changes  in 
these  respects  if  the  pipes  are  rough  or  foul. 


FRICTIONAL  HEAD  IN  MAIN  AND  DISTRIBUTION  PIPES, 
= h'\  in  each  1000  feet  length. 


FRICTIONAL  HEADS  IN  PIPES. 


495 


TABLE  No.  1 O 1 . 

Frictional  Head  in  Main  and  Distribution  Pipes  (in  each 
i ooo  feet  length),  h"  = (^v'2  (4m) ■ 


Diam. 

of 

pipe. 


Inches 

4 


Volume  of> 
water 


Velocity 

of 

flow. 


Cu.  ft.  per 
min. 

5 

7-5 

10 

12.5 
15 
17-5 
20 

17-5 

20 

22.5 

25 

27.5 
30 
35 
40 

45 

30 

35 

40 

45 

50 

55 

60 

65 

70 

75 

80 

85 

90 

60 
70 
80 
90 
100 
no 
120 
130 
140 
150 


Feet  per 
second. 

■933 

1.400 

1.867 

2.333 

2.300 

3-367 

3-733 

1- 435 

I.698 

1.910 
2.I2I 

2- 333 
2.546 
2.971 

3- 395 

3.819 

1-432 

1.671 

1. 910 
2.149 
2.387 
2.626 

2.86s 

3.104 

3-342 

3-53i 

3.820 
4.058 
4.297 

1- 334 

2.139 

2- 445 

2- 750 

3.056 

3- 362 
3.667 

3- 973 

4- 278 

4-584 


Coefficient 

of 

friction. 


.00773 

.00729 

.00704 

.00684 

.00668 

.00653 

.00644 

.O06S7 

.00674 

.00664 

.00657 

.00649 

.00643 

.00631 

.00621 

.00612 

.00657 

.00645 

.00635 

.00627 

.00620 

.00612 

.00607 

.00602 

.00596 

.00592 

.00587 

.005S3 

.00579 

.00610 

.00601 

.00592 

.00585 

■00579 

•00573 

.00567 

.00563 

.00559 

.00555 


Frictional  head 
per  1000  feet. 


Feet. 

I. 255 
2.663 
i. 57 3 
6.953 

' 9.758 
13.773 
16.723 

1.877 

*.w 

3.054 
3.705 
4.388 
5.177 
6. 9 IS 
8.891 

II. 081 

1.284 
1.678 
2.158 
2.698 
3.291 
3.945 
4.6 10 

5.404 

6.202 

7.073 

7.980 

.8.945 

9.960 

1.530 

2.118 

2.639 

3.298 

4.031 

Ji-827 

57683 

6.625 

7.627 

8.694 


U.  S.  gallons 
in  24  hours. 


Gallons. 

53.S56 

80,784 

107,712 

134,640 

l6l,56S 

iS8,4g6 

215,424 

188,496 

215,424 

242,352 

269,280 

296,208 

323,126 

376,992 

430,848 

484,704 


323,136 
376,992 
430,84s 
484,704 
538,560 
592,4i6 
646,272 
700, 128 
753,984 
807,840 
861,696 
915,552 
969,408 

646,272 

753,984 

861,696 

969,408 

1,077,120 

1,184,832 

1,292,544 

1,400,256 

1,507,968 

1,615,680 


496 


FRICTIONAL  HEADS  IN  PIPES. 


TABLE  No.  lO  1 — (Continued). 

Frictional  Head  in  Main  and  Distribution  Pipes  (in  each 
1000  feet  length). 


Diam. 

of 

pipe. 

Volume  of 

Velocity 

Coefficient 

of 

friction. 

Frictional  head 

U.  S.  gallons 

water 

flow. 

per  1000  feet. 

in  24  hours. 

Inches. 

Cu.  ft . per 
min. 

Feet  per 
second. 

m. 

Feet. 

Gallons. 

12 

120 

2.546 

.00571 

2.299 

1,292,544 

140 

2.971 

.00560 

3.070 

1,505,968 

160 

3-395 

.00553 

3.959 

1,723,392 

180 

3.820 

-00547 

4.958 

1,938,816 

200 

4.244 

.00541 

6.052 

2,154,240 

220 

4.668 

.00536 

7.254 

2,369,664 

24O 

5-093 

.00532 

8.571 

2,585,088 

14 

175 

2.728 

.00547 

2.167 

1,884,960 

200 

3.118 

.00541 

2.800 

2,154,240 

225 

3-508 

•00534 

3.498 

2,423,520 

250 

3-897 

.OO529 

4.277 

2,692,800 

275 

4-287 

.OO525 

5.137 

2,962,080 

300 

4.676 

.00521 

6.065 

3,231,360 

325 

5.067 

.00517 

7.060 

3,500,640 

350 

5-557 

.00513 

8.434 

3,769,920 

16 

225 

2.686 

.00532 

1.787 

2,423,520 

250 

2.984 

.00526 

2.157 

2,692,800 

275 

3.283 

.00522 

2.621 

2,962,080 

300 

3-58i 

.00518 

3.095 

3,231,360 

325 

3.879 

.OO514 

3.603 

3,500,640 

350 

4.178 

.00511 

4.155 

3,769,920 

375 

4-476 

.00508 

4-741 

4,039,200 

400 

4-775 

.OO505 

5.364 

4,308,480 

425 

5-073 

.00502 

6.018 

4.577,760 

450 

5-372 

.00500 

6.722 

4,S47,040 

475 

5.671 

.00498 

7.461 

5,116,320 

500 

5.968 

.00496 

8.230 

5,385,600 

18 

300 

2.829 

.00513 

1.700 

3,231,260 

350 

3.291 

.00506 

2.218 

3,769,920 

400 

3-763 

.00501 

2.938 

4,308,480 

450 

4.244 

.00496 

3.700 

4,847,040 

500 

4-7i6 

.OO492 

4-531 

5,385.600 

550 

5.186 

.00488 

5.435 

5,924,160 

600 

5.658 

.00485 

6.429 

6,462,720 

650 

6.130 

.00482 

7.397 

7,ooi,2So 

675 

6.365 

.00480 

8.052 

7,270,560 

FRICTIONAL  HEADS  IN  PIPES. 


497 


TABLE  No.  lO  1 — (Continued). 

Frictional  Head  in  Main  and  Distribution  Pipes  (in  each 
1000  feet  length). 


Diam. 

of 

pipe. 

Volume  of 

Velocity 

of 

flow. 

Coefficient 

of 

friction. 

Frictional  head 

U.  S.  gallons 

water 

per  1000  feet. 

in  24  hours. 

Inches . 

Cu.  ft.  per 
min. 

Feet  per 
second. 

111. 

Feet. 

Gallons. 

20 

350 

2.674 

.00500 

1.332 

3,769,920 

400 

3.056 

.00495 

1.723 

4,308,480 

450 

3-438 

.00491 

2.163 

4,847,040 

500 

3.820 

.00487 

2.61f8 

5,385,600 

550 

4.202 

.00483 

3.252 

5,924,160 

600 

4.584 

.00480 

3.759 

6,462,720 

650 

4.966 

.00478 

4-451 

7,ooi,2So 

700 

5.348 

.00476 

5.073 

7,539.840 

750 

5.730 

.00474 

5.802 

8,078,400 

800 

6.112 

.00472 

6.571 

8,616,960 

850 

6.494 

.00470 

7.387 

9A55.520 

goo 

6.875 

.00469 

8.261 

9,694,080 

24 

550 

2.918 

.00470 

1.243 

5,924,160 

600 

3-183 

.00467 

1.469 

6,462,720 

650 

3.448 

.00465 

1.716 

7,001,280 

700 

3-714 

.00463 

1.983 

7,539.840 

750 

3-979 

.00461 

2.267 

8,078,400 

800 

4.243 

.00459 

2.566 

8,616,960 

850 

4.508 

.00457 

2.951 

9.155,520 

900 

4-774 

.00455 

3.220 

9,694,080 

950 

5-039 

.00454 

3.580  . 

10,232,640 

1000 

5-304  * 

■00453 

3.967 

10,771,200 

1050 

5.569 

.00452 

4.353 

11,309,760 

1100 

5.835 

.00451 

4.769 

11,848,320 

1150 

6. 100 

.00450 

5.200 

12,386,880 

1200 

6.366 

.00449 

5.651 

12,925,440 

1250 

6.631 

.00448 

6.118 

13,464,000 

27 

800 

3-353 

.00450 

1.396 

8,616,960 

900 

3-772 

.00446 

1.752 

9,694,080 

1000 

4.192 

.00444 

2.154 

10,771,200 

1100 

4.611 

.00442 

2.594 

11,848,320 

1200 

5-031 

.00441 

3.081 

12,925,440 

1300 

5-450 

.00439 

3. 60 4 

14,002,560 

1400 

5.869 

.00437 

4.155 

15,079,680 

1500 

6.289 

.00436 

4.996 

16,156,800 

1600 

6. 708 

.00435 

5.403 

I7,233,92C) 

1700 

7.127 

.00434 

6.085 

18,311,040 

198 


DISTRIBUTION"  SYSTEMS,  AND  APPENDAGES. 


TABLE  No.  lO  1 — (Continued). 

Frictional  Head  in  Main  and  Distribution  Pipes  (in  each 
1000  feet  length). 


Diam. 

of 

pipe. 

Volume  of 

Velocity 

Coefficient 

Frictional  head 

V.  S.  gallons 

water 

flow. 

friction. 

per  1000  feet. 

in  24  hours. 

Inches. 

Cu.  ft.  per 
min. 

Feet  per 
second. 

771. 

Feet. 

Gallotts. 

30 

IOOO 

3-395 

•00435 

1.24.6 

10,771,200 

1200 

4.074 

.00431 

1.781 

12,925,440 

1400 

4-753 

.00428 

2.402 

15,079,680 

1600 

5-432 

.00426 

3.123 

17,233,920 

1800 

6.112 

.00424 

3.935 

19,388,160 

2000 

6-791 

.00422 

4.835 

21,542,400 

2200 

7-470 

.00420 

5.823 

23,696,640 

24OO 

8.149 

.00418 

6.906 

25,850,880 

36 

1500 

3-537 

.00408 

1.057 

16,156,800 

2000 

4.716 

.00404 

1.822 

21,542,400 

2500 

5-895 

.00400 

2.878 

26,928,000 

3000 

7-074 

■00397 

4.113 

32,313,600 

3500 

8.252 

■00395 

5.582 

37,699,200 

4000 

9-431 

.00393 

7.237 

43,084, Soo 

486.  Relative  Discharging  Capacities  of  Pipes. — 

The  volume  of  water  delivered,  q,  hv  a pipe,  is,  as  we  have 
seen  (§  296),  equal  to  the  product  of  its  section  Sf  into  its 
mean  velocity  of  flow  v, 


q — So. 

The  equation  of  velocity  is, 


v = 


2 grin, 

m j ’ 


hence  we  have,  for  full  pipes, 


By  uniting  the  two  terms  of  d , 
have  the  equation  of  volume,  q = 


’ = .7854#  • 

within  the  vinculum, 

6 303  { m, } * aDd 


we 


RELATIVE  CAPACITIES  OF  PIPES. 


499 


q = V2g  . 

q — ,3927c  . -! 


(.6168 5d'i)i 
4 m 

dh 


- - V2gJi . 


.61685^)1 
4 ml 


(2) 


The  relative  discharging  powers  of  pipes,  are  as  the 

/ d = ? 

quotients,  y — , or  as  c . d 2 or  nearly  as  the  square  roots 

of  the  fifth  powers  of  the  diameters. 

By  transposition  of  the  equation  for  volume,  q , we  have 
the  equation  for  diameter  of  long  pipes, 


d = .4789^  Hit 
V ll  ’ 


, , f q'l 

and  d = m 


(3) 


The  relative  diameters  required  for  equally  effective 
deliveries  are  as  the  products  V q* in,  or  fyq1  -r-  c’,  nearly  as 
the  fifth  roots  of  the  squares  of  the  volumes. 

487.  Table  of  Relative  Capacities  of  Pipes. — The 
following  table  (No.  102)  of  approximate  relative  discharg- 
ing powers  of  pipes,  will  facilitate  the  proper  proportioning 
of  systems  of  pipe  distributions.  It  shows  at  a glance  the 
ratio  of  the  square  root  of  the  fifth  power  of  any  diameter, 
from  3 to  48  inches,  to  the  square  loot  of  the  fifth  power  of 
any  other  diameter  within  the  same  limit. 

In  the  second  column  of  this  table,  the  diameter  1 foot 
is  assumed  as  unit,  and  the  ratios  of  the  square  roots  of  the 
fifth  powers  of  the  other  diameters,  in  feet , are  given  oppo- 
site to  the  respective  diameters  in  feet  written  in  the  first 
column.  Thus  the  approximate  relative  ratio  of  discharging 
power  of  a 3-foot  pipe  to  that  of  a 1-foot  pipe  is  as  15.588  to 
1 ; and  of  a .5  foot  pipe  to  a 1-foot  pipe  as  .1768  to  1 ; also 
the  relative  discharging  power  of  a 4-foot  pipe  is  to  that  of 
a 2-foot  pipe  as  32  to  5.657. 


Relative  Discharging  Capacities  of  Full,  Smooth  Pipes. 


500  DISTRIBUTION  SYSTEMS,  AND  APPENDAGES. 


DEPTHS  OF  PfPES. 


501 


The  last  vertical  column  gives  the  diameters  in  inches, 
as  does  also  the  horizontal  column  at  the  head  of  the  right- 
hand  section  of  the  table. 

The  numbers  in  the  intersections  of  the  horizontal  and 
vertical  columns  from  the  diameters  in  inches  give  also 
approximate  relative  discharging  capacities.  For  instance, 
a 48-inch  pipe  is  equal  in  discharging  capacity  to  15.59  six- 
teen-inch pipes,  or  8.92  twenty-inch  pipes,  or  5.65  twenty- 
four-inch  pipes,  or  1.58  forty-inch  pipes,  etc. 

In  domestic  pipe  systems  the  usual  limit  given  to 
frictions  of  flow  modifies  these  relative  capacities  by  allow- 
ing lesser  velocities  in  the  large  pipes.  For  instance,  in 
the  combined  fire  and  domestic  pipe  system  a 36-inch 
pipe  is  deemed  equivalent  to  13|  instead  of  151  twelve-inch 
pipes,  a 24-inch  pipe  is  equivalent  to  13.66  instead  of  15.58 
eight-inch  pipes,  and  a 16-inch  pipe  to  11  instead  of  11.6 
six-inch  pipes,  etc. 

488.  Depths  of  Pipes.— The  depths  at  which  pipes 
are  to  be  placed,  so  they  shall  not  be  injured  by  traffic  or 
frost,  is  a matter  for  special  local  study,  general  rules  being 
but  partially  applicable.  The  depth  is  controlled  in  each 
given  latitude,  or  thermic  belt,  by  first,  the  stability  of  the 
earth,  whether  it  be  soft  and  quaky,  or  heavy  clay,  or  close 
sand,  or  rock ; second,  whether  the  ground  be  saturated  by 
surface  waters  that  remain  and  freeze  and  conduct  down 
frost,  or  by  living  springs  flowing  up  and  opposing  deep 
penetration  of  frost ; third,  whether  the  ground  be  porous, 
well  underdrained  to  a level  below  the  pipes,  and  the  pores 
filled  with  air,  which  is  a good  non-conductor  ; and  fourth, 
whether  the  winds  sweep  the  snows  off  from  given  localities 
and  leave  them  unprotected,  or  given  localities  are  shaded 
and  the  severity  of  night  is  uncounteracted  at  noonday. 

Along  those  thermic  lines  whose  latitudes  at  the  Atlan- 


502 


DISTRIBUTION  SYSTEMS,  AND  APPENDAGES. 


tic  coast  are  as  given,  the  depths  of  the  axes  of  the  pipes,  in 
close  gravelly  soils,  may  he  approximately  as  follows : 


T A B L E No.  103. 

Approximate  Depths  for  Axes  of  Water-pipes. 


Diam. 

Latitude 
40°  North. 

Latitude 
42°  North. 

Latitude 
44°  North. 

Diam. 

Latitude 
40°  North. 

Latitude 
42°  North. 

Latitude 
44 : North. 

Depth  of 

Depth  of 

Depth  of 

Depth  0/ 

Depth  0/ 

Depth  of 

axis. 

axis. 

axis . 

axis. 

axis. 

axis. 

// 

t // 

/ /r 

/ // 

// 

1 // 

/ // 

t ir 

4 

4-8 

5—2 

6 — 2 

20 

4 — 10 

5—  5 

6—3 

6 

4-8 

5—2 

6 — 2 

22 

4 — 10 

5—  5 

6—3 

8 

4—7 

5—i 

6 — 2 

24 

4-1 1 

5—  6 

6-4 

10 

4—7 

5— i 

6 — 2 

27 

4-1 1 

5—  7 

6-4 

12 

4-7 

5— r 

6 2 

30 

5—  0 

5-  8 

6-4 

14 

4—7 

5—2 

6 — 2 

33 

5—  0 

5—  9 

6—5 

16 

4-8 

5—3 

6 — 2 

36 

5—  0 

5—10 

6-6 

18 

4—9 

5—4 

6—3 

40 

5-  1 

5 — n 

6—7 

There  is  a general  impression  that  the  water  passed  into 
pipes,  will  in  a very  short  time  take  the  temperature  of  the 
ground  in  which  the  pipes  are  laid.  Close  observation  does 
not  confirm  this  impression. 

If  water  at  a high  temperature  is  admitted  to  a deep 
pipe  system,  in  the  early  summer,  while  the  ground  is  yet 
cool,  the  consumers  will  derive  but  little  benefit  from  the 
coolness  of  the  earth,  and  this  is  especially  the  case  when 
the  pipes  are  coated  and  lined  with  cement. 

Frost  also  penetrates  at  various  points  as  low  as  the 
bottoms  of  sub-mains,  without  seriously  interfering  with 
the  flow,  and  water-pipes  are  often  suspended  beneath 
bridges,  where  ice  forms  in  the  river  near  by,  a foot  or  more 
in  thickness,  without  their  flow  being  interfered  with.  An 
eight  or  ten  inch  pipe  will  resist  cold  a long  time  before  it 
will  freeze  solid. 

The  hydrants,  small  dead  ends,  and  service-pipes  are 


RATES  OF  CONSUMPTION  OF  WATER. 


503 


most  sensitive  to  cold,  and  their  depths  and  coverings  should 
receive  especial  attention. 

Dead  ends  should  be  avoided  as  much  as  possible,  and 
circulation  maintained  for  the  protection  of  the  pipes  against 
frost,  as  well  as  to  maintain  the  purity,  and  to  reenforce 
How  to  the  fire  hydrants. 

489.  Elementary  Dimensions  of  Pipes.— A table 
of  the  elementary  dimensions  of  pipes  facilitates  so  mucin, 
pipe  calculations,  that  we  insert  it  here  (p.  504).  The  last 
column  gives  also  the  quantity  of  water  required  to  fill  each 
lineal  foot  of  the  pipes,  when  laid  complete,  or  the  quan- 
tities they  contain. 

490.  Distribution  Systems. — We  have  now  reduced 
to  tabular  form  the  data  that  will  assist  in  establishing  the 
proportions  of  the  several  parts  of  a system  of  distribution 
pipes,  for  the  domestic  and  fire  supply  of  a town  or  city. 

For  illustration,  let  us  assume  a case  of  a thriving  young 
city  of  25,000  inhabitants,  situated  on  the  bank  of  a naviga- 
ble river,  and  that  the  contour  of  the  land  had  permitted 
its  streets  to  be  straight,  and  to  intersect  at  right-angles. 
In  such  case  its  system  of  distribution  pipes  will  form  a 
series  of  parallelograms,  inclosing  one,  two  or  more  of  the 
city  blocks,  as  circumstances  require,  substantially  as  is 
shown  in  the  plan  of  a system  of  pipes,  Fig.  1 1 3. 

491.  Rates  of  Consumption  of  Water. — The  healthy 
growth  of  the  city  gives  reason  to  anticipate  an  increase  to 
35,000  inhabitants  within  a decade,  and  this  number  at 
least  should  be  provided  for  in  the  first  supply  main,  the 
first  reservoir,  and  such  parts  as  are  expensive  to  duplicate, 
and  a larger  number  should  be  provided  for  in  the  con 
duit,  and  such  parts  as  are  very  expensive  and  difficult  to 
duplicate. 

The  continued  popularization  of  the  use  of  water,  and 


504 


DISTRIBUTION  SYSTEMS,  AND  APPENDAGES. 


TAB  L E N o.  1 04. 

Elementary  Dimensions  of  Pipes. 


Diameter 

Diameter. 

Contour. 

Sectional  area. 

Hydraulic 
mean  radius. 

Cubical  con- 
tents per  lineal 
foot 

Inches. 

Feet. 

Feet. 

Sq.  feet. 

Cubic  feet. 

I 

~2 

.0417 

.1310 

.001366 

.0104 

.001366 

3 

.0625 

.1965 

.003068 

.0156 

.003068 

i 

.083 

.2618 

•005454 

.0208 

•005454 

.1250 

•3927 

.01227 

.0312 

.01227 

if 

•MS8 

.4581 

.01670 

.0364 

.01670 

2 

.1667 

•5235 

.02185 

.0418 

.02232 

3 

.250 

•7854 

.04909 

•0625 

.04909 

4 

•3333 

I.O47 

.08726 

•0833 

.08726 

6 

.5000 

i-57i 

•19635 

.1250 

•19635 

8 

.6667 

2.094 

•3490 

. 1666 

• 3490 

IO 

•8333 

2.618 

•5454 

.2083 

•5454 

12 

1. 0000 

3-142 

.7854 

.2500 

• 7854 

14 

1. 1667 

3-^65 

1.069 

.2916 

1.069 

16 

1-3333 

4.189 

!-397 

•3333 

!-397 

18 

1.5000 

4.713 

1.767 

•3750 

1.767 

20 

1.6667 

5-235 

2. 181 

.4166 

2. 181 

24 

2.0000 

6.283 

3.142 

.5000 

3-142 

27 

2.2500 

7.069 

3-976 

• 5625 

3-976 

30 

2.5000 

7-854 

4.909 

.6250 

4.909 

33 

2.7500 

8.639 

5-940 

.6875 

5-940 

36 

3.0000 

9-425 

7.069 

• 7500 

7.069 

40 

3-3333 

10.47 

8. 726 

• 8333 

8.726 

44 

3.6667 

11.52 

10.558 

.9166 

10.558 

48 

4.0000 

12.56 

12.567 

1. 0000 

12.567 

54 

4.5000 

14.14 

15-905 

1.1250 

I5-905 

60 

5.0000 

I5-7I 

I9-635 

1. 2500 

I9-635 

72 

6.0000 

19.29 

29.607 

1. 5000 

29.607 

84 

7.0000 

21.99 

38.484 

1-7500 

38.484 

96 

8.0000 

25-45 

50.265 

2.0000 

50.265 

PLAN  OK  A DISTRIBUTION  sWBic. 


Fro.  113. 


506 


DISTRIBUTION  SYSTEMS,  AND  APPENDAGES. 


the  increasing  demand  for  it  for  domestic,  irrigating,  orna- 
mental, and  mechanical  purposes,  with  the  increasing  waste 
to  which  they  all  tend,  requires  that  at  least  an  annual 
average  of  75  gallons  per  capita  daily  must  he  provided  for 
the  35,000  persons. 

In  our  discussion  of  the  varying  consumption  of  water 
(§  19),  it  is  shown  that  in  certain  seasons,  days  of  the  week, 
and  hours  of  the  day,  the  rate  of  consumption,  independent 
of  the  fire  supply,  is  seventy-five  per  cent,  greater  than  the 
average  daily  rate  for  the  year.  In  anticipation  of  this 
varying  rate,  we  should  proportion  our  main  for  not  less 
than  fifty  per  cent,  increase  (=  75  x 1.50  = 112.5),  or  for  a 
rate  of  112.5  gallons  per  capita  daily,  which  for  35,000  per- 
sons equals  a rate  of  365  cubic  feet  per  minute. 

492.  Rates  of  Fire  Supplies. — For  fire  supply  we 
anticipate  the  possibility  of  two  fires  happening  at  the  same 
time  requiring  ten  hose  streams  each.  The  minimum  fire 
supply  estimate  is,  then,  twenty  hose  streams  of  say  30 
cubic  feet  per  minute,  or  a total  of  600  cubic  feet  per  minute. 

The  combined  rate  of  flow  of  fire  and  domestic  supply  is 
(365  + 600)  965  cubic  feet  per  minute. 

493.  Diameter  of  Supply  Main. — Turning  now  to  the 
table  of  Frictional  Head  in  Distribution  Pipes,  and  looking 
for  volume  in  the  second  column,  we  find  that  a 24-inch 
pipe  will  deliver  965  cubic  feet  per  minute,  with  a velocity 
of  flow  of  about  5 feet  per  second,  and  with  a loss  of  head 
of  about  3.7  feet  in  each  thousand  feet  length  of  main.  A 
20-incli  pipe  will  deliver  the  same  volume  with  a velocity 
of  flow  of  about  7.38  feet  per  second,  and  with  a loss  of 
head  of  about  10  feet  in  each  thousand  feet  length.  Fnless 
the  main  is  short,  this  velocity,  and  this  loss  of  head,  in- 
creased by  the  loss  at  angles  and  valves,  is  too  great.  We 
adopt,  therefore,  the  24-inch  diameter  for  supply  main. 


MAXIMUM  VELOCITIES  OF  FLOW. 


507 


494.  Diameters  of  Sub-Mains. — We  now  compute 
the  portions  of  the  whole  supply  that  will  be  required  in 
each  section  of  the  city.  If  our  plan  of  distribution  is 
divided  into  twelve  sections,  then  the  average  section  sup- 
ply is  one-twelfth  of  the  whole.  We  find,  for  instance,  that 
Sec.  1 requires  85  per  cent,  of  the  average  ; Sec.  3,  125  per 
cent,  of  the  average  ; Sec.  12,  100  ppr  cent,  of  the  average  ; 
Sec.  22,  95  per  cent,  of  the  average,  for  domestic  use,  etc. 

Now,  with  the  aid  of  the  table  of  relative  discharging 
powers  of  pipes,  and  the  table  of  frictional  heads  in  pipes, 
we  can  readily  assign  the  diameters  to  the  sub-mains  that 
are  to  distribute  the  waters  to  the  several  sections,  adding 
to  both  domestic  and  fire  supply  volumes  for  the  nearest 
sections  the  estimated  volumes  that  are  to  pass  beyond  them 
to  remoter  sections. 

This  done,  we  may  sum  up  the  frictional  losses  of  head 
along  the  several  lines  from  the  supply  to  any  given  point, 
and  deduct  the  sum  from  the  static  head,  and  see  if  the 
required  effective  head  remains.  The  volume  and  effective 
head  are  matters  of  the  utmost  importance,  when  the  pipes 
are  depended  upon  exclusively  to  supply  the  waters  re- 
quired for  fire  extinguishment.  The  lack  of  these  has  cost 
several  of  our  large  cities  a million  dollars  and  more  in  a 
single  night. 

An  inspection  of  the  table  of  Frictional  Head  shows  how 
rnpidly  the  friction  increases  when  velocity  increases.  The 
increase  of  frictions  are,  in  the  same  pipe,  as  the  increase  of 
squares  of  velocities  ( v2m ),  nearly. 

495.  Maximum  Velocities  of  Flow. — As  a general 
rule,  the  velocities  in  given  pipes  should  not  exceed,  in  feet 
per  second,  the  rates  stated  in  the  following  table  for  the 
respective  diameters. 


508 


DISTRIBUTION  SYSTEMS,  AND  APPENDAGES. 


TABLE  No.  lOS. 

Maximum  Velocities  of  Flow  in  Supply  and  Distribution  Pipes. 


Diameter,  in  inches 

4 

6 

8 

IO  12  14  j l6  | l8  20  22 

24 

27  3° 

33 

36 

Velocity,  in  ft.  per  sec. . . . 

31 

3-9 

4-5 

5-o  5-5  5-8  6.0  6.2  6.5  6.6 

1 1 1 1 1 1 

6.7 

6.9  7.0 

1 

7-i 

7* 

496.  Comparative  Frictions. — As  regards  friction 
alone  in  any  given  pipe,  it  does  not  matter  whether  the 
water  is  flowing  up  a hill  or  down  a hill,  or  materially  if 
the  pressure  is  great  or  little;  or  in  long,  conical,  and 
smooth  pipes,  whether  the  water  is  flowing  toward  the  large 
end  or  toward  the  small  end.  The  total  friction  will  he  the 
same  in  both  directions  in  the  first  case,  and  will  also  be  the 
same  in  both  directions  in  the  last  case.  In  the  conical 
pipe,  however,  the  friction  per  unit  of  length,  or  per  lineal 
foot,  will  be  less  than  the  average  at  the  large  end,  because 
the  velocity  of  flow  will  be  less  there,  and  more  than  the 
average  at  the  small  end.  The  total  frictional  head  will  be 
the  same  as  though  the  whole  pipe  had  a uniform  diameter 
just  equal  to  the  diameter  in  the  conical  pipe  at  the  point 
where  the  friction  is  equal  to  the  average  for  the  whole 
length. 

497.  Relative  Rates  of  Flow  of  Domestic  and 
Fire  Supplies. — The  actual  consumption  of  water  by  the 
fire  department  for  the  extinguishment  of  fires,  in  any  city, 
per  annum,  is  very  insignificant  wheu  compared  with  either 
the  domestic,  the  irrigation  and  street  sprinkling,  or  the 
mechanical  supply  for  the  same  limit  of  time,  yet  it  has 
appeared  above  that  the  pipe  capacity  required  for  the  fire 
sendee,  in  the  general  main  of  a small  city,  exceeds  that 
required  for  the  whole  remaining  consumption.  If  we 
examine  this  question  still  closer,  taking  a length  of  120C 
feet  of  distribution  pipe  in  a closely  built  up  section  of  the 


REQUIRED  DIAMETERS  FOR  FIRE  SUPPLIES. 


509 


city,  we  find  on  tlie  1200  feet  length,  say  40  domestic  service 
pipes,  and  consumption  of  say  750  gallons  each  per  day,  or 
total  of  15000  gallons  per  day.  Making  due  allowance  for 
fifty  per  cent,  increase  of  flow  at  certain  hours,  we  have  a 
required  delivery  capacity  of  1.5  cubic  feet  per  minute  to 
cover  this  whole  consumption.  On  the  same  1200  feet  of 
pipe  there  are,  say  four  fire-hydrants.  If  in  case  of  fire  we 
take  from  these  hydrants  only  four  streams  in  all,  of  30 
cubic  feet  per  minute  each,  we  require  a delivery  capacity 
of  120  cubic  feet  per  minute.  In  this  case,  which  is  not  an 
uncommon  one,  the  required  capacity  for  the  fire  service  is 
to  that  for  the  remaining  service  as  80  to  1. 

If  the  given  pipe,  1200  feet  long,  is  an  eight-inch  pipe, 
supplied  at  both  ends,  then  the  delivery  for  fire  at  each  end 
is  sixty  cubic  feet  per  minute.  Referring  to  the  table  of 
frictional  head,  we  find  that  this  quantity  requires  a velocity 
of  flow  of  2.865  feet  per  second,  and  consumed  head,  in  fric- 
tion, at  the  rate  of  4.6  feet  per  thousand  feet. 

If  the  120  cubic  feet  per  minute  must  all  come  from  one 
end  of  the  pipe,  then  the  pipe  should  be  ten  inches  diam- 
eter, in  which  case  the  velocity  will  be  nearly  four  feet  per 
second  and  the  head  consumed  at  the  rate  of  about  eight 
feet  per  thousand  feet  length. 

498.  Required  Diameters  for  Fire  Supplies. — 
As  a general  rule,  the  minimum  diameters  of  pipes  for  sup- 
plying given  numbers  of  hydrant  streams,  when  the  given 
pipes  are  one  thousand  feet  long,  and  static  head  of  water 
one  hundred  and  fifty  feet,  are  as  follows : 


510 


DISTRIBUTION  SYSTEMS,  AND  APPENDAGES. 


TABLE  No.  106. 

Diameters  of  Pipes  for  Given  Numbers  of  Hose  Streams. 


Number  of  hose  streams 

Approximate  total  quantity  of  water,  in 

cubic  feet  per  minute 

Required  diameter  of  pipe,  in  inches.  . . 

i 

3° 

6 

2 

60 

8 

3 

90 

8 

4 

120 

10 

s'  6 

150  l80 

lol  12 

7 

210 

12 

8 

240 

12 

9 

270 

M 

10 

300 

14 

11 

330 

14 

12 

360 

H 

Number  of  hose  streams 

13 

14 

15 

16 

17  18 

19 

20 

21 

22 

23 

24 

Approximate  total  quantity  of  water,  in 
cubic  feet  per  minute 

390 

420 

450 

480 

510  540 

S70 

600 

630 

660 

690 

720 

Required  diameter  of  pipe,  in  inches 

16 

16 

l6 

16 

18  18 

1 

18 

18 

18 

18 

20 

20 

If  the  pipes  are  short,  the  velocities  of  flow  may  be 
increased  somewhat,  for  a greater  ratio  of  loss  of  head  per 
unit  of  length  is  then  permissible. 

If  the  pipe  is  supplied  from  both  ends,  then  the  number 
of  hose  streams  may  be  doubled  without  increase  of  the 
frictional  head  ; hence  the  advantage  of  so  distributing  the 
sub-mains  as  to  deliver  a double  supply  to  as  many  points 
as  possible,  for  this  is  equivalent  to  doubling  the  capacity 
of  the  minor  pipes.  If  the  pipes  are  several  thousand  feet 
long,  and  have  a large  proportionate  domestic  draught, 
then  a due  increase  should  be  given  to  the  diameters. 

499.  Duplication  Arrangement  of  Sub-Mains. — 
When  the  sub-mains  can  be  distributed  in  parallel  lines,  at 
several  squares  distance,  and  “gridironed”  across  by  the 
smaller  service  mains,  as  in  the  plan,  Fig.  113,  or  arranged 
in  some  equivalent  manner,  then  a most  excellent  system 
will  be  secured.  In  such  case,  if  an  accident  happens  to  a 
pipe,  or  valve,  or  hydrant,  in  any  central  location,  there  are 
at  least  two  lines  of  sub-mains  around  that  point,  and  the 
supply  will  with  certainty  be  maintained  at  points  beyond. 

Pipes  are  always  liable  to  accident  in  consequence  of 
building  excavations,  sewerage  excavations,  sewer  over- 
flows, quicksand  or  clay  slides,  floods,  and  various  other 
causes  that  cannot  be  foreseen  when  the  pipes  are  laid ; and 


STOP-VALVE  SYSTEM. 


511 


.Fig.  118. 


when  new  hydrants  are  to  he  attached,  or  large  pipe  con- 
nections to  he  made,  or  repairs  to  he  made,  it  is  frequently 
necessary  to  shut  off  the  water.  The  advantage  of  dupli- 
cate lines ' of  supply  to  all  points  is  apparent  in  such  case. 
When  a city  has  become  dependent  on  its  pipes  for  its 
water  supply  and  protection  from  fire,  it  is  absolutely  neces- 
sary that  the  supply  he  maintained,  and  the  result  may  he 
disastrous  if  it  fails  for  an  hour. 

500.  Stop-Valve  System.— It  is  equally  advantage- 
ous to  have  a sufficient  number  of  stop-valves,  or  “gates,” 
as  they  are  frequently 
termed,  upon  the  pipe, 
so  the  water  may  he  shut 
off  from  any  given  point 
without  cutting  off  the 
supply  from  both  a long 
and  a broad  territory,  or 
even  a very  long  length 
of  pipe.  The  sub-main 
parallelogram  system 
shown  in  the  plan,  Fig. 

113,  permits  of  such  an  ar- 
rangement of  stop- valves, 
chiefly  of  small  diameters 
and  inexpensive,  that  an 
accident  at  any  point  will 
not  leave  that  point  with- 
out a tolerable  fire  pro- 
tection from  both  sides. 

For  instance,  if  it  is 
necessary  to  shut  off  in 
Section  2 a part  of  East 
Fourth  Street  between  Avenues  A and  D,  the  hydrants  at 


EDDY  S STOP-VALVE. 

(R.  D.  Wood  & Co.,  Philadelphia.) 


012 


DISTRIBUTION  SYSTEMS,  AND  APPENDAGES. 


the  corners  of  East  Third  and  Fifth  Streets  will  still  he  avail 
able.  If  the  gates  are  placed  at  each  branch  from  the  sub- 
mains,  and  at  the  intersections  of  the  sub-mains,  as  they 
should  be,  then  an  accident  to  a sub-main  will  not  neces- 
sitate the  shutting  off  of  any  service-main  joining  it,  for  the 
service-main  supplies  can  be  maintained  from  the  opposite 
ends.  Wherever  cross  service-mains  are  required,  as  in 
Avenues  B and  C,  in  Section  3 in  the  plan,  they  may  pass 
under  the  other  service-mains  whose  lines  they  cross  and 
have  gates  at  their  end  branches  only,  which  admits  of  their 
being  readily  isolated. 

501.  Stop-Valve  Locations. — A systematic  disposi- 
tion of  the  pipes  generally  should  be  adopted.  If  the  pipes 
are  not  placed  in  the  centres  of  streets,  they  should  be  placed 
with  strict  uniformity  at  some  certain  distance  from  the 
centre  of  the  street,  and  carefully  aligned,  and  uniformly 
upon  the  same  geographical  side,  as,  upon  the  northerly  and 
westerly  side.  The  stop-valves  should  be  disposed  also, 
with  rigid  system,  as,  always  in  the  line  of  the  street  boun- 
dary, the  line  of  the  curb,  or  some  fixed  distance  from  the 
centre  of  the  street.  An  accident  may  demand  the  prompt 
shutting  of  any  gate  of  the  whole  number,  at  any  moment 
of  day  or  night ; and  if,  perchance,  its  curb-cover  is  hidden 
by  frozen  earth  or  by  snow,  it  is  important  to  know  exactly 
where  to  strike  without  first  journeying  to  the  office  and 
searching  for  a memorandum  of  distances  and  bearings. 
Searching  for  a gate-cover  buried  under  frozen  earth  is  a 
tedious  operation,  and  it  is  not  always  possible  to  uncover 
every  one  of  several  hundred  gates  after  every  thaw  and 
every  snow-storm  in  winter. 

Strict  adherence  to  a system  in  locating  gates  enables 
new  assistants  to  readily  learn  and  to  know  the  exact  posi- 
tion of  them  all. 


STOP-VALVE  DETAILS. 


513 


Strict  adherence  to  system  in  locating  pipes  is  requisite 
for  the  strict  location  of  gates,  and  pipes  should  be  cut,  if 
necessary,  to  bring  the  gates  to  their  exact  locations.  If  a 
gate  is  a half-length  of  pipe  out  of  position,  it  may  cost 
several  hours  delay  in  digging  earth  frozen  hard  as  a sand- 
stone rock,  to  find  the  gate-cover. 

502.  Blow-off,  and  Waste  Valves.— When  pipes  are 
located  upon  undulating  ground,  blow-off  valves  and  pipes 
will  be  required  in  the  principal  depressions  of  the  mains 
and  sub-mains,  to  flush  out  the  sediment  that  is  deposited 
from  unfiltered  water.  The  diameters  of  the  blow-off  pipes 
may  be  about  half  the  diameters  of  the  mains  from  which 
they  branch.  Smaller  wastes  will  answer  for  the  drainage 
of  the  service-main  sections  for  repairs  or  connections,  and 
these  may  lead  into  sewers,  or  wherever  the  waste-water 
may  be  disposed  of. 

503.  Stop- Valve  Details. — A variety  of  styles  of  stop- 
valves  are  now  offered  by  different  manufacturers,  and  a 
special  advantage  is  claimed  for  each,  so  that  no  little  prac- 
tical sagacity  is  required  on  the  part  of  the  engineer  to  pro- 
tect his  works  from  the  introduction  of  weak  and  defective 
novelties,  that  may  prove  very  troublesome. 

He  must  observe  that  the  valve  castings  are  so  designed 
as  to  be  strong  and  rigid  in  all  parts,  that  there  are  no  thin 
spots  from  careless  centring  of  cores ; that  flat  parts,  if  any, 
are  thickened  up,  or  ribbed,  so  they  will  not  spring ; that 
the  valve-disks  are  so  supported  as  not  to  spring  under 
great  pressures,  and  that  they  and  their  seats  are  faced  with 
good  qualities  of  bronze  composition  and  smoothly  scraped, 
ground,  or  planed,  and  that  they  will  not  stick  in  their 
seats ; that  the  valve-stems  are  particularly  strong  and  stiff, 
with  strong  square  or  half-V  threads,  and  that  they  and 
their  nuts  are  of  a tough  bronze  or  aluminum  composition. 

33 


614 


DISTRIBUTION  SYSTEMS,  AND  APPENDAGES. 


Fig.  119. 


Fig.  119a. 


Ludlow’s  Stop-valve — (Ludlow  Manufacturing  Co.,  Troy). 

Figs.  114  to  119a  illustrate  the  principal  features  of 
valves  that  have  "been  well  introduced. 

A majority  of  the  good  valves  have  double  disks,  that 
are  self-adjusting  upon  their  seats,  and  their  seats  are 
slightly  divergent,  so  that  the  pressure  of  the  screw  can  set 
the  valve-disks  snug  upon  the  seats. 

The  loose  disks  should  have  but  a slight  rocking  move- 
ment between  their  guides,  and  must  not  be  permitted  to 
chatter  when  the  valve  is  partially  open. 

The  blow-off  valves  may  be  solid  or  single-disk  valves, 
but  the  valves  in  the  distribution  must  be  tight  against 
pressure  from  both  and  either  sides,  whether  the  difference 
of  pressure  upon  the  two  sides  be  much  or  little. 

Yalves  exceeding  twenty  inches  diameter  are  usually 
placed  upon  their  sides,  except  in  chambers,  and  the  disks 
have  lateral  motions,  or  sometimes  the  valve-cases  are  so 


VALVE  CURBS. 


515 


arranged  that  the  disks  have  vertical  downward  motions. 
Otherwise  the  water  in  the  valve-domes  would  he  too  much 
exposed  to  frost  in  winter,  as  it  would  rise  nearly  to  the 
ground  surface. 

504.  Valve  Curbs. — The  stop-valve  curbs  are  some- 
times of  chestnut  or  pitch-pine  plank,  with  strong  cast-iron 
covers,  and  sometimes  of  cast-iron,  placed  upon  a founda- 
tion of  bricks  laid  in  cement. 

The  plank  curbs  are  about  eighteen  by  twenty-four 
inches  dimensions  at  top,  flaring  downward  according  to 


Fig.  120. 


the  size  of  the  valve,  and  they  are  often  of  such  dimensions 
as  to  admit  a man,  with  room  to  enable  him  conveniently  to 
renew  the  packing  about  the  valve-stem. 


516 


DISTRIBUTION  SYSTEMS,  AND  APPENDAGES. 


The  cast-iron  curbs  are  usually  elliptical  in  section. 
The  writer  has  used  in  several  cities,  for  the  smaller  gates, 
up  to  twelve  inches  diameter,  circular  curbs  (Fig.  120 » of 
beton  coignet , with  cast-iron  necks  and  covers.  The  neck  is 
six  inches  clear  diameter  at  the  road  surface,  fifteen  to 
eighteen  inches  deep,  according  to  the  size  of  the  valve,  and 
flares  to  the  size  of  the  cement  curb,  which  is  just  large 
enough  to  slip  over  the  dome-flange  of  the  valve-case.  The 
cement  curb  rests  upon  a foundation  of  brick  or  stone  laid 
in  cement  mortar. 

When  these  are  paved  about,  the  whole  surface  exposed 
is  only  seven  and  one-lialf  inches  diameter,  and  they  are 
not  as  objectionable  in  the  streets  as  the  larger  covers. 

All  gate-curbs  must  be  thoroughly  drained,  so  that 
water  cannot  stand  in  them,  and  freeze  in  winter. 

505.  Fire-Hydrants. — The  design  of  a fire-hydrant 
that  is  a success  in  every  particular  is  a great  achievement. 
It  ranks  very  nearly  with  the  design  of  a successful  water- 
meter. 

Nearly  every  speculative  mechanic,  it  would  seem,  who 
has  had  employ  in  a machine-shop  for  a time,  lias  felt  it 
his  duty  to  design  the  much-needed  successful  hydrant ; as 
so  many  doctors  and  lawyers  have  grappled  with,  and 
believed  for  a time,  that  they  had  solved  the  great  meter 
problem. 

Innumerable  patterns  of  hydrants  are  urged  upon  water 
companies  and  engineers,  and  are  accompanied  by  an 
abundance  of  certificates  setting  forth  their  excellence ; and 
many  of  them  have  good  points  and  will  answer  all  practi- 
cal purposes  until  an  emergency  comes,  when  they  fail,  and 
the  experiment  winds  up  with  a loss  that  would  have  paid 
for  a thousand  reliable  hydrants. 

A considerable  practical  experience  with  hydrants,  and 


HYDRANT  DETAILS. 


517 


Fig.  121. 


an  expert  knowledge  of  tlie  qualities  demanded  in  tlie 
design  and  materials  of  a hydrant,  are  necessary  to  enable 
one  to  judge  at  sight  of  the  value  of  a new  pattern. 

506.  Post-Hydrants. — In  the  smaller 
towns  and  in  the  suburbs  of  cities,  jpost- 
hydrants , of  which  Fig.  121  illustrates  one 
pattern,  are  more  generally  preferred,  as 
they  are  more  readily  found  at  night,  and 
are  usually  least  expensive  in  first  cost. 

They  are  placed  on  the  edge  of  the 
sidewalk,  and  a branch  pipe  from  the 
service  main  furnishes  them  with  their 
water.  If  the  service  main  is  of  sufficient 
capacity,  the  post-liydrant  may  have  one, 
two,  three,  or  four  nozzles.  In  cities  where 
steam  fire-engines  are  used,  a large  nozzle 
is  added  for  the  steamer  supply,  and  if 
there  is  a good  head  pressure,  two  nozzles 
are  usually  supplied  for  attaching  leading 
hose. 

For  the  supply  of  two  hose  streams,  or 
a steamer  throwing  two  or  more  streams, 
the  hydrant  requires  a six-inch  branch 
pipe  from  the  service  main,  and  a valve  of 
equal  capacity.  The  supply  to  post-hy- 
drants has  too  often  been  throttled  down, 
when  there  was  no  head  pressure  to 
spare,  and  the  effectiveness  of  the  hy- 
drant very  much  reduced  thereby. 

507.  Hydrant  Details. — In  New 
England  and  the  Northern  States,  a 
frost-case  is  a necessary  appendage  to  Mathew’s  hvdrant— 

J 1 r ° (R.D.  Wood  & Co., 

a post-hydrant,  and  it  must  be  free  to  Philadelphia). 


518 


DISTRIBUTION  SYSTEMS,  AND  APPENDAGES. 


move  up  and  down  with  the  expansion  and  contraction  of 
the  earth,  without  straining  upon  the  hydrant  "base.  In 
clayey  soils,  these  frost  cases  are  often  lifted  several  inches 
in  one  winter  season,  and  if  the  post  is  not  supplied  with 
the  movable  case  in  such  instances,  it  is  liable  to  be  tom 
asunder. 

A waste-valve  must  be  provided  in  every  hydrant  that 
will  with  certainty  drain  the  hydrant  of  any  and  all  water 
it  contains  as  soon  as  the  valve  is  closed,  and  the  waste 
must  close  automatically  as  soon  as  the  valve  begins  to 
open. 

The  main  valve  must  be  'positively  tight , or  great  trouble 
will  be  experienced  with  the  hydrant  in  severe  winters.  A 
moderate  leakage,  as  in  some  stop-valves,  cannot  be  per- 
mitted. A free  drainage  must  be  provided  to  pass  away 
the  waste  water  from  the  hydrant,  or,  if  the  hydrant  is  fre- 
quently opened,  for  testing  or  use,  the  ground  will  soon  be 
come  saturated  and  the  hydrant  cannot  properly  drain. 

If  the  valve  closes  “with”  the  pressure  there  must  be 
no  slack  motion  of  its  stem,  or  when  the  valve  is  being 
closed  and  has  nearly  reached  its  seat,  the  force  of  the  cur- 
rent will  throw  it  suddenly  to  its  seat  and  cause  a severe 
water-ram. 

The  screw  motion  of  hydrant  valves  must  be  such  that 
the  hydrant  cannot  be  suddenly  closed,  or  with  less  than 
ten  complete  revolutions  of  the  screw.  The  valves  should 
move  slowly  to  their  seats  in  all  cases,  as,  if  several  hydrants 
happen  to  be  closed  simultaneously,  the  water-ram  caused 
thereby  may  exert  a great  strain  upon  the  valves,  and  the 
shock  will  be  felt  to  some  extent  throughout  the  whole 
system  of  pipes.  The  sudden  closing  of  a hydrant  may 
make  a gauge,  attached  to  the  pipes,  that  is  more  than  a 
mile  distant,  kick  up  fifty  or  sixty  pounds. 


HYDRANT  DETAILS. 


519 


Fig.  122. 


If  a hydrant  branch  is  taken  from  a main-pipe  or  sub- 
main,  there  should  be  a stop-valve  between  the  main  and 
hydrant,  so  the  hydrant  may  be  repaired  without  shutting 
off  the  flow  through  the  main. 

In  1874  the  writer  made  some 
measurements  of  the  quantities  of 
water  delivered,  under  different 
heads,  through  Boston  Machine 
Co.  Post  Hydrants,  which  are  sim- 
ilar in  form  to  the  Mathews  Hy- 
drant (Fig.  121).  The  volume  of 
water  was  measured  by  passing  it 
through  a 3-inch  Union  water-meter, 
which  was  connected  to  each  hy- 
drant by  a length  of  fire-hose. 

The  length  of  hose  between  the 
hydrant  and  meter  in  each  and 
every  experiment  was  49  feet  10 
inches.  The  bores  of  the  hydrant 
nozzles  and  of  the  hose  and  meter 
couplings  were  two  and  one-quar- 
ter inches  diameter.  The  hydrant 
branches  were  six  inches  in  di- 
ameter, and  hydrant  barrels  four 
and  one-half  inches  diameter.  The 
lengths  of  hose  given,  following, 
were  in  all  cases  beyond  the  meter, 
and  were  attached  to  the  meter. 

The  hydrant  was  filled  with 
water  and  pressure  without  flow,  faken  by  a gauge  just 
previous  to  the  beginning  of  each  test. 

The  following  tests,  at  different  elevations,  covers  a range 
of  head  pressures  between  42  feet  and  1 83  feet : 


520 


DISTRIBUTION  SYSTEMS,  AND  APPENDAGES. 


TABLE  No.  107. 

Experimental  Volumes  of  Hydrant  Streams. 


A. 


Remarks. 


42  Feet  Head. 


Pressure 
before 
test  lbs. 


Open  nozzle  of  meter,  2\  inch  diameter 

£ inch  nozzle  attached  to  meter 

ii  “ “ “ “ “ 

i J “ “ on  55  feet  -I  inch  of  hose. . 

H “ “ “ 108  “ ill  “ “ “ .. 

Open  butt  of  108  “ ni  “ “ “ .. 

B.  llO  Feet  Head. 

Open  nozzle  of  meter,  2\  inch  diameter 

i|  inch  nozzle  attached  to  meter  

“ “ on  53  feet  n inches  of  hose. 

ji  a a a I0g  a I3u  « <*  .< 

C.  136. S Feet  Head. 


18.23 


it 

tl 

it 


47-74 

(( 


it 


Open  nozzle  of  meter,  2\  inch  diameter ......I  59.24 

inch  nozzle  attached  to  meter “ 

ij  “ “ on  55  feet  ^ inch  of  hose “ 


Delivery 
cu.  ft. 

per  minute. 


20.376 

9.372 

12.550 

12.096 

ri.382 

15-342 


40.000 

24.666 

21.276 

20.408 


43-974 

24.390 

23.526 


D.  183.18  Feet  Head, 
ll-  inch  nozzle  on  55  feet  10  inches  of  hose 

1 1 “ “ “ 108  “ 4h  “ “ “ 

I-J-  “ “ “ 162  “ 7 “ “ “ 

Open  butt  of  162  “ 7 “ “ “ 


7Q;5 


27.648 

25-974 

24.643 

33-672 


Friction  of  flow  in  ordinary  fire-hose  consumes  pressure 
rapidly,  the  reduction  being  directly  in  proportion  to  the 
length,  and  also  as  the  square  of  the  volume  or  velocity  of 
water  flowing,  except  as  the  couplings  disturb  these  nearly 
uniform  increments.  The  friction  in  2£  inch  ordinary  fire- 
hose will  be  found  approximately  by  the  following  formulas 
expressing  loss  of  head  in  pounds,  p,  per  square  inch. 


For  smooth  rubber-lined  hose, 


V = 


¥ . 

4150#  ’ 


U 


fr’  . 
1801#  ’ 


(4) 


(5) 


PRESSURE  LOST  BY  FRICTION  IN  FIRE  HOSE.  £20 a 


in  which  l — length  of  hose  in  feet,  q = gallons  of  water 
discharged  from  the  hose  per  minute,  and  d the  diameter 
of  the  hose  in  inches,  and  Ji  — friction  head,  in  feet. 


TABLE  No.  107«. 

Pounds  Pressure  Lost  by  Friction  in  each  ioo  feet  of 
Smooth  Rubber  2^-inch  Fire-Hose,  for  given 
Discharges  of  Water  per  Minute. 


Pressure  at  Hose  Nozzle. 


.2  8 
OS 

Head,  in  lbs.  per  sq.  in. 
“ “ feet 

20 

46.2 

30 

69-3 

40 

92.4 

50 

TI5-5 

60 

I38.6 

70 

161.7 

80 

184.3 

90 

207.9 

100 

231.0 

C Gallons  discharged 

100 

123 

I42 

159 

174 

188 

201 

213 

224 

{ Friction,  lbs 

2.2 

3-3 

4-4 

5-6 

6.9 

8.1 

9-3 

10.4 

«-5 

C Gallons  discharged 

132 

161 

186 

208 

228 

246 

263 

279 

=95 

} Friction,  lbs 

4.0 

5-8 

8.0 

10.0 

12.0 

14.0 

i6-3 

17.8 

19.8 

C Gallons  discharged 

168 

206 

238 

266 

29I 

314 

336 

356 

376 

i,  in. 

( Friction,  lbs 

6.4 

9-7 

i3-o 

16.3 

19.3 

22.3 

25-5 

28.7 

32.0 

C Gallons  discharged 

209 

256 

296 

331 

363 

392 

419 

444 

468 

( Friction,  lbs 

10. 0 

i5-o 

20.0 

24.6 

29.8 

34-9 

39.8 

44-4 

49.9 

( Gallons  discharged 

25  7 

3H 

363 

406 

445 

480 

5i4 

545 

574 

£ Friction,  lbs 

x5- 1 

22.4 

29.8 

37-5 

45.0 

523 

59-5 

67.0 

73  4 

TABLE  No.  1 07  b. 


Hydrant  and  Hose  Stream  Data.  Horizontal  and  Vertical 
Distances  of  Jets. 


Diam.  ot 
Nozzles. 

Head,  in  lbs.  per  sq.  in. 
“ “ feet  

Pressure  at  Hose  Nozzle. 

20 

46.2 

3° 

69-3 

40 

92.4 

50 

H5-5 

60 

138.6 

70 

161.7 

80 

184.8 

90 

207.9 

IOO 

231.0 

( Gallons  discharged 

132 

161 

186 

208 

228 

246 

263 

279 

295 ' 

1 in. 

< Vertical  distance  of  jet 

35 

51 

64 

73 

79 

85 

89 

92 

96 

( Horizontal  “ “ “ 

37 

47 

55 

61 

67 

72 

76 

80 

83 

( Gallons  discharged 

168 

206 

238 

266 

291 

3T4 

336 

356 

376 

< Vertical  distance  of  jet 

36 

52 

65 

75 

83 

88 

92 

96 

99 

t Horizontal  “ “ “ 

38 

50 

59 

66 

72 

77 

81 

85 

89 

( Gallons  discharged 

209 

256 

296 

331 

383 

392 

419 

444 

468 

m. 

< Vertical  distance  of  jet 

37 

53 

67 

77 

85 

91 

95 

99 

101 

( Horizontal  “ “ “ 

40 

54 

63 

70 

76 

81 

85 

90 

93 

C Gallons  discharged 

257 

315 

363 

406 

445 

480 

514 

545 

574 

1 3/i  in. 

< Vertical  distance  of  jet 

38 

55 

69 

79 

87 

92 

97 

100 

103 

( Horizontal  u “ “ 

42 

56 

66 

73 

79 

84 

88 

92 

96 

520&  DISTRIBUTION  SYSTEMS,  AND  APPENDAGES. 


TABLE  No.  107c. 

Combined  Rates  of  Flow  for  Fire  and  Domestic  Service 
(When  Steam  Fire  Engines  are  Used). 


Population. 

8 

o 

0 

0 

0 

'O 

8 

0^ 

00 

0 

0 

0 

0 

i 

20,000. 

0 

0 

0 

30,000. 

O 

O 

0 

0 

50,000. 

8 

O 

d 

VO 

ITl 

100,000. 

125,000. 

O 

0 

O 

d 

Rate  of  flow  for  J 
domestic  service,  > 

•25 

.30 

• 45 

.60 

I .OO 

I .40 

I .QO 

2.4O 

3.40 

4.40 

5.40 

7.10 

10.00 

13.10 

16.00 

in  mill,  gals ) 

No.  of  hose  streams. 

8 

8 

9 

9 

IO 

II 

12 

12 

*3 

14 

15 

16 

18 

21 

23 

Rate  of  flow  for  i 
fire  service,  in  > 

2.59 

2.59 

2.91 

2.91 

323 

3-55 

3.88 

3.88 

4 . 28 

4 -52 

4-75 

5-17 

582 

6.79 

7-43 

mill,  gals ) 

Combined  rate  of ) 
flow,  in  mill.  > 

2 . 84 

2.89 

3 36 

3 51 

4 23 

4 95 

5 78 

6.28 

7.68 

8 92 

10.15 

12.27 

15.82 

19.89 

23-43 

gals ) 

Diam.  of  single  main. 

14 

14 

14 

14 

l6 

16 

18 

18 

20 

22 

22 

24 

27 

3° 

33 

508.  Flush  Hydrants.— A style  of  flush  hydrant,  that 
may  be  placed  under  a paved  or  flagged  sidewalk,  near  the 
edge,  is  shown  in  Fig.  122.  This  style  may  have  one,  two, 
or  three  fixed  nozzles. 

Figs.  123  and  124  illustrate  a style  of  hydrant  with  a 
portable  head.  This  style  is  manufactured  under  the 
Lowry  patent.  It  is  designed  to  be  placed  at  the  intersec- 
tions of  mains,  in  the  street,  or  in  the  line  of  a main,  but 
may  be  placed  in  the  sidewalk.  In  either  case  it  is  placed 
within  an  independent  curb,  and  the  cast-iron  case  rises 
about  to  the  surface.  The  portable  head  is  of  brass  and 
composition,  nicely  finished,  as  light  as  is  consistent  with 


Fig.  123. 


Fig  124. 


LOWRY’S  FLUSH  HYDRANT.  — (Boston  Machine  Co.*  Boston.) 


522 


DISTRIBUTION  SYSTEMS,  AND  APPENDAGES. 


strength,  and  is  usually  carried  upon  the  steamer  or  the 
hose  carriage.  It  has  any  desired  number  of  nozzles,  from 
one  to  eight,  each  of  which  has  its  independent  supplemen 
tary  valve. 

In  the  centre  of  the  portable  head  is  a revolving  key  that 
operates  the  main  valve  stem. 

509.  Gate  Hydrants. — A variety  of  metallic  “gate’' 
hydrants  have  been  introduced,  from  time  to  time,  and  had 
a brief  existence,  but  the  majority  of  them  have  been  soon 
abandoned.  The  most  minute  particle  of  grit  upon  their 
faces  gives  trouble,  and  they  are  much  more  likely  to  stick 
than  valves  of  good  sole-leather  or  of  rubber  properly  pre- 
pared, and  clamped  between  metallic  plates.  Gate  hydrants 
of  good  design  and  excellent  workmanship,  should  be  fully 
successful  with  filtered  water. 

The  rubber  of  valves  requires  to  be  very  skillfully  tem- 
pered, or  it  will  be  too  soft  or  too  hard.  It  hardens,  also, 
as  the  temperature  of  the  water  lowers. 

510.  High  Pressures. — But  a few  years  since  the 
maximum  static  strain  upon  hydrants,  in  public  water 
supplies,  did  not  exceed  that  of  a hundred  and  fifty  feet 
head,  and  the  majority  of  the  hydrants  in  each  system  had 
not  over  one  hundred  feet  pressures  when  the  water  was  at 
rest.  Hand  or  steam  fire-engines  were  necessities  in  such 
cases,  and  the  pipes  were  so  small  that  often  the  engines 
had  to  exert  some  suctions  on  the  pipes  to  draw  their  full 
supplies.  Now  the  values  of  pressure  that  will  permit  six 
or  eight  effective  streams  to  be  taken  direct  from  the  hy- 
drants in  any  part  of  the  system  is  more  fully  appreciated, 
and  direct  pumping  pressures  equivalent  to  three  or  four 
hundred  feet  head  are  not  uncommon.  The  effect  upon  the 
hydrants  is,  however,  a greatly  increased  strain  which  they 
must  be  able  to  meet. 


AIR-VALVES. 


523 


511.  Air-Valves.  — All  water  contains  some  atmos- 
pheric air.  When  water  has  passed  through  a pumping- 
engine  into  a force-main  under  great  pressure,  it  absorbs 
some  of  the  air  in  the  air-vessel.  If,  then,  it  is  forced  along 
a pipe  having  vertical  curves  and  summits  at  different 
points,  it  parts  with  some  of  the  air  at  those  summits.  In 
time,  sufficient  air  will  accumulate  at  each  summit  to  oc- 
cupy a considerable  part  of  the  sectional  area  at  that  point, 
and  it  will  continue  to  accumulate  until  the  velocity  of  the 
water  is  sufficient  to  carry  the  air  forward  down  the  incline. 

At  such  summits  an  air-valve  is  required  to  let  off  the 
accumulated  air,  as  occasion  requires.  Also,  when  the 
water  is  drawn  off  from  the  pipes,  as  for  repairs  or  any 
other  purpose,  there  is  always  a tendency  to  a vacuum  at 
the  summits  if  no  air  is  supplied  there  ; and  if  the  pipes  are 
not  thick  and  rigid,  they  may  collapse  in  consequence  of 
the  vacuum  strain,  or  exterior  pressure. 

When  pipes  are  being  filled,  there  should  always  be 
ample  escape  for  the  air  at  the  summits,  or  the  air  contained 
in  the  pipes  will  be  compressed  and  recoil,  again  be  still 
more  compressed  and  again  recoil  with  greater  force,  shoot- 
ing the  column  of  water  back  and  forth  in  the  pipe  with 
enormous  force,  and  straining  every  joint. 

In  the  distribution,  hydrants  are  usually  located  upon 
summits,  and  in  such  case  will  perform  the  functions  of 
air-valves. 

If  a stop-valve  is  inserted  in  an  inclined  pipe,  and  is 
closed  during  the  filling  of  the  section  immediately  below  it, 
it  makes  practically  a summit  at  that  point,  and  an  air- 
valve  or  vent  will  be  required  there. 

An  air  and  vacuum  valve,  for  summits,  may  with  advan- 
tage be  combined  in  the  same  fixture,  the  air- valve  motion 
being  positive  in  action  for  the  purpose  of  an  air-valve, 


624 


DISTRIBUTION  SYSTEMS,  AND  APPENDAGES. 


opening  against  the  pressure,  but  automatic  as  a vacuum- 
valve,  opening  freely  to  the  pressure  of  the  atmosphere. 

Fig.  125  is  a com- 
bined air  and  vacuum 
valve  designed  by  the 
writer,  and  used  in  sev- 
eral cities  with  success. 

A two-inch  air- valve 
answers  tolerably  for 
four,  six,  eight,  and 
ten  inch  pipes,  but  for 
large  pipes  a special 
branch  with  stop-valve 
may  be  used. 

Great  care  should 
be  exercised  in  filling 
pipes  with  water,  and 
the  water  should  not 
be  admitted  faster 
than  the  air  can  give 
place  to  it  by  issue  at 
the  air-valves,  or  open 
hydrant  nozzles,  with- 
out reactionary  con- 
vulsions. 

512.  Union  of  High  and  Low  Services. — Many 
cities  have  high  lands  within  their  built-up  limits  that  are 
so  much  elevated  above  the  general  level  that  it  is  a matter 
of  convenience  to  divide  the  distribution  into  “ high  ” and 
“low  services and  to  give  to  each  its  independent  reservoir. 

In  such  case  the  benefit  of  the  pressure  of  the  high  reser- 
voir may  be  secured  in  the  low  system  in  case  of  a large 
fire,  by  simply  opening  a valve  in  a branch  connecting  the 


Fig.  125. 


COMBINED  RESERVOIR  AND  DIRECT  SYSTEMS.  525 


two  systems.  A check-valve,  Fig.  126,  will  be  required  in 
the  effluent  pipe,  or  supply  main  from  the  lower  reservoir 
to  prevent  the  flow  back  into  the  lower  reservoir. 

A weighted  valve,  automatic  in  action,  may  also  be 
placed  in  the  branch  connecting  the  two  systems,  and  then 


Fig.  126. 


CHECK-VALVE. 


in  case  of  an  accident  xo  the  supply  pipe  of  the  lower  sys- 
tem, or  a malicious  closing  of  its  valve,  the  upper  service 
will  maintain  the  supply  at  a few  pounds  diminished 
pressure. 

If  the  pumps  are  arranged  so  as  to  give  a direct  increased 
pressure  in  the  lower  system  for  fire  purposes,  then  a clieck- 
valve  in  the  branch  connecting  the  two  systems,  opening 
toward  the  high  system,  will  be  an  excellent  relief  and  pro- 
tection against  undue  pressure. 

513.  Combined  Reservoir  and  Direct  Systems. — 
In  the  plan  of  a pipe  system,  Fig.  113,  a pipe  leads  from  the 
pumps  direct  to  the  reservoir,  and  a second  pipe  leads  direct 
from  the  pumps  into  the  distribution,  so  that  water  may  be 
sent  either  to  the  reservoir  or  to  the  distribution,  at  will. 


526 


DISTRIBUTION  SYSTEMS,  AND  APPENDAGES. 


A branch  pipe  connects  these  two  pipes  so  as  to  supply  the 
distribution  from  the  force  main. 

A check-valve  opening  toward  the  distribution  is  placed 
in  this  branch.  If  a fire-pressure  is  put  upon  the  distribu- 
tion through  the  direct  pipe  this  valve  prevents  the  flow 
back  toward  the  reservoir,  but  upon  the  reduction  of  the 
fire-pressure  it  comes  into  action  and  maintains  the  supply 
to  the  distribution  from  the  reservoir. 

For  additional  security  against  unforseen  contingencies, 
another  pipe  may  lead  from  the  reservoir  to  one  of  the  prin- 
cipal sub-mains,  as  shown  in  the  plan,  when  the  relative 
positions  of  the  reservoir  and  distribution  permits,  and  this 
pipe  may  contain  in  the  effluent  chamber  a check-valve 
against  fire-pressure  and  a weighted  relief- valve  to  prevent 
undue  pressure. 

In  the  reservoir  plan,  Fig.  58  (page  333),  the  force  and 
supply  mains  are  shown  to  be  connected  by  a pipe  passing 
along  the  side  of  the  reservoir,  so  that  the  water  may  be  sent 
from  the  pumps  direct  into  the  distribution.  The  supply- 
main  has  a check-valve  in  the  effluent  chamber  in  this  case. 

A combined  reservoir  and  direct  pressure  system,  sub- 
stantially like  that  of  Fig.  113,  including  high  and  low  ser- 
vices, was  designed  by  the  writer  for  one  of  the  large  Xew 
England  cities  in  1872,  and  the  same  was  constructed  with  the 
exception  of  the  high  service  reservoir,  in  the  two  following 
seasons. 

514.  Stand-Pipes. — Several  of  the  American  cities, 
whose  reservoirs  are  distant  from  their  pumping  stations, 
have  placed  a stand-pipe  upon  their  force-main,  to  equalize 
the  resistance  against  the  pumps,  as  in  St,  Louis,  Louis- 
ville, and  Milwaukee.  Other  cities  use  tall  open-topped 
stand-pipes  without  reservoirs,  when  no  proper  site  for  a 
reservoir  is  readily  attainable,  as  at  Chicago  and  Toledo. 

All  the  American  stand-pipes  now'  in  use  are  of  the 


FRICTIONAL  HEADS  IN  SERVICE  PIPES. 


527 


single  leg  class.  The  city  of  Sandusky,  Ohio,  has  now 
(N ov.  1876)  in  process  of  construction  a tank  stand-pipe  of 
25  feet  diameter  and  208  feet  height,  surrounding  a delivery 
stand-pipe  of  3 feet  diameter  and  225  feet  height.  This 
tank  is  being  built  up  of  riveted  metal  plates,  from  designs 
by  J.  D.  Cook,  Esq.,  chief  engineer.  In  Europe,  the  stand- 
pipes are  more  frequently  double-legged,  with  connections 
between  the  up  and  down  legs  at  intervals  of  height. 

The  stand-pipes  as  generally  used,  serve  as  partial  sub- 
stitutes for  relief-valves  combined  or  acting  in  conjunction 
with  tall  and  capacious  air-chambers.  The  surface  of  the 
water  in  the  stand-pipes  vibrates  up  and  down  according  to 
the  rate  of  delivery  into  them  from  the  pumps,  and  the  rate 
of  draught,  if  the  main  over  which  they  are  placed  is  con- 
nected with  the  distribution.  Vide  Chapter  XXV,  and 
table  of  stand-pipe  data  in  the  Appendix. 

The  Boston  Highlands  Stand-pipe  (page  161)  stands 
upon  an  eminence  158  feet  above  tide,  is  of  wrought-iron, 
and  is  80  feet  high,  and  5 feet  interior  diameter.  It  is 
inclosed  in  a masonry  tower. 

The  Milwaukee  stand-pipe  (page  25)  rises  to  210  feet 
above  Lake  Michigan,  and  the  Toledo  stand-pipe  (page  31) 
to  260  feet  above  Maumee  River. 

515.  Frictional  Heads  in  Service-Pipes. — The  fol- 
lowing shows  the  frictional  head  in  clean,  smooth  service- 
pipes,  with  given  velocities,  for  each  one-hundred  feet  length. 

The  numbers  of  the  first  column  are  the  given  velocities, 
in  feet  per  second.  The  second  column  gives  the  head, 
which  is  necessary  to  generate  the  given  velocities  opposite. 

In  the  first  column,  under  each  of  the  given  diameters 
from  \ inch  to  4 inches,  is  the  volume  of  flow,  at  its  given 
velocity ; in  the  next  column  the  corresponding  coefficient 
of  friction  ; and  in  the  next  column  the  frictional  head  per 
each  one  hundred  feet  length  at  its  given  velocity. 


528 


DISTRIBUTION  SYSTEMS,  AND  APPENDAGES. 


TAB  LE  No.  1 O 8. 

Frictional  Head  in  Service  Pipes*  (in  each  ioo  feet  length). 


Velocity,  in  feet 
per  second. 

Velocity  head, 
in  leet. 

J4  IN.  DIAMETER.t 

\ IN.  DIAMETER. 

I IN. 

DIAMETER. 

I y2  IN.  DIAMETER. 

Cubic  feet 
per  minute. 

Coefficient. 

Frictional 

head. 

Cubic  feet 
per  minute. 

Coefficient. 

Frictional 

head. 

Cubic  feet 
per  minute. 

Coefficient 

Frictional 

head. 

dt| 
O 3 

Coefficient. 

Frictional 

head. 

Feet. 

Feet. 

' Feet. 

Feet . 

1.4 

.0^0 

•TI5 

.OO992 

2.896 

.257 

.00930 

1.812 

.458 

.00882  1.289 

1.030 

.00843  <821 

i.6 

.040 

.130 

.OO942 

3.592 

.294 

.00890 

2.265 

•523 

.00854  1-630 

1.178 

.00823  1.646 

1.8 

.050 

.147 

.00900 

4.544 

• 331 

.00856 

2.756 

.589 

.00830  2.005 

1-325 

.00806  1.297 

2.0 

.062 

.164 

.00862 

5.136 

•3*8 

.00830 

3.300 

.654 

.00810  2.516 

1.472 

.CO790  1.570 

2.2 

•075 

.180 

.00845 

6.091 

.405 

.oo8n 

3.902 

.719 

.00790  2.851 

1.619 

.00775  1.865 

2.4 

.090 

.196 

.00810 

6.950 

.442 

.00792 

5.535 

•785 

.00773 ! 5.320 

1.766 

.00760  2.175 

2.6 

.105 

.213 

.OO788 

7.935 

.478 

.00773 

5.193 

.850 

.00758,  3.821 

I*9I4 

.00745  2.520 

2.8 

.122 

.229 

.OO77O 

8.99.3 

•5i5 

.00756 

5.891 

.916 

.00745  5.356 

2. 06 1 

.00730  9.844 

3-o 

.140 

.246 

■00753 

10.07 

•552 

.00745 

6.665 

.981 

.00734  4 .926 

2.209 

.00722  3 229 

3-2 

.l6o 

.262 

.00745 

11.33 

.589 

.00737 

7.501 

1.046 

.00726  5.544 

2.356 

.00714  3.635 

3-4 

.180 

.278 

.00736 

12.67 

.626 

.OO729 

8.373 

1. 1 1-2 

.00720  6.207 

2-503 

.00706  4 .056 

3-6 

.202 

295 

.OO729 

15.01 

.662 

.OO718 

9.255 

1. 177 

.00714,  6.900 

2.651 

.00700  4 .509 

3-» 

.225 

•31 1 

.OO726 

15.62 

.699 

.OO7I4 

10.25 

1-243 

.00708  7.625 

2.798 

.00696  4.994 

4.0 

.250 

.328 

.00722 

17.21 

.736 

.OO7IO 

11.29 

I.309 

.00702  8.376 

2.945 

.00692  5.502 

4.2 

•275 

•344 

.OO7I9 

18.89 

•773 

.OO706 

12.38 

i-374 

.00698  9.182 

3.092 

.00687,  6.022 

4-4 

.302 

.360 

.00715 

20.62 

.810 

.00702 

13.51 

1.440 

.00694  10.02 

3-239 

.00683 1 6.571 

4.6 

•330 

•377 

.OO7II 

■22.51 

.846 

.OO699 

15-70 

1-505 

.00601  10.90 

3-387 

.00680  7.749 

4-8 

.360 

•393 

.00/08 

25.30 

.883 

.OO696 

15.95 

I-57I 

.00687  11.80 

3-53+ 

.00677  7.7  51 

5-° 

•39° 

.410 

.OO7O4 

.920 

.00694 

I7.22 

1.636 

.00684  12.75 

3.681 

.00675  8-386 

5-2 

.422 

.426 

.OO7OI 

28.2  k 

•957 

.OO689 

18.52 

1. 701 

.00681  13.73 

3.828 

.00671  9.017 

5-4 

■455 

•442 

.00698 

30.32 

■993 

.00686 

19.88 

1.767 

.00678  14.74 

3-975 

.00668  9.880 

5-6 

.49c 

•459 

.OO695 

32.57 

1.030 

.OO683 

21.29 

1.832 

.00675  15.79 

4-I25 

.00665  10.37 

5.8 

•525 

•475 

.OO692 

35.76 

1.067 

.00680 

22.7  k 

1.898 

.00672  16.86 

4.270 

.00662  11.07 

6.o 

.562 

.492 

.OO689 

36.95 

1. 104 

.OO678 

2k. 2 6 

1.963  .00670  17.99 

4.417 

.00660  11.S1 

6.2 

.600 

.508 

.00686 

39.28 

1.141 

.OO67S 

25.79 

2.028 

.00667  19.12 

4.564 

.00657  12.55 

6.4 

.640 

•524 

.00683 

51.67 

1.177 

.00672 

27.35 

2.094 

.00664  20.28 

4-711 

.00654  1SJ1 

6.6 

.680 

.541  .00681 

55.09 

1. 214 

.OO669 

28.96 

2.159 

.00661 21.57 

4.S59 

.006=2  15.11 

6.8 

.722 

•557 

.OO678 

56.70 

1. 251 

.00666 

30.61 

2.225 

.00659  22.72 

3.006 

.00650  14.54 

7.0 

.765 

•574 

.00675 

59.27 

1.288 

.OO664 

32.35 

2.291 

.00657  ~4 .01 

5-153 

.00648  15.78 

* This  table  does  not  include  the  resistances  of  the  stop-cocks  and  short 
bends  in  service  pipes.  Such  resistances,  as  services  are  usually  laid,  reduce 
the  effective  delivery  of  water  fully  fifty  per  cent, 
f Vide  table  104,  p.  504,  for  values  of  d in  feet. 

Vide  table  of  weights  of  lead  service  pipes  in  the  Appendix. 


Mechanical  Filter  Plant,  Chattanooga,  Tenn.  New  York  Filter  Co. 


F 

r 

% 

1 G- 

THE  WARREN  FILTER. 


FRICTIONAL  HEAD  IN  SERVICE  PIPES. 


529 


TABLE  No.  108  — (Continued). 


Frictional  Head  in  Service  Pipes  (in  each  100  feet  length). 


o 

tT 

cS 

0) 

U 

. a 

J.s 

'o 

> 

1%  IN.  DIAMETER. 

2 IN.  DIAMETER. 

3 IN- 

DIAMETER. 

4 IN. 

DIAMETER. 

Velocity,  in  f< 
per  second 

Cubic  feet 
per  minute. 

Coefficient. 

Frictional 

head. 

Cubic  feet 
per  minute. 

Coefficient. 

Frictional 

head. 

Cubic  feet  1 
per  minute. 

Coefficient. 

Frictional 

head. 

Cubic  feet 
per  minute. 

Coefficient. 

c • 

0 0 

1.4 

.030 

I.4O3 

.00800 

Feet . 
.668 

1.875 

.OO763 

Feet. 

.557 

4.123 

.00724 

Feet. 

.353 

7-330 

.OO697 

Feet. 

.255 

1.6 

.040 

1.603 

.00786 

.857 

2.142 

.OO75O 

.715 

4.712 

00716 

.556 

8.377 

.OO69O 

.342 

1.8 

.050 

1.804 

.OO769 

1.062 

2.410 

.OO74I 

.895 

5-3°r 

.00708 

■570 

9.424 

.00684 

.515 

2.0 

.06c 

2.004 

.00757 

1.200 

2.678 

.OO73I 

1.090 

5.891 

.00700 

.696 

10.47 

.00678 

.505 

2.2 

•075 

2.204 

•00743 

1.536 

2.Q46 

.OO724 

1.306 

6.480 

.00693 

.833 

11.52 

.OO672 

.606 

2.4 

.OOO 

2.405 

•00733 

1. 7°0 

•3-2I4 

.OO7I7 

1.539 

7.069 

.00687 

.983 

12. c6 

.00666 

.7 15 

2.6 

.105 

2.605 

.OO723 

2.083 

3.481 

.0070 

1.791 

7.685 

.00681 

1.155 

13.61 

.00660 

.832 

2.8 

.122 

2.806 

.OO7I3 

2.382 

3-794 

.00 704 

2.057 

8.247 

.00674 

1.315 

14.66 

.00655 

.957 

3-° 

.I40 

3.006 

.OO7O7 

2.711 

4.018 

.00692 

2.321 

8.846 

.00670 

1.598 

15-71 

.OO65O 

1.090 

3-2 

.160 

3.206 

.OO7OO 

3.055 

4.286 

.00686 

2.618 

9-435 

.00665 

1.692 

16.76 

.OO645 

1.231 

3-4 

.180 

3-407 

.OO694 

3.518 

4-554 

.00681 

2.935 

10.02 

.00661 

1.899 

17.80 

.OO64I 

1.381 

3-6 

.202 

3.607 

.00688 

3.799 

4.821 

.00677 

3.270 

1O.61 

.00657 

2.117 

18.85 

.OO637 

1.538 

3-8 

.225 

3.808 

.00685 

5 .215 

5-089 

.00674 

3.628 

11.20 

.00654 

2.357 

19.90 

.00634 

1.706 

4.0 

.250 

4.008 

.00682 

4 .649 

5-357 

.00671 

5.002 

11.78 

.006^1 

2.588 

20.94 

.OO63I 

1.882 

4.2 

•2  75 

4.208 

.OO678 

5.096 

5-625 

.00667 

5.385 

I2-37 

.00647 

2.836 

21.99 

.00628 

2.065 

4.4 

.302 

4.409 

.OO674 

5.560 

5-893 

.00663 

5.785 

12.96 

.00644 

3.098 

a3-°3 

.00625 

2.255 

4.6 

•33° 

4.609 

.OO67O 

6.050 

6.160 

.00660 

5.205 

*3-55 

.00641 

3.370 

24.08 

.OO62V 

2.557 

4.8 

.360 

4.8lO 

.OO667 

6.5 47 

6.428 

.00657 

5.653 

14.14 

.00638 

3.653 

25-I3 

.006201 

2.662 

S-o 

•39° 

5.010 

.OO664 

7.065 

6.696 

.00654 

6.095 

I4-73 

.00636 

3.951 

26.l8 

.006l8 

2.880 

5-2 

.422 

5-210 

.00661 

7.615 

6.064 

.00651 

6.561 

I5-32 

.00633 

5-253 

27.23 

.00615 

3.099 

5.4 

•455 

5-411 

.OO658 

8.175 

7.232 

.00648 

7.055 

I5-9I 

.00630 

U .565 

28.27 

.006l2l 

o.326 

S.6 

.490 

5.611 

.00655 

8.751 

7-499 

.00645 

7.550 

16.50 

.00627 

5.886 

30.32 

.OO609 

3.559 

5.8 

.525 

5-812 

.OO652 

9.355 

7-76? 

.00642 

8.059 

I7-°9 

.00624 

5.167 

30-37 

.00607 

3.816 

6 .0 

.562 

6.012 

.OO65O 

9.970 

8-°35 

.0064c 

8.587 

17.67 

.00622 

5.565 

3I-4I 

.00605 

5.059 

6.2 

.600 

.6.212 

.OO647 

10.59 

8 -3°3 

.00637 

9.126 

18.25 

.00619 

5.912 

32.46 

.00603 

5 .320 

6.4 

.640 

6.413 

.00645 

11.26 

8-57x 

8.838 

.00635 

9.695 

18.85 

.00616 

6.269 

33-50 

.00601 

5.588 

6.6 

.680 

6.613 

.00643 

11.93 

.00633 

10.28 

19.44 

.00614 

6 656 

34-55 

.00599 

5.863 

6.8 

.722 

6.814 

.OO64I 

12.63 

9.106 

.00631 

10.88 

20.03 

.00612 

7.032 

35.60 

.00597 

5.155 

7.0 

.765 

7.014 

.OO639 

13.35 

9-374 

.00629 

11.59 

20.62 

.00610 

7.527 

36.65 

.00595 

5.535. 

CHAPTER  XXIII. 


CLARIFICATION  OF  WATER. 

516.  Rarity  of  Clear  Waters. — A small  but  favored 
minority  of  the  American  cities  have  the  good  fortune  to 
find  an  abundant  supply  of  water  for  their  domestic  pur- 
poses, within  their  reach,  that  remains  in  a de suable  state 
of  transparency  and  limpidity. 

The  origin  and  character  of  the  impurities  that  are 
almost  universally  found  in  suspension  in  large  bodies  of 
water,  have  been  already  discussed  in  the  chapters  devoted 
to  “Impurities  of  Water”  (Chap.  VIII),  and  to  “Supplies 
from  Lakes  and  Rivers”  (Chap.  IX) ; so  there  remains  now 
for  investigation  only  the  methods  of  separating  the  foreign 
matters  before  pointed  out. 

511.  Floating-  Debris. — The  running  rivers,  that  are 
subject  to  floods,  bring  down  all  manner  of  floating  debris, 
from  the  fine  meadow  grasses  to  huge  tree-trunks,  and 
buildings  entire.  These  are  all  visible  matters,  that  remain 
upon  the  surface  of  the  water,  and  their-  separation  is 
accomplished  by  the  most  simple  mechanical  devices. 

Coarse  and  fine  racks  of  iron,  and  fine  screens  of  woven 
copper  wire  are  effectual  intercepted  of  such  matters  and 
prevent  their  entrance  into  artificial  water  conduits. 

518.  Mineral  Sediments. — Next  among  the  visible 
sediments  may  be  classed  the  gravelly  pebbles,  sand,  disin- 
tegrated rock,  and  loam,  that  the  eddy  motions  continually 


ORGANIC  SEDIMENTS. 


531 


toss  up  from  tlie  channel  bottom,  and  the  current  bears 
forward. 

These  are  not  intercepted  by  ordinary  screens,  but  are 
most  easily  separated  from  the  water  by  allowing  them 
quickly  to  deposit  themselves,  in  obedience  to  the  law  of 
gravitation,  in  a basin  where  the  waters  can  remain  quietly 
at  rest  for  a time. 

When  the  water  is  received  into  large  storage  reservoirs, 
it  is  soon  relieved  of  these  heavy  sedimentary  matters,  by 
deposition  ; and  a season  of  quietude,  even  though  but  a few 
hours  in  duration,  is  a valuable  preparation  for  succeeding 
stages  of  clarification. 

Next  are  more  subtle  mineral  impurities,  consisting  of 
the  most  minute  particles  of  sand  and  finely  comminuted 
clay,  which  consume  a fortnight  or  more,  while  the  water  is 
at  rest  in  a confining  basin,  in  them  leisurely  meanderings 
toward  the  bed  of  the  basin. 

If  these  mineral  grains  are  to  be  removed  by  subsidence 
for  a public  water  supply,  the  subsidence  basin  must 
usually  be  large  enough  to  hold  a two-weeks  supply,  and 
must  be  narrow  and  deep,  so  the  winds  will  stir  up  but  a 
comparatively  thin  surface  stratum,  and  also  so  the  exposed 
water  will  not  be  heated  unduly  in  midsummer. 

519.  Organic  Sediments. — Next  are  the  organic 
fragments,  including  the  disintegrating  seeds,  leaves,  and 
stalks  of  plants,  the  legs  and  trunks  of  insects  and  Crusta- 
cea, and  the  macerated  mill  refuse,  and  also  various  algae. 

All  these  have  so  nearly  the  same  specific  gravity  as  the 
water,  that  they  remain  in  suspension  until  decomposition 
has  removed  so  much  of  their  volatile  natures  that  the 
mineral  residues  can  finally  gravitate  to  the  bottom. 

If  these  are  to  be  removed  by  subsidence,  the  basin  must 
hold  one  full  month  supply,  at  least,  and  be  so  formed 


632 


CLARIFICATION  OF  WATER 


and  protected  as  to  neither  generate  or  receive  other  im- 
purities. 

In  addition,  are  the  throngs  of  living  creatures  that 
people  the  ponds  and  streams,  and  their  spawns  and 
spores.  These,  during  their  active  existence,  cannot  be 
removed  by  subsidence,  without  coagulation,  and  repro- 
duction will,  in  part,  balance  their  destruction. 

530.  Organic  Solutions.— Still  more  subtle  than  all 
the  above  impurities,  that  remain  in  suspension , are  the 
dissolved  organic  matters  that  the  water  takes  into  solution. 
‘These  include  the  dissolved  remains  of  animate  creatures, 
dissolved  fertilizers,  and  dissolved  sewage. 

All  the  former  may  be  treated  mechanically  with  toler- 
able success,  but  the  latter  pass  through  the  finest  filters 
and  yield  only  to  chemical  transformations. 

531.  Natural  Processes  of  Clarification.— Nature’s 
process  for  removing  all  these  impurities,  to  fit  the  water 
for  the  use  of  animals,  is  to  pass  them  through  the  pores  of 
the  soil  and  fissures  of  the  rocks.  The  soil  at  once  removes 
the  matters  in  suspension , and  they  become  food  for  the 
plants  that  grow  upon  the  soil,  and  are  by  the  plants  recon- 
verted into  their  original  elements.  The  minerals  of  the 
soil  reconvert  the  organic  matters  in  solution  into  other 
combinations  and  separate  them  from  the  water. 

533.  Chemical  Processes  of  Clarification. — Arti- 
ficial chemical  processes,  more  or  less  successful  in  their 
action,  have  been  employed  from  the  remotest  ages  to  sep- 
arate quickly  the  fine  earthy  matters  from  the  waters  of 
running  streams.  The  dwellers  on  the  banks  of  streams, 
who  had  no  other  water  supply,  treated  them,  each  for 
themselves,  and  in  like  manner  have  others  treated  the  rain 
waters  which  they  caught  upon  their  roofs,  when  they  had 
no  other  domestic  supplies. 


PROCESSES  OF  CLARIFICATION.  533 

Many  centuries  ago  the  Egyptians  and  Indians  liad  dis- 
covered that  certain  hitter  vegetable  substances  which  grew 
around  them  were  capable  of  hastening  the  clarification  of 
the  waters  of  the  Nile,  Ganges,  Indus,  and  other  sediment' 
ary  streams  of  their  countries. 

The  Canadians  have  long  been  accustomed  to  purify 
rain-water  by  introducing  powdered  alum  and  borax,  in 
the  proportions  of  3 ounces  of  each  to  one  barrel  (31 J gals.) 
of  water ; and  alum  is  used  by  dwellers  on  the  banks  of 
the  muddy  Mississippi  to  precipitate  its  clay.  Arago  ob- 
served also  the  prompt  action  of  alum  upon  the  muddy 
water  of  the  Seine.  One  part  of  a solution  of  alum  in  fifty 
thousand  parts  of  water  results  in  the  production  of  a floc- 
culent  precipitate,  which  carries  down  the  clayey  and 
organic  matters  in  suspension,  leaving  the  water  perfectly 
clear. 

Dr.  Gunning  demonstrated  by  many  experiments  that 
the  impure  waters  of  the  river  Maas,  near  Rotterdam,  could 
be  fully  clarified  and  rendered  fit  for  the  domestic  supply 
of  the  city,  by  the  introduction  of  .032  gramme  of  per- 
chloride  of  iron  into  one  liter  of  the  water.  The  waters  of 
the  Maas  are  very  turbid  and  contain  large  proportions  of 
organic  matter,  and  they  often  produce  in  those  visitors  who 
are  not  accustomed  to  their  use,  diarrhoeas,  with  other  un- 
pleasant symptoms. 

Dr.  Bischoff, -Jr.,  patented  in  England,  in  1871,  a process 
of  removing  organic  matter  from  water  by  using  a filter  of 
spongy  iron,  prepared  by  heating  hydrated  oxide  of  iron 
with  carbon.  The  water  is  said  to  be  quite  perceptibly 
impregnated  with  iron  by  this  process,  and  a copious  pre 
cipitate  of  the  hydrated  oxide  of  iron  to  be  afterwards 
separated. 

Horsley’s  patent  process  for  the  purification  of  water 


534 


CLARIFICATION  OF  WATER. 


covers  the  use  of  oxalate  of  potassa,  and  Clark’s  the  use  of 
caustic  lime. 

Mr.  Spencer  has  used  in  England  with  great  success,  in 
connection  with  sand  filtration,  the  crushed  grains  of  a car- 
bide of  iron,  prepared  by  roasting  red  hematite  ore,  mixed 
with  an  equal  part  of  sawdust,  iu  an  iron  retort.  This  he 
mixes  with  one  of  the  lower  sand  strata  of  a sand  filter,  and 
its  office  is  to  decompose  the  organic  matters  in  solution  in 
the  water.  The  carbide  is  said  to  perform  its  office  thor- 
oughly several  years  in  succession  without  renewal.  Mr. 
Spencer’s  process  may  be  applied  on  a scale  commensurate 
with  the  wants  of  the  largest  cities,  and  has  been  adopted 
in  several  of  the  cities  of  Great  Britain. 

Dr.  Medlock  was  requested  by  the  Water  Company  of 
Amsterdam  to  examine  the  water  gathered  by  them  from 
the  Dunes  near  Haarlem,  for  delivery  in  the  city.  The 
water  had  a peculiar  “ fish -like”  odor,  and  after  standing 
awhile,  deposited  a reddish-brown  sediment. 

Under  the  microscope,  the  deposit  was  seen  to  consist  of 
the  filaments  of  decaying  algse,  including  numerous  micro- 
scopic plants,  of  various  hues,  from  green,  through  pale- 
yellow,  orange,  red,  brown,  dark-brown,  to  black. 

The  Doctor  found  the  open  water  channels  lined  with  a 
luxuriant  growth  of  aquatic  plants,  and  the  channel-bed 
covered  with  a deposit  of  black  decaying  vegetal  matter. 
He  discovered  also  that  the  reddish-brown  sediment  was 
deposited  in  greatest  abundance  about  the  iron  sluice-gates. 
Copper,  platinum,  and  lead,  in  finely-divided  states,  were 
known  by  him  to  have  the  power  of  converting  ammonia 
into  nitrous  acid,  and  he  was  led  to  suspect  that  iron  pos- 
sessed the  same  power.  Experiments  with  iron  in  various 
states,  and  finally  with  sheet-iron,  demonstrated  that  strips 
of  iron  placed  in  water  containing  ammonia,  or  organic 


CHARCOAL  PROCESS. 


535 


matter  capable  of  yielding  it,  acted  almost  as  energetically 
as  the  pulverized  metal.  The  organic  matters  of  the  Thames 
water  in  London,  and  the  Rivington  Pike  water  in  Liver- 
pool, as  well  as  the  Dune  water  in  Amsterdam,  were  found 
to  be  completely  decomposed  or  thrown  down  by  contact 
with  iron,  and  the  iron  acted  effectually  wdien  introduced 
into  the  water  in  strips  of  the  sheet  metal  or  in  coils  of  wire. 
This  simple  and  easy  use  of  iron  may  be  employed  in  sub- 
sidence basins  or  reservoirs  on  the  largest  scale  for  towns, 
as  well  as  on  a smaller  scale  for  a single  family. 

The  results  of  these  experiments  with  iron  were  consid- 
ered of  such  great  hygienic  and  national  importance  by  Dr. 
Sheridan  Muspratt  that  he  has  put  an  extended  account  of 
them  on  record.* 

523.  Charcoal  Process. — The  charcoal  plate  filters 
prepared  under  the  patent  of  Messrs.  F.  IT  Atkins  & Co., 
of  London,  have  not  been  introduced  here  as  yet,  so  far  as 
the  writer  is  informed. 

The  valuable  chemical  and  mechanical  properties  of 
animal  charcoal  for  the  purification  of  water  have  long  been 
recognized,  and  it  was  the  practice  in  the  construction  of  the 
early  English  filter-beds,  as  prepared  by  Mr.  Thom,  to  mix 
powdered  charcoal  with  the  fine  sand. 

If  there  is  either  lime  or  iron  in  the  water,  as  there  is  in 
most  waters,  the  chemical  action  results  in  the  formation  of 
an  insoluble  precipitate  upon  the  grains  of  charcoal,  when 
they  become  of  no  more  value  than  sand,  and  their  action 
is  thenceforth  only  mechanical.  Messrs.  Atkins  & Co.  have 
devised  a method  of  overcoming  this  difficulty,  in  part  at 
least,  by  forming  the  charcoal  into  plates,  usually  one  foot 
square  and  three  inches  thick,  and  so  him  that  their  coated 
surfaces  can  be  scraped  clean.  These  plates  may  b«  set  in 


* Muspratt’s  Chemistry,  p.  1085,  Vol.  11- 


536 


CLARIFICATION  OF  WATER 


Fig  129. 


CHARCOAL-PLATE  FILTERS. 


frames,  Fig.  129,  as  lights  of  glass  are  set  in  a sash,  and  the 
water  be  made  to  flow  through  them.  They  are  compound- 
ed for  either  sloiv  or  quick  filtration ; the  dense  plates  (a 
square  foot)  passing  30  to  40  imperial  gallons  per  diem,  the 
porous  80  to  100  gallons,  and  the  very  porous  250  to  300 
gallons  per  diem,  when  clean.  The  water  may  be  first 
passed  through  sand,  fc-r  the  removal  of  the  greater  part  of 
the  organic  matters. 

The  use  of  charcoal  has  heretofore  been  confined  almost 
entirely  to  the  laboratory,  so  far  as  relates  to  the  purifica- 
tion of  water,  and  animal  charcoal  has  been  found  very 
much  superior  to  wood  aud  peat  coals.  Its  success  has 
undoubtedly  been  due  largely  to  its  intermittent  use  and 
frequent  cleanings  and  opportunities  for  oxidation.  Its 
power  of  chemical  action  upon  organic  matter  is  very 
quickly  reduced,  and  it  must  be  often  cleaned  to  be 


INFILTRATION  BASINS. 


537 


effectual.  Some  very  interesting  and  valuable  experiments 
to  test  the  purification  powers  of  charcoal  upon  foul  waters, 
were  described  to  the  members  of  the  Institution  of  Civil 
Engineers,  by  Edward  Byrne,  in  May,  1867. 

524.  Infiltration.— If  any  water  intended  for  a do- 
mestic supply  is  found  to  be  charged  with  organic  matter 
in  solution , the  very  best  plan  of  treatment,  relating  to  that 
water,  is  to  let  it  alone,  and  take  the  required  supply  from 
a purer  source. 

The  impurities  in  suspension  in  wader  may  best  be 
treated  on  Nature’s  plan,  by  which  she  provides  us  with  the 
sparkling  limpid  waters  of  the  springs  that  bubble  at  the 
bases  of  the  hills  and  from  the  fissures  in  the  rocks. 

525.  Infiltration  Basins. — In  the  most  simple  natural 
plan  of  clarification,  a well,  or  basin,  or  gallery,  is  excavated 
in  the  porous  margin  of  a lake  or  stream,  down  to  a level 
below  the  water  surface,  where  the  water  supply  will  be 
maintained  by  infiltration. 

All  those  streams  that  have  their  sources  in  the  mount- 
ains, and  that  flow  through  the  drift  formation,  transport  in 
flood  large  quantities  of  coarse  sand  and  the  lesser  gravel 
pebbles.  These  are  deposited  in  beds  in  the  convex  sides 
of  the  river  bends,  and  the  finer  sands  are  spread  upon  them 
as  the  floods  subside.  From  these  beds  may  be  obtained 
supplies  of  water  of  remarkable  clearness  and  transparency. 

The  volume  of  water  to  be  obtained  from  such  sources 
depends,  first,  upon  the  porosity  of  the  sand  or  gravel  be- 
tween the  well,  basin,  or  gallery,  and  the  main  body  of 
water,  the  distance  of  percolation  required,  the  infiltration 
area  of  the  well  or  gallery,  and  the  head  of  water  under 
which  the  infiltration  is  maintained. 

A considerable  number  of  American  towns  and  cities 
‘cave  already  adopted  the  infiltration  system  of  clarification 


538 


CLARIFICATION  OF  WATER. 


of  their  public  water  supplies,  aud  although  it  is  not  one 
that  can  be  universally  applied,  it  should  and  will  meet 
with  favor  wherever  the  local  circumstances  invite  its  use 
Attention  has  not  as  yet  become  fairly  attracted  in  America 
to  the  benefits  and  the  necessities  of  filtration  of  domestic 
water  supplies,  and  many  of  the  young  cities  have  been 
obliged  to  make  an  herculean  effort  to  secure  a public  water 
supply,  having  even  the  requisite  of  abundancej  and  they 
have  been  obliged  to  defer  to  days  of  greatei  financial 
strength  the  additional  requisite  of  clarification.  A knowl- 
edge of  the  processes  of  clarification,  which  are  simple  for 
most  waters,  is  being  gradually  diffused,  and  this  is  a sure 
precursor  of  the  more  general  acceptance  of  its  benefits. 

In  some  of  the  small  western  and  middle  State  towns, 
the  infiltration  basins  have  heretofore  taken  the  form  of  one 
or  more  circular  wTells,  each  of  as  large  magnitude  as  can 
be  economically  roofed  over,  or  of  narrow  open  basins.  In 
the  eastern  States  the  form  has  usually  been  that  of  a cov- 
ered gallery  along  the  margin  of  the  stream  or  lake,  or  of  a 
broad  open  basin.  Some  of  these  basins  are  intended  quite 
as  much  to  intercept  the  flow  of  water  from  the  land  side 
toward  the  river  as  to  draw  their  supplies  from  the  river, 
and  the  prevailing  temperatures  and  chemical  analyses  of 
the  waters,  as  compared  with  the  temperatures  and  analyses 
of  the  river  waters,  give  evidence  that  their  supplies  are  in 
part  from  the  land. 

A thorough  examination  of  the  substrata,  on  the  site  of 
and  in  the  vicinity  of  the  proposed  infiltration  basin,  down 
to  a level  eight  or  ten  feet  below  the  bottom  of  the  basin 
will  permit  an  intelligent  opinion  to  be  formed  of  its  percola- 
tion capacity. 

520.  Examples  of  Infiltration. — Pig.  130  illustrates 
a section  of  the  infiltration  gallery  at  Lowell,  Mass.  This 


EXAMPLES  OF  INFILTRATION. 


539 


gallery  is  a short  distance  above  the  city  and  above  the 
dam  of  the  Locks  and  Canal  Co.  in  the  Merrimac  River, 
that  supplies  some  10,000  liorse-power  to  the  manufacturers 
of  the  city.  The  gallery  is  on  the  northerly  shore  of  the 
stream,  parallel  with  it,  and  lies  about  one  hundred  feet 
from  the  shore. 

Its  length  is  1300  feet,  width  8 feet,  and  clear  inside 
height,  8 feet.  Its  floor  is  eight  feet  below  the  level  of  the 
crest  of  the  dam.  The  side  walls  have  an  average  thickness 
of  two  and  three-fourths  feet,  and  a height  of  five  feet,  and 
are  constructed  of  heavy  rubble  masonry,  laid  water-tight 
in  hydraulic  mortar. 


Fig.  130. 


The  covering  arch  is  semicircular,  of  brick,  one  foot 
thick,  and  is  laid  water-tight  in  cement  mortar. 

Along  the  bottom,  at  distances  of  ten  feet  between 
centres,  stone  braces  one  foot  square  and  eight  feet  long, 
are  placed  transversely  between  the  side  walls  to  resist  the 
exterior  thrust  of  the  earth  and  the  hydrostatic  pressure. 


540 


CLARIFICATION  OF  WATER. 


The  bottom  is  covered  with  coarse  screened  gravel,  one  foot 
thick,  up  to  the  level  of  the  top  of  the  brace  stones. 

The  Merrimac  River  is  tolerably  clear  of  visible  impure 
ties  during  a large  portion  of  the  year,  but  during  high- 
water  carries  a large  quantity  of  clay  and  o:  a silicious  sand 
of  very  minute,  microscopic  grains. 

An  inlet  pipe,  thirty  inches  in  diameter,  connects  the 
lower  end  of  the  gallery  directly  with  the  river,  for  use  in 
emergencies,  and  to  supplement  the  supply  temporarily  at 
low- water  in  the  river,  when  it  is  usually  clear.  At  the  ter- 
minal chamber  of  the  gallery  into  which  the  inlet  pipe  leads, 
and  from  which  the  conduit  leads  toward  the  pumps,  are 
the  requisite  regulating  gates  and  screens. 

This  gallery  was  completed  in  1871,  and  during  the 
drought  and  low  water  of  the  summer  of  1873,  a test  devel- 
oped the  continuous  infiltration  capacity  of  the  gallery  to 
be  one  and  one-half  million  gallons  per  twenty -four  hours, 
or  about  one  hundred  and  fifty  gallons  for  each  square  foot 
of  bottom  area  per  twenty-four  hours. 

At  Lawrence,  Mass. , is  a similar  infiltration  gallery  along 
the  eastern  shore  of  the  Merrimac  River,  from  which  the 
city’s  supply  is  at  present  drawn. 

The  infiltration  gallery  for  the  supply  of  the  town  of 
Brookline,  Mass.,  completed  in  1874,  lies  near  the  margin 
of  the  Charles  River.  The  bottom  is  six  feet  below  the 
lowest  stage  of  water  in  the  river,  its  breadth  between  walls 
four  feet,  and  length  seven  hundred  and  sixty-two  feet.  The 
side  walls  are  two  feet  high,  laid  without  mortar,  and  the 
covering  arch  is  semicircular,  two  courses  thick,  and  tight. 

During  a pump  test  of  thirty-six  hours  duration,  this 
gallery  supplied  water  at  a rate  of  one  and  one-half  million 

* A considerable  percentage  of  the  flow  into  this  and  some  other  infiltration 
basins  is  judged,  from  experimental  tests,  analyses,  and  temperatures,  to  b« 
intercepted  “ ground  water  ” that  was  flowing  toward  the  river. 


EXAMPLES  OF  INFILTRATION. 


541 


gallons  in  twenty-four  hours,  or  four  hundred  and  ninety 
gallons  per  square  foot  of  bottom  area  per  twenty-four 
hours.  The  ordinary  draught  up  to  the  present  writing  is 
about  one-third  this  rate. 

The  pioneer  American  infiltration  basins  were  constructed 
for  the  city  of  Newark,  N.  J.,  under  the  direction  of  Mr. 
Geo.  H.  Bailey,  chief  engineer  of  the  Newark  water- works. 
These  basins  are  somewhat  more  than  a mile  above  the 
city,  on  the  bank  of  the  Passaic  River.  There  are  two 
basins,  each  350  feet  long  and  150  feet  wide,  distant  about 
200  feet  from  the  river.  They  are  revetted  with  excellent 
vertical-faced  stone  walls,  and  everything  pertaining  to 
them  is  substantial  and  neat.  An  inlet  pipe  connects  them 
with  the  river  for  use  as  exigencies  may  require. 

At  Waltham,  Mass.,  a basin  was  excavated  from  the 
margin  of  the  Charles  River  back  to  some  distance,  and 
then  a bank  of  gravel  constructed  between  it  and  the  river, 
intended  to  act  as  a filter. 

The  excavation  developed  a considerable  number  of 
springs  that  flowed  up  through  the  bottom  of  the  basin, 
and  these  are  supposed  to  furnish  a large  share  of  the 
water  supply. 

At  Providence,  two  basins  have  been  excavated,  one  on 
each  side  of  the  Pawtuxet  River.  These  are  near  the  mar- 
gin of  the  River,  and  are  partitioned  from  the  floods  by 
artificial  gravelly  levees. 

At  Hamilton  and  Toronto,  in  Canada,  basins  have  been 
excavated  on  the  border  of  Lake  Ontario.  The  Hamilton 
basin  has,  at  the  level  of  low-water  in  the  lake,  a water  area 
of  little  more  than  one  acre. 

At  Toronto,  the  infiltration  basin  lies  along  the  border 
of  an  island  in  the  lake,  nearly  opposite  to  the  city.  It  is 
excavated  to  a depth  of  thirteen  and  one-half  feet  below 


542 


CLARIFICATION  OF  WATER. 


low-water  in  the  lake,  has  an  average  bottom  width  of  26| 
feet,  side  slopes  2 to  1,  and  length,  including  an  arm  of 
390  feet,  of  3090  feet.  This  basin  is  distant  about  150  feet 
from  the  lake. 

The  top  of  the  draught  conduit,  which  is  four  feet  diam- 
eter, is  placed  at  six  and  one-lialf  feet  below  low-water,  or 
the  zero  datum  of  the  lake  ; and  the  water  area  in  the  basin, 
if  drawn  so  low  as  the  top  of  the  conduit,  will  then  be  3.75 
acres,  and  when  full  to  zero  line  is  5.64  acres,  the  average 
surface  width  being  then  eighty  feet. 

During  a six  days  test  this  basin  supplied  about  four 
and  one-quarter  million  imperial  gallons  per  twenty-four 
hours  under  an  average  head  of  live  feet  from  the  lake,  or 
at  the  rate  of  fifty -two  imperial  gallons  per  square  foot  of 
bottom  area  per  twenty-four  hours. 

At  Binghamton,  A.  Y.,  two  wells  of  thirty  feet  diameter 
each,  were  excavated  about  150  feet  from  the  margin  of  the 
Susquehanna  River,  one  on  each  side  of  the  pump-house. 
These  wells  are  roofed  in. 

At  Schenectady  there  is  a small  gallery  along  the  margin 
of  the  Mohawk  River. 

Columbus  opened  her  works  with  a basin  on  the  bank 
of  the  Scioto,  and  has  since  added  a basin  with  a process 
of  sand  filtration. 

Other  towns  and  cities  have  formed  their  infiltration 
basins  according  to  their  peculiar  local  circumstances. 

These  basins  generally  clarify  the  water  in  a most  satis- 
factory manner,  and  accomplish  all  that  can  be  expected 
of  a mechanical  process,  but  they  have  not  always  delivered 
the  expected  volumes  of  water;  but  perhaps  too  much  is 
sometimes  anticipated  through  ignorance  of  the  true  nature 
of  the  soil  and  false  estimate  of  ground  water”  flow. 

527.  Practical  Considerations. — The  experience  with 


PRACTICAL  CONSIDERATIONS. 


543 


the  American  and  European  infiltration  basins  shows  that 
when  judiciously  located  they  should  supply  from  150  to 
200  U.  S.  gallons  per  square  foot  of  bottom  area  in  each 
twenty-four  hours  continuously.  This  requires  a rate  of 
motion  through  the  gallery  inflow  surface,  of  from  twenty 
to  twenty-five  lineal  feet  per  twenty-four  hours. 

Tins  inflow  is  dependent  largely  upon  the  area  of  short 
surface  through  which  the  water  tends  toward  the  basin, 
and  the  cleanliness  and  porousness  of  that  surface. 

We  have  not  here  the  aid  of  Nature’s  surface  process,  in 
(vhich  the  intercepted  sediment  is  decomposed  by  plant 
action,  and  the  pores  thrown  open  by  frost  expansions,  but 
are  dependent  upon  floods  and  littoral  currents  to  clean  off 
the  sediment  separated  from  the  infiltering  water.  If  the 
infiltering  surface  is  not  so  cleaned  periodically  by  currents, 
it  becomes  clogged  with  the  sediment,  and  its  capability  of 
passing  water  is  greatly  reduced. 

A uniform  sized  grain  of  sand  or  gravel  offers  greater 
percolating  facilities  than  mixed  coarse  and  fine  grains. 
The  proportion  of  interstices  in  uniform  grains  is  from  thirty 
to  thirty-three  per  cent,  of  the  bulk,  and  the  larger  the  grains 
the  larger  the  interstices  and  the  more  free  the  flow.  On 
the  other  hand,  the  smaller  the  grains,  or  the  more  the  ad- 
mixture of  smaller  with  predominating  grains,  the  smaller 
the  interstices,  and  the  less  the  flow,  but  the  more  thorough 
the  clarification  and  the  sooner  the  pores  are  silted  with 
sediment. 

If  there  is  much  fine  material  mixed  with  the  gravel, 
water  will  percolate  very  slowly,  and  a larger  proportional 
infiltration  area  will  be  required  to  deliver  a given  volume 
of  water. 

It  will  be  remembered  that  we  found  gravel  (§  351)  with 
due  admixtures  of  graded  fine  materials  to  make  the  very 


544 


CLARIFICATION  OF  WATER. 


best  embankment  to  retain  water,  even  under  fifty  or  more 
feet  liead. 

The  best  bank  in  which  to  locate  an  infiltration  basin  is 
one  which  is  made  up  of  uniform  silicious  sand  grains  of 
about  the  size  used  for  hydraulic  mortar,  and  which  has  a 
thin  covering  of  finer  grains  next  the  body  of  water  to  be 
filtered.  The  silting  will  in  such  case  be  chiefly  in  the  sur- 
face layer,  and  the  cleaning  by  flood  current  then  be  most 
effectual. 

The  distance  of  the  basin  from  the  body  of  water  is  gov- 
erned by  the  nature  of  the  materials,  being  greater  in  coarse 
gravel  than  in  sand.  It  should  be  only  just  sufficient  to 
insure  thorough  clarification  when  the  surface  is  cleanest. 
A greater  distance  necessitates  a greater  expense  for  greater 
basin  area  to  accomplish  a given  duty,  and  a lesser  distance 
will  not  always  give  thorough  clarification. 

The  distance  should  be  graduated  in  a varying  stratum, 
so  that  the  work  per  unit  of  area  shall  be  as  uniform  as 
possible. 

528.  Examples  of  European  Infiltration. — Mr.  Jas. 
P.  Kirkwood,  C.  E.,  in  his  report*  to  the  Board  of  Water 
Commissioners  of  St.  Louis,  by  whom  he  was  commissioned 
to  examine  the  filtering  processes  practised  in  Europe,  as 
applied  to  public  water  supplies,  has  given  most  accurate 
and  valuable  information,  which  those  who  are  interested  in 
the  subject  of  filtration  will  do  well  to  consult. 

From  Mr.  Kirkwood’s  elaborate  report  we  have  con- 
densed some  data  relating  to  European  infiltration  galleries. 

Perth,  in  Scotland,  has  a covered  gallery  located  in  an 
island  in  the  River  Tay.  Its  inside  width  is  4 feet,  height 
8 feet,  and  length  300  feet.  Its  floor  is  2 A feet  below  low- 
water  surface  in  the  river.  Its  capacity  is  200,000  gallons 


* Filtration  of  River  Waters,  Van  Nostrand/New  York,  1869. 


EUROPEAN  INFILTRATION. 


545 


per  diem,  and  rate  of  infiltration  per  square  foot  of  bottom 
area,  182  gallons  per  diem. 

Angers,  in  France,  has  a covered  gallery  located  in  an 
island  in  the  River  Loire.  This  gallery  has  two  angles  of 
slight  deflection,  dividing  it  into  three  sections.  The  two 
end  sections  are  3'-4"  wide  and  the  centre  section  6-0"  wide. 
The  floors  of  the  two  end  sections  are  7J  below  low- water  in 
the  river,  and  of  the  central  section  9]  feet  below.  The 
combined  length  of  these  galleries  is  288  feet,  and  their  de- 
livery 187  gallons  per  diem  per  square  foot  of  bottom  area. 

These  were  constructed  in  1856,  and  rest  on  a clayey 
substratum  ; consequently  the  greater  part  of  their  inflow 
must  be  through  the  open  side  walls. 

More  recently,  these  have  been  reinforced  by  a new 
gallery,  with  its  floor  5.1  feet  below  low- water  surface  in  the 
river,  and  not  extending  down  to  the  clay  stratum.  This  ia 
5 feet  wide  and  8 feet  high,  and  delivers  300  gallons  per 
diem  per  square  foot  of  bottom  area. 

Lyons,  in  France,  has  two  covered  galleries  along  the 
banks  of  the  Rhone,  the  first  16  -6"  wide  and  394  feet  long. 
The  second  is  33  feet  wide,  except  at  a short  section  in  the 
centre,  where  it  is  narrowed  to  8 feet,  and  is  328  feet  long. 
There  are  also  two  rectangular  covered  basins.  The  com- 
bined bottom  areas  of  the  two  galleries  is  17,200  square 
feet,  and  of  the  two  basins  40,506  square  feet.  The  total 
delivery  at  the  lowest  stage  of  the  river  is  nearly  six  mil- 
lion gallons  per  diem,  or  100  gallons  per  square  foot  of 
bottom  area.  The  capacity  of  the  33-foot  gallery  alone  is, 
however,  147  gallons  per  square  foot  of  bottom  area.  About 
6-|-  feet  head  is  required  for  the  delivery  of  the  maximum 
quantity.  The  average  distance  of  the  galleries  from  the 
river  is  about  80  feet,  and  the  two  basins  are  behind  one  of 
the  galleries. 

35 


546 


CLARIFICATION  OF  WATER. 


At  Toulouse,  France,  three  covered  galleries  extend 
along  the  hank  of  the  Garonne.  The  first  two,  after  being 
walled,  were  filled  with  small  stones. 

The  new  gallery  has  its  side-walls  laid  in  mortar,  is  cov- 
ered with  a semicircular  arch,  is  7 -6  wide,  8 -8"  high,  and 

1180  feet  long.  Its  floor  is  8-7"  below  low-water  surface  in 
the  river.  Its  total  capacity  is  a little  in  excess  of  2\  mil- 
lion gallons,  or  228  gallons  per  diem,  per  square  foot  of 
bottom  area. 

For  the  supply  of  Genoa,  in  Italy,  which  lies  upon  the 
Mediterranean,  a gallery  lias  been  constructed,  in  a valley 
of  a northern  slope  of  the  Maritime  Alps,  at  an  altitude  of 

1181  feet  above  the  sea.  This  gallery  extends  in  part 
beneath  the  bed  of  the  River  Scrivia,  transversely  from  side 
to  side,  and  in  part  along  the  banks  of  the  stream.  The 
width  is  5 feet,  height  7 to  8 feet,  and  length  1780  feet. 

The  extraordinarily  large  delivery,  per  lineal  foot,  is 
6412  gallons  per  diem. 

The  waters  are  conveyed  down  to  Genoa  in  cast-iron 
pipes,  with  relieving-tanks  at  intervals. 

529.  Example  of  Intercepting  Well. — The  great 
well  in  Prospect  Park,  Brooklyn,  L.  I.,  is  a notable  instance 
of  intercepting  basin,  such  as  is  sometimes  adopted  to  inter- 
cept the  flow  of  the  land  waters  toward  a great  valley,  oi 
the  sea,  or  to  gather  the  rainfall  upon  a great  area  of  sandy 
plain. 

This  portion  of  Long  Island  is  a vast  bed  of  sand,  which 
receives  into  its  interstices  a large  percentage  of  the  rainfall. 
The  rain-water  then  percolates  through  the  sand  in  steady 
(low  toward  the  ocean.  Although  the  surface  of  the  land 
lias  considerable  undulation,  the  subterranean  saturation  is 
found  to  take  nearly  a true  plane  of  inclination  toward  the 
sea,  and  this  inclination  is  found  by  measurements  in 


FILTER-BEDS. 


547 


numerous  wells  to  be  at  the  rate  of  about  one  foot  in  770  ft., 
or  seven  feet  per  mile.  So  if  a well  is  to  be  dug  at  one-lialf 
mile  from  the  ocean  beach,  water  is  expected  to  be  found 
at  a level  about  three  and  one-half  feet  above  mean  tide ; 
or,  if  one  mile  from  the  beach,  at  seven  feet  above  mean 
tide,  whatever  may  be  the  elevation  of  the  land  surface. 
If  in  such  subsoils  a well  is  excavated,  and  a great  draught 
of  water  is  pumped,  the  surface  of  saturation  will  take  its 
inclination  toward  the  well,  and  the  area  of  the  watershed 
of  the  well  will  extend  as  the  water  surface  in  the  well  is 
lowered.  If  the  well  has  its  water  surface  lowered  so  as  to 
draw  toward  it  say  a share  equal  to  twenty-four  inches  of 
the  annual  rainfall  on  a circle  around  it  of  one-quarter  mile 
radius,  then  its  yield  should  be  at  the  rate  of  very  nearly 
one-half  million  gallons  of  water  daily. 

The  Prospect  Park  well,  Fig.  131  (p.  102),  is  50  ft.  in  diam- 
eter. A brick  steen  or  curb  of  this  diameter,  resting  upon 
and  bolted  to  a timber  shoe,  edged  with  iron,  was  sunk  by 
excavating  within  and  beneath  it,  fifty-nine  feet  to  the  sat- 
uration plane,  and  then  a like  curb  of  thirty -five  feet  diam- 
eter was  sunk  to  a further  depth  of  ten  feet.  The  top  of  the 
inner  curb  was  finished  at  the  line  of  water  surface.  A 
platform  was  then  constructed  a few  feet  above  the  water 
surface,  within  the  large  curb,  to  receive  the  pumping 
engine.  The  boilers  were  placed  in  an  ornate  boiler-house 
near  the  well. 

On  test  trial,  the  well  was  found  to  yield,  after  the  water 
surface  in  the  well  had  been  drawn  down  four  and  one-half 
feet,  at  the  rate  of  850.000  gallons  per  twenty-four  hours. 

530.  Filter-beds. — A method  of  filtration,  more  arti- 
ficial than  those  above  described,  must  in  many  cases  be 
Tesorted  to  for  the  clarification  of  public  water  supplies. 

The  most  simple  of  the  methods  that  has  had  thorough 


548 


CLARIFICATION  OF  WATER. 


trial,  consists  in  passing  the  water  downward,  in  an  arti- 
ficial basin  specially  constructed  for  the  purpose,  through 
layers  of  fine  sand,  coarse  sand,  fine  gravel,  coarse  gravel, 
and  broken  stone,  to  collecting  drains  placed  beneath  the 
whole,  Fig.  132. 


FILTER-BEDS. 


549 


The  basins  in  such  cases  are  usually  from  100  to  200 
feet  wide,  and  from  200  to  300  feet  long,  each.  Each  basin 
is  made  quite  water-tight,  the  horizontal  bottom  or  floor 
being  puddled,  if  necessary,  and  sometimes  also  covered 
with  a paving  of  concrete,  or  layer  of  bricks  in  cement 
mortar.  The  sides  are  revetted  with  masonry,  or  have 
slopes  paved  with  substantial  stone  in  mortar,  or  with 
concrete. 

A main  drain  extends  longitudinally  through  the  centre 
of  the  basin,  rests  upon  the  floor,  and  is  about  two  feet 
wide  and  three  feet  high.  From  the  main  drain,  on  each 
side,  at  right-angles,  and  at  distances  of  about  six  feet 
between  centres,  branch  the  small  drains.  These  are  six  or 
eight  inches  in  diameter,  of  porous,  or,  more  generally,  per- 
forated clay  tiles,  resting  upon  the  bottom  or  floor,  and  they 
extend  from  the  central  drain  to  the  side  walls,  where  they 
have  vertical,  open-topped,  ventilating,  or  air-escape  pipes, 
rising  to  the  top  of  the  side  walls. 

These  pipes  and  the  central  drain  form  an  arterial  sys- 
tem by  which  water  may  be  gathered  uniformly  from  the 
whole  area  of  the  basin. 

This  arterial  system  is  then  covered,  in  horizontal  layers, 
according  to  the  suitable  materials  available,  substantially 
as  follows,  viz.:  two  feet  of  broken  stone,  like  “road 
metal one  foot  of  shingle  or  coarse-screened  gravel ; one 
foot  of  pea-sized  screened  gravel ; one  foot  of  coarse  sand ; 
and  a top  covering  of  one  and  one-half  to  three  feet  of  fine 
sand,  of  .013  inch,  or  .33  millimeter  grains. 

This  combination  is  termed  a filter-bed , and  over  it  is 
flowed  the  water  to  be  clarified. 

Provision  is  made  for  flowing  on  the  water  so  as  not  to 
disturb  the  fine  sand  surface.  This  inflow  duct  is  often 
arranged  in  the  form  of  a tight  channel  on  the  top  of  the 


550 


CLARIFICATION  OF  WATER. 


covering  of  the  central  gathering  drain,  and  the  water  flowa 
over  its  side  walls,  during  the  regular  feeding  of  the  filter, 
to  right  and  left,  with  slow  motion. 

The  depth  of  water  maintained  upon  the  filter-bed  is 
four  feet  or  more,  according  to  exposure  and  climatic  effects 
upon  it. 

At  the  outflow  end  of  the  central  gathering  drain  is  an 
effluent  chamber,  with  a regulating  gate  over  which  the 
filtered  water  flows  into  the  conduit  leading  to  the  dear- 
water  basin.  The  water  in  the  effluent  chamber  is  connected 
with  the  water  upon  the  filter-bed  through  the  drains  and 
interstices  of  the  bed  ; consequently,  if  there  is  no  draught, 
its  surface  has  the  same  level  as  that  upon  the  bed,  but  if 
there  is  draught,  the  surface  in  the  chamber  is  lowest,  and 
the  difference  of  level  is  the  head  under  which  water  flows 
through  the  filter-bed  to  the  effluent  chamber. 

The  regulating  gate  in  the  effluent  chamber  controls  the 
outflow  there  to  the  clarified  water  basin,  and  consequently 
the  head  under  which  filtration  takes  place,  and  the  rate  of 
flow  through  the  filter-bed. 

531.  Settling  and  Clear- water  Basins. — When  the 
water  is  received  from  a river  subject  to  the  roil  of  floods,  it 
should  be  received  first  into  a settling  basin,  where  it  will 
be  at  rest  forty-eight  horns  or  more,  so  that  as  much  as 
possible  of  the  sediment  may  be  separated  by  the  gravity 
process,  before  alluded  to.  Its  rest  in  large  storage  basins 
prepares  it  very  fully  for  introduction  to  the  filter-bed, 
which  is  to  complete  the  separation  of  the  microscopic 
plants,  vegetable  fibres,  and  animate  organisms,  that  can- 
not be  separated  by  precipitation. 

Since  the  domestic  consumption  of  the  water  at  some 
hours  of  the  day  is  nearly  or  quite  double  the  average  con- 
sumption per  diem,  the  clarified  water  basin  should  be 


FILTER-BED  SYSTEM. 


553 


large  enough  to  supply  the  irregular  draught  and  permit 
the  flow  through  the  Alter  to  he  uniform. 

This  system  of  clarification  in  perfection  includes  three 
divisions,  viz. : the  Settling  Basin , the  Filter-bed , and  the 
Clear -water  Basin. 

The  settling  and  clear- water  basins  may  be  constructed 
according  to  the  methods  and  principles  already  discussed 
for  distributing  reservoirs  (Chap.  XVI).  The  capacity  of 
each  should  be  sufficient  to  hold  not  less  than  two  days 
supply,  and  the  depth  of  water  should  be  not  less  than 
ten  feet,  so  that  the  water  may  not  be  raised  to  too  high 
a temperature  in  summer,  and  that  its  temperature  may 
be  raised  somewhat  in  winter  before  it  enters  the  distribu- 
tion-pipes. 

532.  Introduction  of  Filter-bed  System. — Pough- 
keepsie. on  the  Hudson,  was  the  first  American  city  to 
adopt  the  filter-bed  system  of  clarification  of  her  public 
water-supply. 

The  Poughkeepsie  works  were  constructed  in  1871,  to 
take  water  from  the  Hudson  River.  During  the  spring 
floods,  the  river  is  quite  turbid.  These  filtering  works  con- 
sist of  a small  settling  basin  and  two  filter-beds,  each  73|  ft 
wide  and  200  ft.  long.  Each  bed  is  composed  of 

24  inches  of  fine  sand. 

6 “ “ pinch  gravel. 

6 “ “ -J-inch  gravel. 

6 “ “ i-inch  broken  stone. 

24  “ “ 4 to  8-inch  spalls. 

66  “ total. 

The  floors  on  which  the  beds  rest  are  of  concrete,  twelve 
inches  thick. 

The  clear- water  basin  is  28  by  88  feet  in  plan,  and  17  ft 
deep. 


552 


CLARIFICATION  OF  WATER. 


Water  is  lifted  from  the  river  to  the  settling  basin  by  a 
pump,  and  it  flows  from  the  clear- water  basin  to  the  suction 
chamber  of  the  main  pump,  giving  some  back  pressure. 
From  thence  it  is  pumped  to  the  distributing  reservoir. 

Since  the  issue  of  early  editions  of  this  book,  the  State 
Board  of  Health  of  Massachusetts  has  performed  experi- 
ments in  sand  filtration  of  inestimable  value,  under  direc- 
tion of  Hiram  F.  Mills,  C.  E.,  a member,  and  has  jrablislied 
results  obtained  by  its  careful  and  precise  methods.  These 
reports  contain  valuable  suggestions  relating  to  the  com- 
position of  filters,  and  methods  and  rates  of  their  opera- 
tion, and  their  successes  in  the  removal  of  bacterium. 

Hudson  and  Poughkeepsie  have  increased  their  beds ; 
Lawrence  and  Nantucket,  Mass.,  Ilion  and  Mount  Vernon, 
N.  Y. , and  Grand  Forks,  N.  D. , have  constructed  new  beds ; 
and  several  European  cities  have  built  new,  or  extended 
their  sand-bed  filters,  with  marked  improvement  of  health 
and  reductions  of  death  rate  among  their  populations. 

When  our  American  water  consumers  are  more  familiar 
with  this  filter-bed  system  of  clarification,  now  in  such  gen- 
eral use  in  England  and  Scotland  and  on  the  Continent,  its 
use  will  be  oftener  demanded.  Subsidence,  as  we  have 
before  remarked,  does  not  completely  clarify  the  water, 
even  in  a fortnight’s  or  three  weeks’  time,  but  a good  sand 
filter,  if  not  overworked,  intercepts  not  only  the  visible  sedi- 
ment and  fine  clay,  but  the  most  minute  vegetable  fibres 
and  organisms  and  the  spawn  of  fish,  and  it  is  highly  im- 
portant that  these  should  be  separated  before  the  water  is 
passed  to  the  consumer. 

533.  Capacity  of  Filter-Beds. — Experience  indicates 
that  the  flow  through  a filter-bed,  such  as  we  have  above 
described,  should  not  exceed  the  rate  of  14  feet  lineal  per 
diem,  or  be  reduced  by  silting  of  the  sand  layer  to  less  than 


CLEANING  OF  FILTER-BEDS. 


553 


4. 5 feet  per  diem.  It  must  not  be  so  rapid  as  to  snck  the 
Band  grains  or  clay  particles  or  the  intercepted  fibres 
through  the  bed,  or  its  whole  purpose  will  be  entirely 
defeated. 

A rate  of  about  one-half  foot  per  hour,  or  twelve  lineal 
feet  per  diem,  when  the  filter  is  tolerably  clean,  is  generally 
considered  the  best.  This  gives  the  filter-bed  a capacity  of 
twelve  cubic  feet,  or  89.76  gallons,  per  square  foot  of  sur- 
face per  twenty -four  hours,  and  requires,  in  work,  about 
12,000  square  feet  of  filtering  surface  for  each  million  gal- 
lons of  water  to  be  filtered  per  diem. 

534.  Cleaning  of  Filter-Beds.— The  filter-beds  upon 
the  English  streams  require  cleaning  about  once  a week, 
when  the  rivers  are  in  their  most  turbid  condition,  and 
ordinarily  once  in  three  or  four  weeks. 

The  process  of  cleaning  consists  of  removing  a slice 
of  about  one-half  inch  thickness  from  the  surface  of  the 
fine  sand,  more  or  less  according  to  the  grain  of  the  sand 
and  nature  of  both  the  sediment  and  water.  Slicing  is 
repeated  until  renewal  of  the  sand  is  necessary.  This 
requires  the  water  to  be  drawn  off  from  the  bed  to  be  cleaned, 
and  of  course  puts  the  portion  of  filter  area  being  cleaned 
out  of  service.  According  to  the  usual  practice,  the  water  is 
drawn  down  only  about  a foot  below  the  sand  surface  for 
the  cleaning ; but  there  is  a great  advantage,  though  an  in- 
convenience, in  drawing  the  water  entirely  out  of  the  bed, 
for  this  admits  the  air  to  oxidize  the  organic  matters  that 
are  drawn  into  the  filter,  which  is  of  great  importance. 

To  provide  for  cleaning,  the  required  area  for  service 
should  be  divided  into  two  or  more  independent  beds,  and 
then  one  additional  bed  should  be  provided  also,  so  that 
there  shall  always  be  one  bed  surplus  that  may  be  put  out 
of  use  for  cleaning. 


554 


CLARIFICATION  OF  WATER. 


The  greater  the  number  of  equal  divisions  the  less  will 
be  the  surplus  area  to  be  provided,  and  on  the  other  hand, 
each  division  adds  something  to  the  cost,  so  that  both  con 
venience  and  finance  are  factors  controlling  the  design  as 
well  as  the  form  and  extent  of  lands  available. 

As  a suggestion  merely,  it  is  remarked  that  the  divisions 
may  be  approximately  as  follows,  for  given  volumes,  de- 
pendent on  the  turbidness  of  water  and  local  circumstances : 

TABLE  No.  109. 

Dimensions  of  Filter-Beds  for  Given  Volumes. 


For 

i 

million  gallons  per  diem,  3 

beds 

60  feet 

X 

100  feet 

“ 

2 

“ 

3 

“ 

OO 

O 

X 

150  “ 

“ 

3 

" 

tc 

“ 

3 

te 

IOO  “ 

X 

180  “ 

“ 

4? 

“ 

“ 

4 

“ 

IOO  “ 

X 

180  “ 

“ 

6 

“ 

4 

IOO  " 

X 

240  “ 

“ 

8 

tl 

“ 

4 

120  “ 

X 

270  “ 

IO 

“ 

“ 

ce 

5 

ft 

120  “ 

X 

270  “ 

535.  Renewal  of  Sand  Surface. — When  the  repeated 
parings  from  the  surface  have  reduced  the  top  fine-sand 
layer  to  about  twelve  inches  thickness,  a new  coat  should 
be  put  on  restoring  it  to  its  original  thickness. 

If  good  fine  sand  is  difficult  of  procurement,  the  parings 
may  perhaps  be  washed  for  replacing  with  economical 
result. 

This  is  sometimes  accomplished  by  letting  water  flow 
over  the  sand  in  an  inclined  trough  of  plank,  having  cleats 
across  it  to  intercept  the  sand,  or  by  letting  water  flow  up 
through  it  in  a wood  or  iron  tank.  In  the  latter  case  watei 
is  admitted  under  pressure  through  the  bottom  of  the  tank, 
and  the  sand  rests  upon  a grating  covered  with  a fine  wire 
cloth,  placed  a short  distance  above  the  bottom  of  the  tank. 
The  current  is  allowed  to  flow  up  through  the  sand  and  ovei 
the  top  of  the  tank  until  it  runs  clear. 


BASIN  COVERINGS. 


555 


536.  Basin  Coverings. — The  British  and  Continental 
filter-beds  are  rarely  roofed  in,  although  the  practice  is 
almost  universal  of  vaulting  over  the  distributing  reservoirs 
that  are  near  the  towns. 

The  intensity  of  our  summer  heat  and  intensity  of  winter 
cold  in  our  northern  and  eastern  States,  makes  the  roofing 
in  of  our  filter-beds  almost  a necessity,  though  we  are  not 
aware  that  this  has  been  done  as  yet  in  any  instance. 

The  use  of  the  shallow  depth  of  four  feet  of  water,  so 
common  in  the  English  filters,  would  be  most  fatal  to  open 
filters  here,  for  the  water  would  frequently  be  raised  in 
summer  to  temperatures  above  80°  Fall,  and  sent  into  the 
pipes  altogether  too  warm,  with  scarce  any  beneficial 
change  before  it  reached  the  consumer.  Such  tempera- 
tures induce  also  a prolific  growth  of  algce  upon  the  sides 
of  the  basin,  and  upon  the  sand  surface  when  it  has  become 
partially  clogged,  and  soon  produce  a vegetable  scum  upon 
the  water  surface  also.  As  these  vegetations  are  rapidly 
reproduced  and  are  short-lived,  their  gases  of  decomposi- 
tion permeate  the  whole  flow,  and  render  the  water  ob- 
noxious. 

Depth  of  water  and  protection  from  the  direct  heating 
action  of  the  sun  are  the  remedies  and  preventives  for 
such  troubles.  A free  circulation  of  air  and  light  must, 
however,  be  provided,  and  also  the  most  convenient  facili- 
ties for  the  cleansing  and  renewal  of  the  bed. 

In  Fig.  132  is  presented  a suggestion  for  a roof-covering 
that  will  give  the  necessary  protection  from  sun  and  frost,  and 
the  requisite  light,  ventilation,  and  convenience  of  access. 

The  side  walls  are  here  proposed  to  be  of  brick,  and  the 
truss  supporting  the  roof  to  be  of  the  suspended  trapezoidal 
class.  The  confined  air  in  the  hollow  walls,  and  the  saw 
dost  or  tan  layer  over  the  truss,  are  the  non-conductors  that 


556 


CLARIFICATION  OF  WATER. 


assist  in  maintaining  an  even  temperature  within  the  basin, 
and  resist  the  effects  of  intense  heat  and  intense  cold. 

The  Parisian  reservoirs  at  Memlmontant,  and  the  splen- 
did new  structure  at  Moutrouge,  are  covered  with  a system 
of  vaulting,  after  the  manner  practised  by  the  Romans,  and 
this  system  is  also  followed  by  the  British  engineers  in  their 
basin  covers. 

A substantial  cover  over  a filter  basin  will  reduce  the 
difficulties  with  ice  to  a minimum,  and  remove  the  risk  of 
the  bed  being  frozen  while  the  water  is  drawn  off  for  clean- 
ing in  winter.  In  such  case,  if  the  water  is  drawn  imme- 
diately from  a deep  natural  lake,  or  a large  impounding 
reservoir,  the  only  ice  formation  will  be  a mere  skimming 
over  of  the  surface  in  the  severest  weather,  and  the  inflow 
of  water,  at  a temperature  slightly  above  freezing,  will  tend 
constantly  to  preserve  the  surface  of  the  water  uncongealed, 
and  the  sand  free  from  anchor  ice. 

53 6«.  Mechanical  Filters. — The  promising  results 
secured  by  the  treatment  of  water  with  iron  mentioned  in 
article  522,  led  to  further  experiments  with  other  methods  of 
bringing  water  in  contact  with  scraps  of  iron.  For  instance, 
William  Anderson,  C.  E.,  devised  a revolving  cylinder  with 
inflow  and  outflow  pipes  leading  through  its  trunnions,  the 
cylinders  having  a diameter  equalling  about  five  diameters 
of  the  inflow  pipe.  Small  scraps  of  iron,  such  as  the 
punchings  of  boiler  plates,  or  iron  borings,  fill  about  one- 
sixth  diameter  of  the  cylinder.  The  cylinder  is  revolved  by 
independent  power  and  the  flow  of  water  through  the  cylin- 
der goes  on  continuously.  A current  of  air  is  usually  blown 
into  the  outflowing  current  of  water.  The  mechanical  action 
is  to  carry  up  the  iron  and  scatter  it  from  the  successively 
inclining  shelves  within  the  cylinder  and  thus  to  shower  the 
iron  through  the  slowly  flowing  stream. 


CLARIFICATION  OF  WATER. 


556a 


In  apparatus  accomplishing  similar  mechanical  results, 
the  continual  motions  and  frictions  of  the  iron  particles  pre- 
vent tendencies  to  caking  as  when  the  iron  is  mixed  in 
sand,  and  the  frictions  constantly  detach  minute  particles 
of  the  iron  surfaces  keeping  them  bright  and  facilitating 
chemical  action  upon  the  impurities  in  the  water.  If  the 
water  contains  dissolving  organic  matters,  their  carbonic 
acids  dissolve  minute  portions  of  the  metal  and  form  fer- 
rous carbonate,  a protosalt  of  iron,  which  on  contact  with 
the  oxygen  of  the  inflowing  current  of  air  is  converted  into 
the  insoluble  form  of  ferric  hydroxide.  A coagulation  results 
among  the  particles  of  organic  matter  suspended  in  the 
water,  by  their  encasement  in  part  with  the  ferric  oxide, 
and  entanglement  together,  until  a flocculent  precipitate  is 
formed  which  has  not  only  increased  specific  gravity  and 
tendency  to  settle,  but  is  so  assembled  into  groups  as  to  be 
well  adapted  to  the  usual  straining  process  of  a sand  filter. 

Suspended  clays  and  micro-organisms  in  the  water  are 
also  similarly  caught  in  the  flocculence,  and  are  thus  more 
readily  precipitated  or  separated  by  filtration. 

The  flocculence  produced  is  similar  to  that  heretofore 
observed  when  alum  or  the  per-chlorides  of  iron,  aluminum, 
magnesium  and  calcium  have  been  introduced  in  solutions 
into  similar  waters. 

Intimate  contacts  of  iron  scraps  with  the  water  may  be 
made  by  causing  the  water  to  flow  upward  through  a series 
of  screens  on  which  are  placed  several  inches  depth  of  iron 
puncliings.  The  flow  would  be  at  a rate  that  would  keep 
the  iron  in  a motion  resembling  ebulition  in  the  water,  and 
the  power  would  be  obtained  from  the  main  pumping-engine 
through  a slight  increase  of  pressure  in  the  force  main. 

Preliminary  treatments  of  water  by  contact  with  iron 
scraps  or  by  introductions  of  proper  solutions  of  metallic 


556 b 


CLARIFICATION  OF  WATER. 


salts  not  only  causes  the  water  to  more  rapidly  precipitate 
its  impurities  in  subsidence  basins  but  also  reduces  ma- 
terially the  area  of  sand  filter  required  to  clarify  it.  Such 
preliminary  treatments  facilitate  the  action  of  mechanical 
filters. 

The  shells  of  the  mechanical  filters  are  usually  cylinders 
of  iron  adapted  to  receive  internal  pressures.  They  have 
inflow  and  outflow  pipes  and  contain  beds  of  sand  through 
which  the  water  flows  for  clarification.  They  are  usually 
cleaned  by  sending  a powerful  reversed  current  of  clean 
water  through  the  sand,  the  sand  being  stirred  at  the  time 
mechanically  or  by  the  force  of  the  water.  The  duty  of 
these  filters  is  simply  to  strain  the  water  by  arresting  the 
mechanical  impurities  held  in  suspension,  whether  or  not 
coagulated.  The  usual  velocity  of  flow  through  mechan- 
ical filters  indicates  the  severe  work  given  them.  The 
catalogues  of  several  makers  state  the  capacity  of  a ten 
foot  diameter  vertical  filter,  having  74.58  square  feet  of 
filter  surface,  as  360,000  gallons,  or  48,12S  cubic  feet  of 
water  filtered  per  24  hours.  This  volume  requires  a net 
velocity  of  flow  through  the  sand  of  25.5  feet  per  hour,  or 
612  feet  per  day.  This  rate  is  about  fifty  times  as  fast  as 
is  found  safe  in  sand  bed  filters,  and  is  only  attained  by 
the  use  of  coarse  sand  or  quartz  fragments  of  about  the 
size  of  common  granulated  sugar  grains.  Preliminary 
coagulations  by  alum  or  perchlorides  of  metals  given  tc 
waters  containing  clays  or  organic  matters,  aid  the  coarse 
sand  in  stopping  the  flocculated  sediments  in  the  water, 
and  water  apparently  clear  is  the  result  often  attained. 
Dangerous  water  thus  rapidly  treated  through  coarse  sande 
should  be  daily  examined  for  bacteria,  lest  the  germs  flow 
or  grow  through  in  large  numbers. 


BATES  OF  FILTRATION  THROUGH  SAND.  556c 

5361).  Results  with  Saiul  Filters. — The  processes 
of  screening,  subsidation,  and  filtration  must  not  be  con- 
founded. The  filter  should  do  no  work  that  can  be  done  by 
the  much  cheaper  mechanical  racks  and  screens.  The  filter 
shordd  be  relieved  of  all  the  work  that  can  be  done  by  subsi- 
dation, without  chemical  precipitation  if  practicable,  or 
with  the  aid  of  moderate  quantities  of  some  simple  precipi- 
tants  such  as  alum  or  the  perchloride  of  iron.  The  most  im- 
portant work  of  the  filter  may  be  considered  as  a delicate 
refining  process,  stopping  the  disintegrating  organic  frag- 
ments that  cloud  the  transparency  of  the  water,  detaining 
the  active  micro-organisms,  such  as  may  be  discovered 
battling  by  hundreds  in  a teaspoonful  of  pond  water, 
and  almost  entirely  straining  out  the  bacterial  micro- 
organisms, sometimes  discovered  by  thousands  in  a cubic 
centimeter  (approximately  one  teaspoonful)  of  water,  and 
some  of  which  may  be  the  dreaded  disease-bearing  germs. 

When  the  sand  bed  filter  has  been  properly  constructed, 
then,  as  it  is  first  filled,  or  whenever  it  is  subsequently 
filled,  it  is  advisable  that  its  saturation  be  from  the  bot- 
tom, upward,  and  at  a slow  rate,  that  will  not  disturb  its 
sand  layers.  The  perfection  of  its  working  is  largely 
dependent  on  the  uniformity  of  texture  of  the  whole  sand 
bed,  which  insures  a uniform  rate  of  filtration  through  all 
parts  of  the  bed.  An  increased  rate  of  flow  at  one  point 
tends  to  a cutting  of  the  sand  bed  at  that  point  and  to 
defective  filtration  there.  Overworking  the  filter  by  too 
rapid  filtration  induces  cutting  at  points  and  may  thus 
defeat  in  part  the  object  of  filtration. 

A rate  of  filtration  of  one  million  gallons  per  day  equals 
a rate  of  133,682  cubic  feet  per  day.  A net  velocity  of  flow 
of  3.07  feet  per  24  hours  requires  one  acre  area  per  million, 
and  a net  velocity  of  12  feet  per  day  requires  a little  more 


55 6d 


CLARIFICATION  OF  WATER. 


than  one-quarter  acre  surface  in  action  for  each  million 
gallons  per  day.  Other  rates  of  flow,  acres  required,  and 
filtrations  per  acre  are  as  follows : 


TABLE  No.  1 O 9 a . 

Rates  of  Filtration  through  Sand  Beds. 


Velocity  of  Flow 
per  24  hours. 

Area  required  for  One  Million  Gallons. 

Million  Gallons  in 
acres. 

Square  Feet. 

A cres. 

3-°  7 

feet. 

43)  5^0 

I. OOO 

I.  OOO 

5 

6 C 

26,736 

.614 

1.629 

6 

a 

22, 280 

•511 

1 - 955 

7 

6i 

*9,°97 

• 438 

2. 281 

8 

U 

16, 710 

• 384 

2.607 

9 

a 

i4,584 

• 341 

2-933 

10 

a 

i3,368 

• 307 

3-258 

11 

a 

I2N53 

.279 

3-  584 

I 2 

6 6 

11,140 

.256 

3-9i° 

A rate  of  filtration  requiring  a velocity  through  the 
bed  exceeding  12  feet  per  21  hours  requires,  with  most 
clear  waters,  exceeding  care  to  maintain  the  bed  in  uni- 
form good  condition.  The  rate  of  ten  feet,  or  three  and 
one-quarter  million  gallons  per  acre,  is  usually  safe  with 
fairly  clear  waters  and  lesser  rates  as  the  microbic  or  sedi- 
mentary matters  increase  in  the  water. 

It  is  usually  found  in  practice  that  a newly  made  sand 
bed  requires  about  three  days  work  in  filtration  before  it 
reaches  its  best  and  permanent  duty  in  the  removal  of 
microbes.  With  downward  filtration  the  finest  clarifica- 
tion is  not  reached  until  a thin  layer  of  intercepted  par- 
ticles has  accumulated  on  the  top  surface  of  the  filter. 
This  surface  accumulation  is  the  efficient  screen  that  inter- 
cepts by  entanglement  the  microscopic  protophyta  and 


CLARIFICATION  OF  WATER. 


55bd 


protozoa,  organisms  invisible  individually  to  the  naked 
eye,  yet  whose  activities  after  they  reach  human  organs 
may  produce  results  most  momentous  in  consequences. 

The  sand  bed  filter  should  remove  95  to  99  per  cent,  of 
all  the  micro-organisms.  Manifestly,  it  is  wise  to  screen 
out  and  settle  before  filtration  the  coarser  particles  from 
the  water,  and  not  encumber  the  filter  with  them.  Mani- 
festly, it  is  dangerous  to  overwork  and  disturb  the  uni- 
formity of  the  sand  bed  when  the  sand  and  its  thin  coating 
are  the  safeguards  as  to  disease  germs. 

When  there  is  danger  from  the  germs,  careful  watch- 
ing and  operation  are  precautions  leading  to  safety. 
Daily  bacteriological  examinations  should  be  made  of  the 
water  flowing  into  the  clear  water  basin,  to  determine  if 
the  work  of  the  filter  is  uniformly  good  and  efficient 
These  are  the  least  permissible  measures  of  vigilance. 


WITH  MECHANICALLY  OPERATED  VALVES, 


556/ 


PUMPS. 


n:u 


REYNOLDS*  TRIPLE  EXPANSION  PUMPING-ENGINE,  CHICAGO. 

Capacity,  18,000,000  gallons  daily. 

Built  by  the  EDW.  P.  ALLIS  CO.,  Milwaukee,  Wis. 


Fig.  133. 


PUMPING  ENGINE  No.  3,  BROOKLYN. 


556/ 


HYDRAULIC  POWER  PUMPS. 


HYDRAULIC  POWER  PUMP. 


CHAPTER  XXIV. 


PUMPING  OF  WATER. 

537.  Types  of  Pumps.— The  machines  that  have  been 
used  for  raising  water  for  public  water  supplies  in  the  United 
States  present  a variety  of  combinations,  but  their  water 
ends  may  be  classified  and  illustrated  by  a few  type  forms. 

Our  space  will  not  permit  a discussion  of  the  theories 
and  details  of  their  prime  movers,  nor  more  than  a general 
discussion  of  the  details  of  the  pumps,  with  their  relations 
to  the  flow  of  water  in  their  force  mains. 

The  horizontal  double-acting  piston  pump  of  the  type, 
Fig.  134,  is  an  ancient  device,  and  in  its  present  form  re- 
mains substantially  as  devised  by  La  Hire,  and  described 
in  the  Memoirs  of  the  French  Academy  in  1716.  This  was 
at  one  time  a favorite  type,  and  was  adopted  for  the  most 
prominent  of  the  early  American  pumping  works,  as  at 
Philadelphia,  Richmond,  New  Haven,  Cincinnati,  Mon- 
treal, etc. 

Several  modifications  of  the  vertical  plunger  pump,  after 
the  modern  Cornish  pattern  (Fig.  135),  were  later  intro- 
duced at  Jersey  City,  Cleveland,  Philadelphia,  Louisville, 
etc.,  and  in  1875  at  Providence. 

The  vertical  bucket  pump  (Fig.  133),  in  various  modifi- 
cations (referring  to  the  water  end  only),  was  introduced  at 
Hartford,  Brooklyn,  New  Bedford,  etc. 

The  bucket-plunger  pump  (Fig.  136,  water  end),  has 
been  more  recently  introduced  at  Chicago,  St.  Louis,  Mil- 
waukee, Lowell,  Lynn,  Lawrence,  Manchester,  etc. 


558 


PUMPS. 


A vertical  acting  differential  plunger  pump,  having  one 
set  of  suction  and  one  set  of  delivery  valves,  each  arranged 
in  an  annular  line  around  the  plunger  chamber,  has  re- 
cently been  invented  by  at  least  two  engineers,  independ- 
ently of  each  other,  and  with  similar  disposition  of  parts. 
This,  like  the  bucket  and  plunger  pump,  is  single-acting  in 
suction  and  double-acting  in  delivery.  This  pump  gives 
promise  of  superior  excellence 

The  double-acting  horizontal  plunger  pump  (page  223), 
itself  an  ancient  and  admirable  invention,  was  first  intro- 
duced in  combination  with  the  Worthington  duplex  engine 
about  the  year  1860,  and  has  since  been  adopted  at  Harris- 
burg, Charlestown,  Newark,  Salem,  Baltimore,  Toledo, 
Toronto,  Montreal,  etc. 


Fig.  134. 


Rotary,  and  gangs  of  small  piston  pumps  have  been  in- 
troduced to  some  extent,  in  direct  pressure  systems,  in  some 
of  the  small  Western  towns. 


EXPENSE  OF  VARIABLE  DELIVERY  OF  WATER.  559 


538.  Several  of  the  earliest  pumps  * of  magnitude  worthy 
of  note  were  driven  by  overshot,  or  breast  water-wheels,  as 
at  Bethlehem,  Pa.,  Fairmount  Works,  Philadelphia,  New 
Haven,  Richmond,  and  Montreal.  Turbines  have,  how- 
ever, taken  the  places  of  the  horizontal  wheels  at  Phila- 
delphia and  Richmond,  and  in  part  at  Montreal,  and  tur- 
bines give  the  motion  at  Manchester,  Lancaster,  Bangor, 
and  at  other  cities. 

Fig.  143  shows  the  latest  improved  form  of  the  Geyelin- 
Jonval  turbine,  which  has  been  used  very  successfully  in 
several  of  the  large  cities  for  driving  pumps. 

The  greater  number  of  the  pumping  machines  now  in 
use  are  actuated  by  compound  steam-engines. 

A considerable  number  of  the  large  pumping  machines 
have  their  pump  cylinders  in  line  with  their  steam  cylin- 
ders, and  their  pump  rods  in  prolongation  of  their  steam 
piston  rods. 

539.  Expense  of  Variable  Delivery  of  Water. — 

It  is  important  that  the  delivery  of  water  into  the  force-main 
from  the  pumping  machinery  be  as  uniform  as  possible, 
and  constant. 

If  the  delivery  of  water  is  intermittent  or  variable,  and 
the  flow  in  the  main  equally  variable,  then  power  is  con- 
sumed at  each  stroke  in  accelerating  the  flow  from  the 
minimum  to  the  maximum  rate. 

The  ms  viva\  of  the  column  of  water  in  the  force-main, 
surrendered  during  the  retardation  at  each  stroke,  is  neutral- 


* Bethlehem,  Pa.,  constructed  in  1762  the  first  public  water  supply  in  the 
United  States  in  which  the  pumps  were  driven  by  water-power.  Philadelphia 
constructed,  in  1797,  on  the  Schuylkill  River,  a little  below  Fairmount,  the 
first  public  water- works  in  the  United  States  driven  by  steam-power.  In  1812 
steam-pumps  were  started  at  Fairmount,  and  the  old  works  abandoned.  In 
April,  1822,  the  hydraulic-power  pumps  were  started  at  Fairmount. 

\ Vide,  “ principle  of  vis  viva,”  in  Moseley’s  “ Mechanics  of  Engineering,” 
p.  115,  New  York,  1860,  and  Poncelet’s  Mecanique  Industrielle,  Art.  135, 
Paris,  1841. 


560 


PUMPS. 


ized  by  gravity,  and  no  useful  effect  or  aid  to  the  piston  of 
the  pump  is  given  back,  as  useful  work  is  given  during  the 
retardation  of  the  fly-wheel  of  an  engine. 

If,  as  when  the  pump  is  single-acting,  motion  is  gener- 
ated during  each  forward  stroke,  and  the  column  comes  to 
rest  during  the  return  stroke  of  the  piston,  or  between 
strokes  of  the  piston,  the  power  consumed  (neglecting  fric- 
tion) to  generate  the  maximum  rate  of  motion,  equals  the 
product  of  the  weight  of  the  column  of  water  into  the  height 
to  which  such  maximum  rate  of  motion  would  be  due  if  the 
column  was  falling  freely,  in  vacuo,  in  obedience  to  the  in- 
fluence of  gravity. 

Let  Q be  the  volume  of  water  to  be  set  in  motion,  in 
cubic  feet,  w the  weight  of  a cubic  foot  of  water,  in  pounds 
(=  62.5  lbs),  ih  the  equivalent  height,  in  feet,  to  wliich  the 


rate  of  motion  is  due  i^=  and  pi  the  power  required  to 


2g 

produce  the  acceleration  ; then 


Pi  = Q x w x hx. 


(1) 


If  the  velocity  is  checked  and  then  accelerated  during 
each  stroke,  without  coming  to  a rest,  let  v be  the  maximum 
velocity,  in  feet  per  second,  and  Vi  the  minimum  velocity ; 
then  the  power  consumed  in  or  necessary  to  produce  the 
acceleration  is 


Pi  = Q x w x 


®2 

W/ 


2 l{ 


(2) 


In  illustration  of  this  last  equation,  which  represents  a 
smaller  loss  than  the  first,  assume  the  force-main,  with  air- 
vessel  inoperative,  to  be  1000  feet  long  and  2 feet  diameter, 
and  the  maximum  aud  minimum  velocities  of  flow  to  be 
5 feet  and  4 feet  per  second  respectively. 

The  weight  of  the  contents  of  the  main  into  its  accelera- 
tion will  be  (.7854^ 2 x l)  x w x -j  ~ x- !'  = 3142  cu.  ft.  x 

v ’ ( 2/7  2(7 ) 


EXPENSE  OF  VARIABLE  DELIVERY  OF  WATER.  561 


62.5  lbs.  x .14  ft.  = 27492.5  foot-lbs.  If  there  are  ten  strokes 
per  minute,  274925  foot  lbs.  = 8J-  HP  will  be  thus  con- 
sumed.  If  the  main  is  twice,  or  four  times  as  long,  the 
power  consumed  will  be  doubled,  or  quadrupled. 

The  power  required  to  accelerate  the  motion  of  the 
column  is  in  addition  to  the  dynamic  power  P1  in  foot-lbs., 
required  to  lift  it  through  the  height  H.  of  actual  lift. 

For  the  equation  of  lifting  power  per  second,  when  Q is 
the  volume  per  second  (neglecting  friction),  we  have 

Pi  = Q x w x H,  (3) 

or  for  any  time, 

Pl  = Qxtx.wxH.  (4) 


The  frictional  resistance  to  how  in  a straight  main  is 
proportional,  very  nearly  to  the  square  of  the  velocity  of 
flow  (to  imf),  and  is  computed  by  some  formula  for  frictional 
head  A”,  among  which  for  lengths  exceeding  1000  feet  is 

4 Imp 

(5) 


7i"  = 


2 gd  ’ 


in  which  Ti"  is  the  vertical  height,  in  feet,  equivalent  to  the 
frictional  resistance, 
length  of  main,  in  feet, 
diameter  of  the  main,  in  feet, 
coefficient,  which  may  be  selected  from 
Table  61,  page  242,  of  values  of  m. 

The  equation  of  power  p",  to  overcome  the  frictional 


l “ 
d “ 
m is  a 


head,  is 


p"  = Q x w x 


4 Imv2 


(6) 


The  equation  of  power  required,  expressed  in  horse- 
powers [ HP. ] of  33,000  foot-pounds  per  minute,  each,  for 
dynamic  lift,  and  frictional  resistance  to  flow  combined,  is 


[HP.]  = 


Q x t x w x (H  -\-  7i") 
33)000 


(7) 


36 


562 


PUMPS. 


The  several  resistances  above  described  are  all  loads 
upon  the  pump-piston,  and  their  sum,  together  with  the 
frictions  at  angles  and  contractions,  is  the  load,  front  the 
flow  in  the  main  which  the  prime  mover  has  to  overcome. 

When  the  delivery  of  the  water  into  the  main  is  constant 
and  uniform,  these  resistances  are  at  their  minimum. 

540.  Variable  Motions  of  a Piston. — If  we  analyze 
the  rates  of  motion  during  the  forward  stroke  of  a piston 
moved  by  a revolving  crank  with  uniform  motion,  whose 
length  or  radius  of  circle  is  1 foot,  we  find  the  spaces  or  dis- 
tances moved  through  in  equal  times  by  the  piston,  while 
the  crank-pin  passes  through  equal  arcs,  to  be  as  in  the  fol- 
lowing table. 

TABLE  No.  lio. 


Piston  Spaces,  for  Equai.  Successive  Arcs  of  Crank  Motion,  i i 


Arcs 

Space,  feet 

o 

o 

11  Vt 

.0246 

0 

2Z]/i 

•0735 

33  Vx 

.II48 

O 

45 

.1521 

0 

56% 

•*795 

0 

.1958 

0 

78K 

.2034 

0 

90 

.2020 

Arc  s 

ioiX 

112  'A 

123% 

135 

146^ 

157^ 

168  k 

180 

Space,  feet 

.1844 

•1715 

.1490 

.1241 

■096s 

.0682 

.0421 

.0138 

The  spaces  are  equal  to  the  above,  but  in  inverse  order 
during  the  return  stroke.  To  compute  spaces  for  other 
lengths  of  crank,  and  the  same  arcs,  multiply  the  given 
lengths  of  crank  in  feet  by  the  above  spaces. 

The  sum  of  the  motions  of  the  piston  while  the  pin  moves 
through  the  first  90°  is  1.115  feet,  and  while  through  the 
second  90°  is. 855  feet;  therefore  the  motion  of  the  piston 
is  faster  during  the  first  and  fourth  parts  of  the  revolution 
than  during  the  second  and  third. 

The  motion  of  the  piston  is  accelerated  through  .5218  of 
its  forward  and  .4782  of  its  return  stroke,  and  is  retarded 
during  the  remaining  parts  of  its  forward  and  backward 


Fig.  135. 


CORNISH  PUMP,  JERSEY  CITY. 


i 


564 


PUMPS. 


motions ; and  with  the  usual  length  of  connecting  rod,  it 
attains  a maximum  velocity  equal  to  about  1.625  times  its 
mean  velocity. 

If  the  pump  is  single  acting,  then  no  delivery  of  water 
takes  place  during  the  return  stroke,  and  this  is  the  most  dif- 
ficult case  of  intermittent  motion  to  provide  for  in  the  main. 

541.  Ratios  of  Variable  Delivery  of  Water. — If  we 
analyze  the  ratios  of  movement  of  a single,  and  the  sums  of 
ratios  of  movement  of  two  or  three  coupled  double-acting 
pump  pistons,  when  the  two  crank-pins  are  90°  apart,  and  the 
three  pins  60°,  we  find  the  ratios,  during  the  forward  motion 
of  piston  No.  1,  for  given  arcs,  approximately  as  in  the 
following  table : 

TABLE  No.  111. 

PROrOETIOXS  OF  PUMP  DELIVERIES, 


In  cu.  ft.  for  equal  successive  arcs  of  of  Crank  Motion.  With  crank  i ft.  length, 
and  piston  i square  foot  area. 


Arcs 

22  y,. 

33X 

45 

56K 

67K 

78K 

90 

i piston 

.0246 

•0735 

.II48 

.1521 

•J795 

.1958 

.2034  : 

.2020 

2 pistons 

.2280 

.2693 

•2943 

•3043 

.2943 

.2603 

.2280 

.2267 

3 pistons 

•370 

•415 

.440 

•443 

.416 

.400 

•433  1 

•443 

o 

o 

o 

O 

c 

0 

Arcs 

101% 

II  2l/2 

123  K 

*35 

I46X 

I57K 

168K 

180 

i piston 

.1894 

•1715 

.1490 

•1243 

.0965 

.0682 

.0421  1 

.0138 

2 pistons 

.2629 

.2863 

•3OXI 

•3039 

.2923 

.2716 

•2442 

.2035 

3 pistons 

•434 

. 403 

•349 

.386 

.388 

•394 

■387 

.362 

The  variations  of  delivery  of  water  during  the  full 
revolution,  on  each  side  of  the  mean  rate  of  delivery  is, 
with  one  double  acting  piston  .62  above  and  .S9  below; 
with  two  double  acting  pistons  about  .22  above  and  .26 
below;  and  with  three  double  acting  pistons  about  .IS 
above  and  .20  below;  that  is,  the  maximum  variations  are 
.87,  .26,  and  .20. 

542.  Office  of  Stand-Pipe  and  Air-Vessel. — It  is 

the  office  of  the  stand-pipe  and  air-vessel  to  take  up  the 


CAPACITIES  OF  AIR-VESSELS. 


565 


excess,  and  to  compensate  for  the  deficiency  of  delivery  by 
the  pump  pistons,  plungers,  or  buckets.  These  are  most 
effective  when  nearest  to  the  pump  cylinders. 

The  excess  of  delivery  enters  the  open-topped  stand-pipe 
and  raises  its  column  of  water,  and  the  column  is  drawn 
from  and  falls  to  supply  the  deficiency.  W ork  is  expended 
to  lift  the  column,  and  this  work  is  given  to  the  advancing 
water  in  the  main  when  the  column  falls  again,  but  when 
the  piston  is  again  accelerated  it  has  the  labor  of  checking 
the  motion  of  the  falling  column  in  the  stand-pipe. 

The  air-vessel  on  the  force  main  is  practically  a shorter, 
closed-top  stand-pipe  containing  an  imprisoned  body  of 
air.  The  excess  of  delivery  of  water  from  the  pumps  enters 
the  air-vessel  and  compresses  the  air,  and  the  expansion  of 
the  air  forces  out  water  to  supply  the  deficiency.  The  reduc- 
tion at  each  stroke  of  the  mean  volume  of  the  air  in  the 
vessel  is  directly  proportioned  to  the  excess  of  water  deliv- 
ered and  received  into  the  air-vessel,  which  is,  for  different 
pumps,  proportional  to  their  variations,  or  if  coupled  or 
working  through  the  same  air-vessel,  to  the  algebraical 
sums  of  their  variations. 

543.  Capacities  of  Air-Vessels. — The  cubical  capa- 
city of  an  air-vessel  for  one  pair  of  double-acting  pumps  is 
usually  about  five  or  six  times  the  combined  cubical  capa- 
city of  one  water  cylinder ; but  we  shall  see  that  the  capa- 
city of  the  cylinders  alone  is  not  the  full  basis  on  which  the 
capacity  of  the  vessel  is  to  be  proportioned. 

If  the  air-vessel  is  filled  with  air  under  the  pressure  of 
the  atmosphere  only,  and  then  is  subjected  to  a greater 
pressure  of  water,  it  will  not  remain  full  of  air,  for  the  air 
will  be  compressed,  and,  according  to  Mariotte’s  law,*  its 


Vide  Lardner’s  Hydrostatics  and  Pneumatics,  p.  158.  London,  1874. 


566 


PUMPS. 


volume  will  be  inversely  proportional  to  the  pressure  under 
which  it  exists,  provided  the  temperature  remains  the  same. 
Thus,  if  the  vessel  was  tilled  under  a pressure  of  15  lbs.  per 
square  inch,  and  the  water  pressure  is  six  times  greater  or 
90  lbs.  per  square  inch,  and  the  temperature  is  unchanged, 
then  the  air-vessel  wTill  be  but  one-sixth  full. 

It  is  the  reduced  volume  of  air  in  the  vessel  that  is  com- 
pressed to  take  up  the  excess  of  water  delivered  by  the 
pumps  ; therefore  the  degree  of  pressure  should  be  a factor 
in  the  equation  of  capacity  of  air-vessel,  as  wTell  as  the  ratio 
of  excess  of  delivery  during  a half  stroke. 

Let  q be  the  volume  of  delivery  of  one  pump  piston 
during  its  forward  stroke,  r the  maximum  variation ; or 
if  two  or  more  pistons  are  coupled,  the  algebraic  sum  of 
variations  of  delivery  of  water  during  the  forward  stroke 
of  No.  1 piston,  n the  maximum  pressure  of  water  in 
atmospheres  (=  14.7  lbs.  per  square  inch  each),  and,/  an 
experience  coefficient  whose  value  will  ordinarily  be  about 
0.  7,  then  the  equation  for  cubical  capacity,  C,  in  cubic  feet, 
of  air-vessel  for  a water  supply  pump,  is 

C = q x (1  + r)  x n x f,  (8) 

or  if  p is  the  maximum  water  pressure,  in  pounds  per  square 
inch,  then  the  equation,  when  f — 0.7,  may  take  the  form 

C = .0467<7  x (1  + r)  x p.  (9) 

The  moving  water  abstracts  an  appreciable  portion  of 
the  air  contained  in  the  air-vessel,  which  should  be  replaced 
by  re-charging  the  vessel  with  air. 

If  the  air-vessel  is  to  be  maintained  full  by  the  pumping 
in  of  air  against  the  pressure  of  water  in  the  main,  then  the 
size  of  the  air-chamber  may  be  much  reduced.  Its  height 
should  be  at  least  three  times  its  diameter. 


Fig.  136. 


568 


PUMPS. 


The  larger  the  water  surface  in  contact  with  the  air  in 
the  air-vessel,  the  faster  the  air  is  absorbed  by  the  water  ; 
therefore  it  is  advisable  to  give  considerable  height  in  pro 
portion  to  diameter  to  the  air-vessel,  and  a disk  of  wood  oi 
other  nearly  or  quite  impervious  material,  one  or  two  inches 
less  in  diameter  than  the  air-vessel,  may  be  allowed  to  he 
on  the  water  in  the  vessel,  and  thus  still  more  reduce  the 
surfaces  of  contact  of  air  and  water. 

544.  Valves. — Pumps  that  have  to  lift  water  to  heights 
greater  than  thirty  feet,  are  usually  of  necessity,  or  for 
convenience  of  access,  placed  between  the  water  to  be 
raised  and  the  point  of  delivery.  When  so  situated  they 
perform  two  distinct  operations,  one  of  which  is  to  draw  the 
water  to  them,  and  the  other  to  force  it  up  to  the  desired 
elevation.  When  the  pump  piston  or  plunger  advances, 


Fig  137. 


the  water  in  front  of  it  is  pressed  forward,  and  at  the  same 
time  the  pressure  of  the  atmosphere  forces  in  water  to  till 
the  space  or  vacuum  that  it  would  otherwise  leave  behind 
it.  The  return  of  the  water  must  be  prevented,  or  the  work 
done  by  lifting  it  will  be  wasted.  Valves  which  open  freely 
to  forward  motion  of  the  water  and  close  against  its  return, 
are,  therefore,  a necessity,  both  upon  the  suction  and  the 
delivery  sides  of  the  pump. 

All  valves  break  up  and  distort,  in  some  degree,  the  ad 
vancing  column  of  water.  Such  distortions  and  divisions 


VALVES. 


569 


cause  frictional  resistance,  which  consumes  power.  The 
valve  that  admits  the  passage  of  the  column  of  water  by  or 
through  it  with  the  least  division  or  deflection  from  its  direct 
course,  neutralizes  least  of  the  motive  power.  Short  bends 
and  contractions  in  water  passages,  that  consume  a great 
deal  of  power  or  equivalent  head,  often  occur  in  their  worst 
degree  in  pump  valves. 

The  piston  valve  which  moves  entirely  out  of  the  water- 
passage,  and  permits  the  flow  of  water  in  a single  cylindrical 
column,  such  for  instance  as  was  used  in  the  Darlington 
and  Junker  water-engines*  is  perhaps  least  objectionable 
in  the  matter  of  frictional  resistance  to  the  moving  water, 
but  is  often  inconvenient  to  use.  The  single  flap-valve 
(Fig.  1 37),  with  area  at  30°  lift  exceeding  the  sectional  area 
of  the  pump  cylinder,  gives  also  a minimum  amount  of  fric- 
tional resistance. 

The  single  annular  form  of  column,  while  passing  through 
the  valve,  is  less  objectionable  than  any  of  the  other  divi- 
sions of  the  water,  and  annular  valve  openings  have  been 
the  favorite  forms  in  nearly  all  the  large  pumping  ma- 
chines. 

In  some  of  the  earlier  pumps  the  suction  was  through  a 
single  valve  with  two  annular  openings,  after  the  Harvey 
and  West  model,  or,  as  more  familiarly  known,  the  Cornish 
donble-beat  valve,  similar  to  Fig.  138,  illustrating  the  valves 
used  in  the  Brooklyn  engines. 

When  pumps  began  to  be  built  of  great  magnitude, 
requiring  large  capacities  for  flow,  and  the  valves  were 
increased  in  size  to  two  feet  diameter  and  upward,  the 
valves  were  found  to  strike  very  powerful  blows  as  they 

* Vim  illustration  of  a water-engine  in  Rankine’s  “Steam  Engine,”  p.  140, 
London,  1873,  and  Lardner’s  Hydrostatics  and  Pneumatics,  p.  312.  London, 
1874 


570 


PUMPS. 


Fig.  138. 


came  upon  their  seats,  and  to  make  the  whole  machine,  the 
building,  and  the  earth  around  the  foundations  tremble. 

This  annoyance  led  to  dividing  the  valves  into  nests  of 
five  or  more  valves  of  similar  double-beat  form.  In  London 
and  other  large  English  cities  the  valves  have  of  late  been 
of  the  four -teat  class,  or  Husband’s  model. 

In  many  pumps  the  valves  have  of  late  been  divided  into 
nests  of  twelve  or  more  rubber-disks  (Fig.  139)  in  each  set, 
seating  upon  grated  openings  in  a flat  valve-plate.  Each 
subdivision  increases  the  frictional  resistance,  but  reduces 
the  force  of  the  blow,  or  water-hammer,  when  the  valve 
strikes  its  seat. 

The  suction  and  delivery  valves  of  the  piston  pumps 
(Fig.  134)  were  usually  of  the  flap  or  hinged  pattern.  These 
piston-pumps  had  sometimes,  though  rarely,  their  cylinders 
placed  vertically,  as  at  the  Centre  Square  Works  erected  in 


MOTION  OF  WATER  THROUGH  PUMPS. 


571 


Philadelphia  in  1801,  and  at  the  Schuylkill  Works  erected 
in  the  same  city  in  1844.  They  were  inclined  ten  or  twelve 
degrees  from  the  horizontal  at  Montreal. 

The  horizontal  plunger, 
or  “Worthington”  pumps 
(page  223),  have  uniformly 
been  fitted  with  nests  of  rub- 
ber disk  valves. 

The  best  of  the  modern 
steam  fire-engines  are  fitted 
with  nests  of  rubber  disk 
valves,  showing  that  this 
class  of  valve  is  a favorite 
when  the  pressure  is  great  and  the  motion  is  rapid. 

The  rubber  disk  valve  (Fig.  139)  was  sketched  from  an 
Amoskeag  fire-steamer  valve. 

545.  Motion  of  Water  Through  Pumps.— Water  is 
so  heavy  and  inelastic  that  large  columns  of  it  cannot  be 
quickly  started  or  stopped,  without  the  exertion  or  opposi- 
tion of  great  power  to  overcome  its  inertia,  or  vis  viva. 
There  is  therefore  an  advantage,  as  respects  the  even  and 
moderate  consumption  of  power,  when  the  piston  or  plunger 
motion  is  reciprocal,  in  making  the  strokes  long,  and  few 
per  minute. 

The  case  is  entirely  different  with  an  elastic  fluid  like 
steam.  The  tendency  of  the  most  successful  modern  steam 
engineering  has  been  toward  quick  strokes  and  high  steam 
pressures,  and  with  high  degrees  of  expansion  in  the  larger 
engines. 

The  “indoor”  ends  of  the  beams  of  the  best  Cornish 
pumping-engines  are  longer  than  the  “outdoor”  ends,  and 
it  is  claimed  as  one  of  their  special  advantages  that  the  in- 
door or  steam  stroke  that  lifts  the  plunger  pole  can  be  made 


Fig.  139. 


572 


PUMPS. 


with  rapidity,  while  the  outdoor  stroke,  or  fall  of  the 
plunger  by  its  own  weight,  can  be  gradual,  and  thus  the 
water  be  pressed  forward  at  a nearly  steady  and  uniform 
rate.  The  single-cylinder,  single-acting,  non-rotative  Cor- 
nish engine  is  admirably  adapted  to  the  work  to  which 
it  was  early  applied  by  Watt  and  Boulton — namely,  the 
raising  of  water  from  the  deep  pits  of  mines  by  sue 
cessive  lifts  to  the  surface  adits,  where  it  flowed  freely 
away ; but  when  applied  to  long  force-mains  of  water- 
supplies,  a stand-pipe  near  the  pump  becomes  a necessity 
to  neutralize  the  straining  and  laborious  effects  of  the  inter- 
mittent action. 

546.  Double-Acting-  Pumping -Engines.— The  de- 
sire to  overcome  the  objectionable  intermittent  delivery  of 
the  single-acting  pump,  as  well  as  the  influence  of  the  sharp 
competition  among  engine-builders,  that  forced  them  to 
study  methods  of  economizing  the  flrst  cost  of  the  machines 
while  maintaining  their  capacity  and  economy  of  action, 
led  to  the  introduction,  for  water-supply  pumping,  of  the 
compound  or  double  cylinder,  double-acting,  rotative  or 
fly-wheel  engine.  This  last  class  of  engines  was  brought  to 
a high  state  of  perfection  by  Mr.  Wicksted  and  Mr.  Simp- 
son at  the  London  pumping  stations.  Some  admirable 
pumping  machines  of  this  class  have  been  constructed  for 
American  water-works  from  designs  of  Messrs.  Wright, 
Cregeir,  Leavitt,  and  others. 

547.  Geared  Pumping- Engines. — Geared  compound 
pumping-engines,  one  style  of  which  (the  Nagle)  is  shown  in 
side  and  end  elevations*  in  Figs.  140  (p.  377)  and  141  (p.  573), 
are  well  adapted  both  for  direct  pumping,  and  also  where 
the  reservoir  and  direct  systems  are  combined.  Advantage 

* From  the  design  adopted  for  the  Providence  High  Service,  and  working 
With  direct  pressure. 


•St, 


Fig.  14L 


fc.  J N\glb. 


/ 8 3 4 S G 7 8 ? '<>  ''  /J  A* 

CROSS  SECTIONAL  ELEVATION. 


NAGLE’S  GEARED  PUMPING  ENGINE, 


574 


PUMPS. 


may  here  he  taken  of  high  pressure  of  steam,  rapid  steam 
piston  stroke,  and  large  degree  of  steam  expansion,  while 
the  water  piston  moves  relatively  slow  with  a minimum 
number  of  reversals. 

548.  Costs  of  Pumping  Water.— The  following  table 
(p.  575)  gives  the  running  expenses  for  pumping  water  in 
various  cities. 

549.  Duty  of  Pumping  Engines. — The  duty  or 
effective  work  of  a steam  pumping-engine,  as  now  usually 
expressed,  is  the  ratio  of  the  product,  in  foot-pounds,  of 
the  weight  of  water  into  the  height  it  is  lifted,  to  one  hun- 
dred pounds  of  the  coal  burned  to  lift  the  water. 

This  standard  is  an  outgrowth  from  that  established 
by  Watt,  about  the  year  1780,  for  the  purpose  of  compar- 
ing the  performances  of  pumping-engines  in  the  Cornish 
mines,  when  Messrs.  Boulton  and  Watt  first  introduced 
their  improved  pumping-engines  upon  condition  that  their 
compensation  was  to  be  derived  from  a share  of  the  saving 
in  fuel.  Watt  first  used  a bushel  of  coal  as  the  unit  of 
measure  of  fuel,  equal  to  about  94  pounds,  and  afterward 
a cwt.  of  coal,  equal  to  112  pounds.  More  recently,  in 
European  practice,  and  generally  in  American  practice, 
100  pounds  of  coal  is  the  unit  of  measure  of  fuel.  In  some 
recent  refined  experiments,  the  weight  of  ashes  and  clinkers 
is  deducted,  and  the  unit  of  measure  of  fuel  is  the  combus- 
tible portion  of  100  pounds  of  coal.  The  use  of  these  sev- 
eral units,  differing  but  slightly  from  each  other  in  value, 
leads  to  confusion  or  apparent  wide  discrepancies  in  results, 
when  the  performances  of  different  pumping-engines  are 
compared,  unless  the  results  are  all  reduced  to  an  uniform 
standard. 

To  construct  an  equation  in  conformity  with  the  more 
generally  accepted  standard  of  duty,  let  Q be  the  volume 


GEARED  PUMPING  ENGINE. 


_TTT 


PLAN.  — ; T.  Fanning,  C.  E. 


GEARED  PUMP  NG  ENGINE 


SIDE  ELEVATION  I T.  Panning, 


TABLE  No.  112. 

Cost  of  Pumping,  per  Million  Gallons,  in  Various  Cities,  in  1875. 


COSTS  OF  PUMPING  WATER. 


575 


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576 


PUMPS. 


of  water  delivered  in  any  given  time  into  the  force-main,  in 
gallons;  w the  weight*  of  a gallon  of  water  in  pounds 
(=  8.34  libs,  approximately) ; H the  dynamic  height  of  lift ; 
h the  height  equivalent  to  the  frictional  resistance  between 
pumps  and  reservoir,  including  resistances  of  flow,  valves, 
bends,  etc.,  in  the  force-main,  but  not  the  work  due  to  in 
termittent  motion  of  pumps,  or  to  bends  and  frictions  within 
the  pump  itself ; W the  weight,  in  pounds,  of  coal  passed 
into  the  furnace  in  the  given  time  ; and  D the  duty  per  100 
pounds  of  coal ; then 


jy  _ Q x w x (H  4-  7i) 
SOW  ' 


(10) 


Sometimes  the  value  of  Q is  expressed  in  cubic  feet,  in 
which  case  w is  the  weight  in  pounds  of  a cubic  foot  of 
water  (=  62.33  lbs.  approximately). 

If  it  is  preferred  to  use  the  area  of  plunger,  its  mean  rate 
of  motion  in  the  given  time,  and  the  pressure  against  which 
it  moves,  as  factors  in  the  calculation,  then  the  equivalent 
equation  of  duty  D,  takes  the  form, 


D = 


cA  x V x l x (P  + p) 
A)1W  1 


(11) 


in  which  A is  the  area,  in  square  feet,  of  the  piston  or 
bucket,  and  c its  coefficient  of  effective  delivery,  which 
varies  from  .60  to  .98,  according  to  design  or  condition  of 
the  valves  and  velocity  of  flow  through  them  ; V the  mean 
rate  of  motion,  in  feet  per  minute,  of  the  plunger  or  bucket ; 
t the  given  time,  in  minutes  ; P + p,  the  pressure  in  pounds 
per  square  foot  in  the  mains  due  to  dynamic  head  and  fric- 
tions between  pump- well  and  reservoir ; and  TT  the  weight  of 


* Vide  Table  38  for  weights  of  water  per  cubic  foot,  at  different  temperatures. 


ECTIONAL  ELEVATION  OF  GASKILL  PUMPING-ENGINE.  Built  by  the  Holly  Manufacturing  Co.  Lockport, 


vWXWV'XXsX'W 


SECTION  OF  GASKILL  PUMPS 


DUTY  OF  PUMPING  ENGINES. 


577 

coal,  in  pounds,  passed  into  the  furnace  in  the  given 
time. 

If  W is  taken  for  denominator  in  the  equation  instead  of 
.01  IF,  then  the  result  gives  the  duty  per  pound  of  coal. 

The  numerator  in  each  equation  refers  to  the  foot-pounds 
of  work  done  by  the  plunger  or  bucket  of  the  pump  in  effec- 
tive delivery  of  water  into  and  efflux  from  the  force-main, 
and  the  denominator  refers  to  the  foot-pounds  of  work  con- 
verted from  the  heat  in  the  coal,  and  effectively  applied  by 
the  combination  of  boiler  and  steam  engine. 

The  coefficient  c and  the  terms  7i  and  p in  equations  10 
and  11  are  ordinarily  appreciably  variable  with  variable 
rates  of  plunger  or  bucket  motion.  Preliminary  to  a general 
duty  test  of  a pump  the  values  of  c for  different  velocities 
or  rates  of  piston  motion,  from  minimum  to  maximum, 
should  be  determined  by  a reliable  and  accurate  weight  or 
weir  test,  and  the  value  of  It  or  p be  accurately  determined 
for  similar  conditions  by  an  accurate  gauge  or  pressure  test, 
and  a scale,  per  unit  of  velocity  prepared  for  each,  so  that 
values  may  be  read  off  for  the  actual  rates  of  piston  motion 
during  the  general  test. 

The  main  parts  or  divisions  which  make  up  a steam 
pumping  engine,  are : 

1.  Boilers  (including  grates,  heating  surfaces,  steam  and 
vvater  spaces,  and  flues). 

2.  Steam  engine  (including  steam  pipes,  cylinders,  valves, 
pistons,  and  condensing  apparatus). 

3.  Pump  (including  water  passages,  cylinders,  plunger 
or  bucket,  and  valves). 

In  comparisons  of  data,  for  the  selection  or  design  of  the 
parts  of  such  a combination,  the  classes  of  each  part  should 
be  considered  in  detail,  independently,  with  prime  costs, 
37 


578 


PUMPS. 


since  if  either  part  gives  a low  duty  alone,  the  duty  of  the 
combination  will  suffer  in  consequence. 

Attention  will  be  given  especially  to  the  evaporative 
power  of  the  boiler  and  its  duty,  or  ratio  of  effective  to 
theoretical  pressure  delivered  into  the  steam  pipe ; the  effec- 
tive piston  pressure  capabilities  or  duty  of  the  steam  cylin- 
der, over  and  above  its  condensations,  enhanced  by  slow 
motion,  leakages  of  steam,  and  frictions  ; and  the  frictional 
resistances  of  the  pump  piston  or  plunger,  and  valves,  and 
reactions  in  the  water  passages. 

Each  pound  of  good  coal,  according  to  the  dynamic 
theory  of  heat,  contains  in  its  combustible  part  about  14,000 
heat  units,  which  are  developed  into  a force  by  the  burning 
of  the  coal  to  produce  steam,  and  this  force  is  capable  of 
performing  a definite  amount  of  work.  From  sixteen  to 
twenty  per  cent,  of  these  heat  units  are,  ordinarily,  lost  by 
escape  up  the  chimney ; sixteen  to  twenty  per  cent  addi- 
tional are  lost  by  condensation  of  the  steam  in  the  pipes 
and  cylinders,  and  by  leakage  past  the  piston  or  valves  into 
the  condenser,  and  about  fifty  per  cent,  of  their  equivalents 
escape  with  the  exhaust  steam  into  the  condenser.  Only 
about  ten  or  twelve  per  cent,  of  these  heat  units  are  ordi- 
narily transformed  into  actual  useful  work  done  by  the 
steam. 

If  the  engine  has  many  nibbing  surfaces,  or  binds  at 
any  bearing,  or  if  the  pumps  have  crooked  water  passages, 
many  divisions  of  the  jet  in  the  valves,  frequent  and  rapid 
startings  and  checkings  of  the  water  column,  or  if  its  binds 
at  any  bearing,  then  each  of  these  resistances  consume  a 
portion  of  the  remaining  ten  or  twelve  per  cent,  of  useful 
work  of  the  steam. 

Stability  and  substantiality  are  matters  of  the  utmost 
importance  to  be  considered  in  the  selection  of  a class  or 


ECONOMY  OF  A HIGH  DUTY. 


579 


manufacture  of  pumping  engines.  By  these  terms,  in  this 
connection,  we  mean  the  capability  of  endurance  of  contin- 
uous action  at  the  standard  rate  and  work,  without  stoppage 
for  repairs,  and  with  the  minimum  expenditure  for  repairs. 

This  power  of  continuous  work  at  a maximum  rate  is  of 
far  greater  value,  ordinarily,  than  an  extremely  high  duty, 
if  stability  is  sacrificed  in  part  for  the  attainment  of  a high 
duty,  for  the  comfort  and  safety  of  the  city  may  be  jeopard- 
ized by  a weakness  in  its  pumping  engine.  Stability  being 
first  attained,  then  duty  becomes  an  element  of  excellence 
and  superiority. 

Fig.  142. 


geyelin’s  duplex-jonval  turbine  (r.  D.  WOOD  ft  CO.,  PHILA.) 


550.  Special  Trial  Duties.— The  following  table  (page 
580)  gives  the  duty  results  obtained  by  special  trials  of 
various  engines,  under  the  direction  of  experts.* 

551.  Economy  of  a High  Duty.— The  financial  value 
of  a high  dnty.  is  too  often  overlooked. 

' 1 * Vide  report  ofi  Messrs.  Bptv,  Roberts  and  Bogart ; in  Journal  of  American 
Society  of  Civil  Engineers.  Yol.  IY,  p.  142. 


TABLE  No.  11  3 — Special  Trial  Duties  of  Various  Pumping  Engines. 


680 


PUMPS. 


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FRONT  ELEVATION.  — I.  T.  Fanning’s  Patent. 


THREE-CYLINDER  TUBULAR  BOILED 

NEWPORT,  R.  I.,  WATER  WORKS. 

[Constructed  for  George  H.  Norman,  Proprietor. 


J,  T.  Fanning,  C.  E. 


TRIPLEX  TUBULAR  BOILER  (Patented). 


COSTS  OF  PUMPING  WATER. 


581 


Engines  of  substantial  construction  can  now  be  readily 
obtained,  that,  when  working  continuously  at  their  stand- 
ard capacities,  will  give  duties  of  from  75  to  100  million 
foot-pounds  per  100  pounds  of  coal.  When  they  are  real- 
izing less  than  their  maximum  duties,  money,  or  its  equiva- 
lent, goes  to  waste. 

We  have  just  seen  (§  549)  that  duty  is  a ratio  of  effec- 
tive work.  If  we  divide  the  dynamic  work  to  be  done  by 
this  ratio,  then  we  have  the  pounds  of  coal  required  to  do 
the  work  when  the  given  duty  is  realized. 

Let  D be  the  given  duty  in  foot-pounds  per  100  pounds 
of  coal ; Q the  volume  of  water  delivered  into  the  force-main 
in  gallons ; w the  weight  of  a gallon  of  water,  in  pounds 
(=  8.34  lbs.,  approximately) ; H the  actual  height  of  lift ; 
h the  height  equivalent  to  the  frictional  resistances  in  the 
main  ; and  W the  weight  of  coal  required,  in  pounds  ; then 
we  have  for  equation  of  weight  of  coal, 

jy  _ lOOg  x w x {H  + h)  ^ 

When  Q and  D are  in  even  millions,  the  computation 
will  be  shortened  by  taking  one  million  as  the  unit  for  those 
quantities. 

Let  us  assume  that  we  have  one  million  gallons  of  water 
to  lift  100  feet  high  in  twenty-four  hours,  then  the  pounds 
of  coal  required  at  various  duties  will  be  approximately 
as  follows : 


TABLE  No.  114. 

Comparative  Consumptions  of  Coal  at  Different  Duties. 


105 

794 

IOO 

834 

95 

878 

90 

927 

85 

get 

80 

1042 

75 

1112 

7° 

1191 

Pounds  of  coal 

Duty,  in  millions 

Pounds  ot  coal 

65 

1283 

60 

1390 

55 

I5x6 

50 

1668 

45 

i853 

40 

2085 

30 

2780 

20 

4I7° 

582 


PUMPS. 


The  relative  costs  per  annum,  in  dollars,  for  lifting 
various  quantities  of  water  daily  100  feet  high,  at  different 
duties,  will  Ibe  approximately  as  in  the  following  table, 
on  the  assumption  that  the  coal  costs  $8  per  ton  of  2000 
pounds,  when  delivered  into  the  furnace. 

TABLE  No.  115. 


Fuel  Expenses  for  Pumping,  Compared  on  Duty  Bases. 


Duty  in 
millions  of 
footpounds. 

Number  of  millions  of  gallons  pumped  daily,  one  hundred  feet  high. 
(Coal  in  furnace  at  $8  per  ton.) 

1 

2 

3 

4 

6 

8 

IO 

Cost  0/  coal  per  annum , 

in  dollars. 

IOO 

$1277.86 

$2556 

$3834 

$5111 

$7667 

$10223 

$12779 

90 

1419.85 

2840 

4260 

5679 

8519 

11359 

14198 

80 

1597-32 

3195 

4792 

6389 

9584 

12778 

15973 

70 

1825.51 

3651 

5477 

7302 

10953 

14604 

18255 

60 

2129.76 

4260 

6389 

8519 

12779 

17038 

21298 

50 

2555.72 

sin 

7667 

10223 

15334 

20446 

25557 

40 

3194.65 

6389 

9584 

12769 

1916s 

25537 

31946 

30 

4259-53 

8519 

12779 

17038 

25557 

34076 

42595 

20 

6389.30 

12768 

19168 

25537 

39336 

5H74 

63893 

If  the  lift  is  150  feet,  then  tlie  annual  cost  will  be  one 
and  one-lialf  times  the  above  amounts  respectively,  if  200 
feet,  twice  tlie  above  amounts,  etc. 

If  we  have  four  million  gallons  per  day  to  pump  100  feet 
high,  then  the  cost  of  coal  per  annum  for  a 100  million 
duty  engine  will  be  about  $5000,  and  with  a 20  million  duty 
engine  about  $25000.  If  we  have  to  pump  the  same  water 
200  feet,  the  coal  for  the  first  engine  will  cost  about  810,200 
and  with  the  second  engine  $51,000.  These  sums  capital- 
ized represent  the  relative  financial  values  of  the  engines, 
so  far  as  relates  to  cost  of  fuel. 

If  pumping-engines  are  sufficiently  strong,  of  good  me- 
chanical workmanship,  and  simple  in  arrangement  of  parts 
then  the  cost  of  attendance,  lubricants,  and  ordinary  re- 
pairs, while  doing  a given  work,  will  be  substantially  the 


COSTS  OF  PUMPING  WATER. 


583 


same  for  different  makes  or  designs.  Beyond  this  the  rela- 
tive merits  of  machines  of  equal  stability,  independent  of 
prime  cost,  are  nearly  in  the  inverse  order  of  the  amount  of 
fuel  they  require  to  do  a given  work. 

But  the  first  costs  of  the  complete  combination  should 
be  made  a factor  in  the  comparison,  including  costs  of  foun- 
dations and  extra  costs  of  buildings,  standpipes,  etc.,  if  re- 
quired, as  in  the  case  of  Cornish  engines.  Then  the  relative 
economic  merits  are  inversely  as  the  products  of  costs  into 
reciprocals  of  duties,  or  directly  as  duty  divided  by  cost. 

Let  Cd  be  the  cost  in  dollars  of  the  complete  pumping- 
engine,  including  foundations,  pump-wells,  etc.,  and  D the 
duty  in  millions,  then  the  most  economic  engine,  so  far  as 
relates  to  cost  of  fuel,  will  be  that  which  has  the  least 
1 C 

product  of  Cd  x jy  or  jy  and  the  relative  result  will  be  very 

nearly  the  same  if  the  cost  of  engine  is  capitalized. 

Let  % be  the  per  cent. , or  rate  of  interest  at  which  the 

cost  is  capitalized,  then  the  most  economic  engine,  as  to 

prime  cost  and  duty,  will  be  that  which  has  the  least  pro- 

, , - Gd  1 1 Cd 

duct  of  — = x or  —j  x — 

% jy  % d 

Let  us  assume  that  we  have  five  million  gallons  of  water 
to  lift  100  feet  high  per  day,  and  that  a standard  engine  of 
suitable  capacity  to  do  the  work,  realizing  one  hundred  mil- 
lion duty,  will  cost  $65,000. 

With  this  standard  let  us  compare,  financially,  engines 
of  less  first  cost  and  giving  less  duties,  as  in  the  following 
table,  in  which  the  ratio  of  the  standard  is  taken  equal 
unity. 


PUMPS. 


m 


TABLE  No.  116. 

Comparison  of  Values  of  Pumping-Engines  of  Various  Prime 
Costs  and  Duties  on  Fuel  Bases. 


Cost  = Cd . 

Duty  = D. 

„ I Cd 

d * D ~ ~d‘ 

Ratio. 

$65,000 

TOO  M. 

650.O 

I. 

60,000 

90  “ 

666.6 

I.025 

50,000 

75  “ 

666.6 

I.025 

45, OOO 

60  “ 

750.0 

I-I53 

35, OOO 

5°  “ 

700.0 

I.077 

25,000 

3°  “ 

833-3 

I.282 

In  tlie  table,  tlie  $50,000  pnmping-engine  giving  a seventy- 
five  million  duty,  is  seen  to  liave  a financial  value  almost 
identical  with  that  of  the  assumed  standard  engine.  If  it 
is  also  freer  from  liability  to  breakage  or  interruption,  if  it 
requires  less  labor  or  less  skill  in  attendance,  if  it  is  easier 
in  adjustment  to  varying  work  when  variable  work  is  to 
be  performed,  or  if  it  is  better  adapted  mechanically  to  the 
special  work  to  be  performed,  then  the  practical  over- 
balances the  financial  advantages,  and  it  is  obviously  en- 
titled to  preference  in  the  selection,  and  good  judgment  will 
lead  to  the  purchase  of  this  rather  than  of  the  assumed 
standard  engine. 

The  proportions  and  duties  of  steam  pumping-engines 
in  large  city  water-works  plants  range  about  as  follows,  in 
the  year  1905  : 

Capacity  of  units,  10  to  30  million  gallons  per  24 
hours. 

Boiler  steam  pressures,  130  to  160  lbs. 


KEYNOLDS  PUMPING  ENGINE. 

Capacity  20  Million  Gallons  against  a Head  of  334  Feet. 


584a 


5846 


PUMPS, 


Pounds  of  steam  per  indicated  horse-power,  10.5  to 
12.5. 

Foot-pounds  duty  per  1000  lbs.  of  steam,  150,000,000  to 
175,000,000. 

Steam-piston  speeds,  180  to  225  feet  per  minute. 


TABLE  No.  11  6a. 


Duties  of  Pumping-engines,  1893  to  1905. 

(From  data  compiled  by  Irving  H.  Reynolds,  Mem.  Am.  Soc.  M.  E.) 


Location  of  Pump. 

Capacity  per  24  Hours. 

Head. 

Ste.  m Pressure. 

Steam  per  I.H.P.  per 
Hour. 

Duty  per  1.000,000 
B.T.U. 

Duty  per  1000  lbs.  of 
Steam. 

City. 

Gallons. 

Ft. 

Lbs. 

Lbs. 

Ft.-lbs. 

Ft.-lbs. 

I 

Milwaukee,  Wis 

18  million 

162 . 6 

I 2 I 

11.68 

1 27,6^6,000 

154,048,700 

2 

Louisville,  Ky 

l6 

1 1 

193  3 

!37 

12.15 

I37.565»000 

148,622,000 

3 

Boston,  Mass 

20 

t < 

r37-2 

176 

11.22 

144,500,000 

I57,843-00° 

4 

Buffalo,  N.  Y 

3° 

i < 

199.0 

167 

12.39 

1.35,000,000 

I 52,000,000 

5 

Indianapolis,  Ind 

20 

< t 

205 

156 

n.26 

150,100,000 

167,800,000 

6 

Cleveland,  Ohio 

20 

< < 

202 

149 

n.45 

145,220,000 

161,990,000 

7 

Wildwood,  Pa 

6 

< 1 

604 

200 

12 . 26 

162,132,500 

149,500,000 

8 

St.  Louis,  Mo.,  No.  7. 

IO 

< < 

294 

r36 

n.63 

143,404,000 

160,455,000 

9 

“ “ “ “ 8. 

IO 

294 

137 

n.63 

144,365,000 

161,250,000 

IO 

Hackensack,  N.  T.  . 

12 

< 1 

267 

x73 

ir.  05 

146,403,400 

168,532,800 

II 

St.-  Louis,  Mo.,  No.  9, 

15 

i ( 

293 

127 

IO.  78 

I55>237)450 

176,419,600 

1 2 

1 ‘ “ “ “ IO 

15 

292 

126 

10.68 

158,077320 

170,454,250 

i3 

Boston,  Mass 

3° 

« « 

140 

185 

IO-  33 

i63>925,3°° 

178,497,000 

14 

Cambridge,  Mass.  . . . 

21 

< < 

190 

178 

12.17 

135,816,000 

146,173,000 

15 

Boston,  Mass 

35 

i < 

45 

I5I. 

1 1 . IO 

141,532,000 

i57,349,°0° 

16 

“ (Spot  Pond).  . 

20 

< < 

T2.5 

150 

1 1 .01 

156,592, ooo 

173,620,000 

17 

New  Bedford,  Mass.  . 

IO 

< < 

i«5 

1S1 

1346 

150,010,000 

140,000,000 

18 

St.  Louis,  Mo.,  No.  11 

15 

c < 

293 

138 

10.84 

155,800,000 

177,300,000 

19 

20 

it  <<  <<  “ I2 

“ “ “ “ 13 

15 

20 

i ( 
f i 

293 

240 

135 

10 . 88 

156,900,000 

177,200,000 

176,866,000 

DUTIES  OF  PUMPING-ENGINES. 


584c 


Percentage  of  mechanical  efficiency,  90  to  95. 
Percentage  of  thermal  efficiency,  18.5  to  20.5. 

Mean  speed  of  water  through  nests  of  valves,  about  3.5 
feet  per  second. 

Efficiencies  of  steam-boilers,  70  to  78  per  cent. 


TABLE  No.  1 1 Q a — Continued. 


Duties  of  Pumping-engines,  1893  to  1905. 

(From  data  compiled  by  Irving  H.  Reynolds,  Mem.  Am.  Soc.  M.  E.) 


Type  of  Engine. 

Builder  or  Designer. 

Date  of  Test. 

Piston  Speed  per  Min- 
ute. 

Water  Pressure  in 
Main. 

Indicated  Horse- 
powers. 

Percentage  of  Mechan- 
ical Efficiency. 

Heat-units  per  I. H.P. 
per  Minute. 

Percentage  of  Thermal 
Efficiency. 

Year. 

Ft. 

Lbs. 

H.P. 

% 

B.T  U 

% 

I 

Vertical  Triple 

Edwd.  P.  Allis  Co. 

1893 

203 

70.4 

574 

91 

217.6 

19.40 

2 

Vert. Comp. 

E.  D.  Leavitt 

1894 

371 

83-7 

643 

93 

222.5 

19.07 

3 

Triple 

‘ 4 

1895 

607 

59-4 

576 

89-5 

204.3 

20. 76 

4 

Lake  Erie  Eng.  Wks. 

1897 

208 

86.0 

1 186 

95 

231.2 

i8-35 

5 

“ 

Snow  Steam  Pump  Co. 

1898 

215 

89.0 

776 

95-4 

207 . 6 

20.45 

6 

Edwd.  P.  Allis  Co. 

1899 

200 

87-5 

77° 

93-7 

213.0 

T9  -9° 

7 

Quad.  Expan. 

Nordberg  Mtg.  Co. 

1899 

256 

262 . 0 

712 

93 

1S6.0 

22 .80 

8 

Vertical  Triple 

Edwd.  P.  Allis  Co. 

1899 

17s 

127-5 

549 

94-3 

216.8 

18.44 

9 

( ( 

( ( 

1899 

175 

127-5 

545 

94.9 

216.5 

18.59 

IO 

1900 

2 1 1 

115° 

603 

94 

2 I I . 9 

20.00 

II 

< < 

i l 

1900 

198 

127.0 

813 

96 

204 . 4 

20.78 

12 

< < 

l l 

1900 

197 

126.0 

802 

96.8 

202  . O 

21.00 

13 

( i 

l i 

1900 

19s 

61 . 0 

748 

93-3 

196 . 0 

21.63 

14 

( i 

E.  D.  Leavitt 

1901 

496 

82 . 0 

780 

93-4 

221.0 

19-43 

is 

< ( 

Holly  Mfg.  Co. 

1901 

3 00 

19-5 

323 

88 

210.0 

20.50 

l6 

i* 

1901 

248 

54-o 

464 

96-5 

203.4 

20.85 

17 

( ( 

E.  D.  Leavitt 

J9°3 

480 

80.0 

342 

95 

223.9 

18.95 

18 

< t 

Edwd.  P.  Allis  Co. 

!9°3 

197 

126.9 

800 

97.2 

204.8 

20. 72 

19 

20 

< i 
i i 

Allis-Chalmers  Co. 

1903 

1904 

197 

198 

126.8 

IO4.O 

796 

97  - 7 

205.2 

« : ! 

° I 

TANK  STAND-PIPE,  SOUTH 


CHAPTER  XXV. 


TANK  STAND-PIPES. 

552.  Their  Function. — Many  municipalities  are  sit- 
uated in  slightly  undulating  districts,  where  elevated, 
embanked,  or  masonry  reservoirs,  of  capacity  to  hold  a 
supply  of  water  equal  to  five  or  six  days’  draught  of  the 
town,  or  more,  are  unattainable.  In  such  places,  the 
metallic  tank  stand-pipe,  or  water-tower,  located  on  some 
moderate  elevation,  or  raised  on  a trestle,  or  masonry  tower, 
becomes  a valuable  adjunct  to  the  water  system,  and  espe- 
cially so  to  the  systems  of  the  smaller  towns  and  villages, 
where  its  capacity  ought  always  to  equal  a full  day’s  domes- 
tic and  several  hours’  fire  consumption  of  water. 

The  tank  stand-pipe  has  great  value  in  connection  with 
steam  pumping  plants  unconnected  with  a large  elevated 
reservoir,  when  compared  with  direct  pressure  alone,  for  a 
steam  boiler  cannot  so  promptly  respond  with  increased 
pressure  to  a demand  for  a large  increase  of  flow  at  the 
hydrants,  as  can  the  water  power  of  the  usual  hydraulic 
pumping  plant.  The  ready  filled  elevated  tank  may  save  a 
delay  in  increased  volume  and  pressure  of  water  that  saves 
also  one-half  the  town  from  destruction  by  fire. 

A one-inch  light  hose  stream  delivers  approximately  two 
hundred  gallons  of  water  per  minute,  and  a 24x100  feet 
tank,  holding  a quarter  of  a million  gallons  of  water,  would 
supply  five  such  streams  four  hours,  or  would  contain  the 
daily  supply  of  fifty  gallons  each  for  five  thousand  persons, 
and  if  its  base  was  sufficiently  elevated  would  allow  of  the’ 


586 


TANK  STAND-PIPES. 


daily  pumping  for  three  thousand  persons  to  be  performed 
in  about  ten  hours  of  each  day,  which  would  give  favorable 
stoppages  of  all  the  machinery  for  inspections,  cleanings 
and  repairs,  and  might  cover  many  contingencies.  For 
instance,  a pumping  machine  might  so  break  as  to  destroy 
its  mate,  a boiler  might  burst  so  as  to  destroy  the  whole 
battery,  the  pump  house  might  burn  or  be  blown  up,  a 
break  in  the  force  main  might  do  serious  injury  to  the 
pump  house,  the  machinery,  its  duplicate  main,  etc.  ; thus 
the  tank  may  save  its  cost  in  one  day,  and  it  is  a perpetual 
protector.  For  many  reasons,  their  use  is  becoming  gen- 
eral where  the  larger  reservoirs  are  impossible. 

553.  Foundations. — An  excellent  class  of  masonry  is 
necessary  for  tall  stand-pipe  foundations,  because  the 
resultant  pressures,  xy , Fig.  143,  from  the  great  weight  of 
water,  combined  with  the  wind  force  upon  the  tank,  or  it. 
inclosing  superstructure,  often  has  its  direction  near  to  the 
edge,  or  outside  the  base  of  the  metal  shell,  and  severe 
pressures  are  thus  thrown  upon  the  outside  edge  of  the 
foundation.  The  wrenching  action  of  the  winds  under  such 
conditions  tends  to  movements  and  disintegrations  of  the 
masonry. 

In  good  coursed  masonry  with  strong  cement  mortar, 
such  pressures  should  be  kept  within  limits  as  follows  : 

Concrete  masonry,  55  lbs.  per  sq.  in 
Brickwork  “ 70  “ “ “ 

Sandstone  “ 104  “ “ “ 

Granite  “ 140  “ “ “ 

The  foundation  should  be  sufficiently  broad,  so  that  the 
direction  of  the  greatest  resultant  of  weight  and  wind  will 
cut  the  base  within  one-fourth  diameter  distance  from  its 


. = 4 tons  per  sq.  foot. 

^ u u u 

= 7-5  “ “ “ 

= 10  “ “ “ 


centre. 


TENDENCY  TO  SLIDE. 


587 


554.  Wind  Strains.  — Tornadoes  attack  uninclosed 
stand-pipes  with  the  most  destructive  forces  they  have  to 
withstand. 

The  severe  forces  of  the  wind  are  to  be  considered  in 
determining  their  materials,  thicknesses  and  anchorages. 

When  the  uninclosed  tank  is  empty,  it  is  least  stable 
against  wind  forces,  as  respects  horizontal  sliding  and  ten- 
dency to  overturn. 

Wind  pressure  upon  the  curved  surface  of  one  semi- 
circumference  of  a vertical  cylindrical  tank  may  be  consid- 
ered as  acting  upon  an  infinite  series  of  equal  tangential 
surfaces  surrounding  the  curve,  and  the  ratio  of  effect  of 
the  force  in  the  direction  of  the  centre  of  the  curve  will,  on 
each  tangent,  equal  the  cosine  of  the  interior  included  angle 
between  the  tangent  and  direction  of  the  wind.  The  mean 
of  the  series  of  cosines  thus  developed  is  .70711  + , and  the 
resultant  effect  of  the  sum  of  forces  in  a direction  parallel 
with  the  general  motion  of  the  wind  is  as  the  square  of  this 
mean  cosine,  or  .5.  The  sum  of  the  series  of  cosines  equals 
the  diameter  of  the  cylinder.  We  may,  therefore,  consider 
the  force  of  the  wind  as  acting  upon  the  diametrical  plane 
of  the  tank,  which  is  perpendicular  to  the  direction  of  the 
wind,  with  .5  its  normal  force,  or  if  the  tank  is  octagonal 
with  .79  its  normal  force,  and  if  the  tank  is  square,  with 
its  full  normal  force.  In  severe  gales,  the  normal  force  of 
the  wind  is  sometimes  40  pounds  per  square  foot. 

555.  Tendency  to  Slide.  — Tanks  as  usually  con- 
structed have  not  sufficient  weight,  when  empty,  to  resist 
the  tendency  to  a sliding  motion  when  a very  strong  wind 
is  pressing  on  them. 

If  we  assume  the  extreme  force  of  the  wind  on  a plane 
at  right  angles  to  its  direction  as  40  pounds  = P per  square 
foot,  and  consider  P as  acting  on  the  diametrical  plane  A 


588 


TANK  STAND-PIPES. 


= diameter  I)  into  height  II  of  tank,  and  the  ratio  of  effect 
equal  .5,  then  we  have  the  total  distributed  force  of  the 
wind  W upon  the  tank,  Fig.  143, 

IF  = .5PPII  = .5PA.  (1) 

If  the  tank  is  not  bolted  or  anchored  in  some  manner  to 
the  foundation,  its  resistance  to  sliding  motion  equals  its 
total  weight  M into  its  coefficient  2 of  friction  (mean  coef. 
about  .25) ; hence  the  product  zM  — 3I0  must  be  greater 
than  .5PA,  or  the  tank  must  be  anchored  in  position. 

556.  Tendency  to  Overturn.  — Tank  stand-pipes 
that  are  relatively  tall  usually  lack  stability  against  ten- 
dency to  overturning  when  a very  strong  wind  is  pressing 
on  them. 

We  have  in  the  last  section  found  the  total  pressure  of 
wind  on  a plain  vertical  cylindrical  tank  to  be 

TF  - .5PA. 

This  pressure  is  distributed  over  an  entire  semi-circum- 
ference of  the  tank,  but  for  computation  of  its  effect  we 
may  consider  its  centre  of  pressure  and  resultant  as  acting 
upon  the  centre  of  gravity  of  the  vertical  diametrical  plane 
which,  in  the  plain  tank  of  equal  diameter  throughout  its 
height,  is  at  the  centre  of  height,  = }II;  therefore  the  lev- 
erage action  in  such  case  equals  1 II  and  the  moment  of 
wind  force  IF, , tending  to  overturn  the  tank,  equals 

TF  = {.5PA)x\H  ^ 51).  (2) 

If  there  are  external  cornices,  ornaments  or  stairways, 
their  wind  resultants  must  be  computed  and  included 
in  TF. 

The  moment  of  resistance  Mx  of  the  empty  tank  to  the 
moment  of  wind  force  equals  its  total  weight.  3 1,  into  the 
resisting  leverage  of  one-half  the  diameter  of  the  base. 


TENDENCY  TO  OVERTURN. 


589 


Mx  = \_DM ; (3) 

lienee,  the  moment  — .5DJ/  must  be  greater  than  the 
moment  Wl  = . 5HW  -s-  .52)  or  the  tank  must  be  anchored 
in  position. 

Table  No.  11 T illustrates  these  wind  and  weight  effects 
on  empty  tanks. 


TABLE  No.  117. 

Tank  Stabilities  of  Position. 

(P=  40  lbs.  per  sq.  ft.,  2?=diam.  in  ft.,  W=height  in  ft.) 


Diameter. 

Height. 

Weight  of  Tank 
M. 

O fcl 

3 Cj  8 

cfl  a1  O 
T.  K,  c* 
O in 

u • 1 

- 1 
5 

Frictional  Stability 
M0—  .25  M. 

Leverage  Moment 
of  Weight. 

M,  = .5  DM. 

c =5 

0 m 

§ . + 

? 1 5 

S 'S  II 

0 Jv 

Feet. 

Tons. 

Tons. 

Tons. 

Tons. 

Tons. 

10  X IOO 

l6. 

IO 

4 

80. 

IOO 

15  X IOO 

31-5 

15 

7-875 

236-25 

IOO 

20  X IOO 

45- 

20 

n.250 

45°- 

IOO 

25  X IOO 

80.5 

25 

20.125 

1006. 25 

IOO 

30  X IOO 

112.8 

3° 

28. 200 

1692. 

IOO 

When  the  leverage  moment  of  wind  TFj  on  the  empty 
tank  exceeds  the  leverage  moment  of  wmight  J/l5  the 
deficiency  is  covered  by  bolting  the  base  of  the  tank  to  its 
foundation,  of  diameter  D„  in  feet. 

The  weight  of  anchorage,  B,  clasped  by  the  bolts  should, 
for  factor  of  safety  equal  2,  be  not  less  than 


j3  _ (.522)  + b x TT 
.12  52>2), 


M, 


(±) 


in  which  b equals  the  depth  the  bolts  extend  into  the 
masonry  foundation.  The  anchor  bolts  must  increase  the 
friction  coefficient  or  resist  the  shear  when  frictional  sta- 
bility is  less  than  weight  of  tank. 

Both  the  breadth  and  batter  of  the  foundation  and  sta- 


590 


TANK  STAND-PIPES. 


bility  of  the  masonry  should  be  increased  as  the  inclina- 
tion of  the  resultant,  x,  y , Figs.  143,  144,  decreases. 

557.  Tank  Materials. — In  metal  tank  construction 
there  is  much  that  is  parallel  with  good  boiler  manufacture, 
but  the  tanks  are  not,  in  use,  subjected  to  the  blistering 
effects  of  hot  furnace  gases,  or  to  so  great  a range  of  expan- 
sion and  contraction. 

Tail  stand-pipes,  that  are  not  inclosed,  are  subject  to 
intense  pressure  strains  tending  to  tear  open  their  vertical 
joints,  and  intense  leverage  strains  tending  to  tear  open 
horizontal  joints  near  their  bases. 

A portion  of  the  upper  section  of  the  tank  of  medium  or 
small  diameter  requires  only  a thin  sheet  of  metal  to  with 
stand  the  pressure  of  the  water  alone,  but  a surplus  of 
metal  is  usually  necessary  near  the  top,  to  give  the  desired 
rigidity,  and  in  many  cases  to  resist  the  strain  from  ice 
that  may  form  on  the  surface  of  the  water  when  it  is  quiet. 
Sheets  of  lower  sections  have  more  pressure  strain  and 
require  a better  quality  of  material,  while  the  lower  sheets 
of  tall  pipes  demand  all  the  best  qualities  of  first  class  iron 
or  steel  boiler  plates,  and  should  be  thoroughly  inspected 
as  to  thickness,  tensile  strength,  and  ductility,  and  be  free 
from  “cold-short”  or  brittle  qualities. 

A weight  * test  of  each  sheet  is  a convenient  check  on 
• the  accuracy  of  the  gauge  test  of  thickness,  and  the  usual 
cold  bend  tests  along  and  across  the  grain  give,  in  the  most 
simple  manner,  indications  of  the  imperative  qualities  of 
toughness  and  ductility  of  the  plates  and  rivets. 

For  reliable  comparative  tests  of  ultimate  tensile  resist- 
ance, limit  of  elasticity  and  uniformity  of  texture,  resort  is 
had  to  a testing  machine  adapted  to  such  experiments. 


Vide  Table  No.  100.  page  488,  for  weights  of  metal  plates. 


RIVETING. 


591 


Metals  used  for  high  pressures  should  be  selected  from 
plates  that  have  been  branded  with  the  name  of  the  manu- 
facturers and  tensile  strength. 

Internal  laminations  in  thick  plates  of  iron  or  puddled 
steel,  caused  by  imperfect  welds  under  the  rolls  ; internal 
porous  strata  of  cinder  or  sand,  and  internal  blisters  may 
be  detected  only  by  careful  tapping  hammer  tests. 

Some  careful  experiments  have  been  made  to  ascertain 
the  comparative  resistances  of  iron  and  steel  to  rust,  when 
in  contact  with  water,  and  the  advantage  was  found  to  be 
slightly  with  the  iron,  therefore  the  reduction  of  thickness 
of  steel  plates  for  a given  strength  may  be  offset  by  the 
weakening  effects  of  oxidation. 

558.  Riveting. — As  plates  are  always  weakest  along 
the  lines  of  rivet  holes,  their  additional  thicknesses  to  give 
joints  the  required  strengths  will  be  considered,  or  included 
in  the  magnitude  of  the  factor  of  safety,  when  adjusting 
their  proportions. 

In  punching  plates,  the  holes  are  laid  out,  so  far  as  pos- 
sible, to  retain  at  least  seventy  per  cent,  of  the  area  of  the 
sheet  along  the  punched  section,  and  on  the  other  hand  the 
rivets  are  as  large  as  necessary  to  limit  the  pressure  on  the 
rivet  bearing  of  the  punched  hole  to  15000  pounds  per 
square  inch  of  “bearing  area,”  so  called,  which  is  found  by 
taking  product  of  diameter  of  hole  into  thickness  of  plate. 

Various  experiments  show  the  relative  strengths  of  riv- 
eted joints  in  one-half  inch  plates  to  have  mean  values  of 
the  full  strength  of  the  plates  about  as  follows  : 


Strength  of  unpunched  plate i.oo 

“ “ single  riveted  lap  joint ' -52 

“ “ double  “ “ 7° 

“ “ “ “ single  welt  joint. . .65 

u “ “ “ double  welt  joint . .78 


592 


TANK  STAND-PIPES. 


These  percentages  are  slightly  greater  in  thinner  and 
slightly  less  in  thicker  plates. 

Double  riveting  of  the  vertical  lap  joints  saves  an  addi- 
tion of  from  twelve  to  fifteen  per  cent,  to  the  thickness  of 
the  plates,  to  cover  weakness  of  joints  under  heavy  pressure 
of  water,  and  the  butt  joint  with  double  covering  plate  gives 
a slight  additional  saving. 

The  rivets  in  the  lower  horizontal  joints  of  tall  stand- 
pipes will  be  relieved  of  much  shearing  strain  if  the  joints 
are  butted  and  covered  with  double  welt  plates.  The  mean 
ultimate  shearing  strength  of  each  rivet  is  about  three- 
fourths  its  ultimate  tensile  resistance. 

The  entire  lap  of  a single  riveted  joint  is  about  three 
times  and  of  a double  riveted  joint  about  five  times  the 
diameter  of  the  rivet,  while  the  width  of  the  covering  plate 
for  a double-riveted  joint  is  nine  or  ten  diameters  of  the 
rivet. 

The  covering  plates  for  single  riveted  joints  should  be 
slightly  thicker  than  the  tank  plates  they  cover. 

Those  plates  subject  to  great  pressure  should  have  their 
edges  planed  so  that  the  calking  may  be  more  uniform  and 
reliable, 

TABLE  No.  118. 

Steel  Rivets  in  Steel  Plates,  ok  Iron  Rivets  in  Iron  Plates. 


(Sizes  in  Inches,) 


Thickness  of  plates 

I 

TT 

t 

tV 

i 

TV 

t 

H 

i TV  I 1 It  I 

Diameter  of  rivets 

tV 

i 

i 

rir 

i 

It 

I 

rTV 

ri  ri  ri  ri 

Pitch  in  single  rivetina; 

ij 

H 

rit 

2 

2tv 

2l 

2f\ 

2TV 

2|  2j  2|  2|  2f 

Pitch  in  double  riveting. . . . 

2^ 

3 

3tV 

3ur 

3t 

3# 

3s 

3f  3l  3t  3s  3s 

Pitch  in  triple  riveting 

2i 

3 

3i 

3 i 

4l 

4tV 

4fv 

4§  4s  4s  4 4 

Coef.  for  single  riveting. . . . 

■ 5i 

■ 50 

• 56 

•54 

• 52 

.51 

.51 

. ^1 

•49  -45  -42  .30' .41 

Coef.  for  double  riveting  . . . 

• 75 

■ 75 

• 72 

.70 

.60 

.67 

.67 

.66 

.67  .64  .64  .62,  .62 

Coef.  for  triple  riveting 

• 75 

• 77 

• 77 

• 77 

• / / 

•77 

■75 

• 74 

-74-73  -7i  -70  .69 

FACTORS  OF  SAFETY. 


598 


559.  Pressures  in  Inclosed  Stand-Pipes.— In  a 

tank  containing  water,  and  protected  from  the  forces  of  the 
winds,  the  bursting  pressure  p of  the  water  per  square 
inch  on  the  interior  surface  of  the  tank  shell  is  directly  as 
the  head  i/of  water  on  the  given  inch,  and  in  pounds  per 
square  inch  equals 

p = .434//.  (5) 

The  theoretical  thickness  t of  the  circular  metal  sheet  at 
any  given  depth  from  full  water  surface  may  be  computed 
by  the  formula  heretofore  given  (§  446,  p.  448)  for  cylindri- 
cal shells,  viz.  : 

* = f X/’  (6) 


in  which  t 

p 

r 

s 

f 

560.  Factors  of  Safety. — In  tall  stand-pipes  the  risk 
of  rupture  in  the  joints  increases  more  rapidly  with  depth 
below  water  surface  than  the  ratio  of  thickness  of  metal, 
due  to  pressure  alone  ; hence  the  coefficient  should  increase 
with  the  depth,  say  from  3 or  4 for  twenty-five  feet  depth 
to  5 or  6 for  one  hundred  and  fifty  feet  depth. 

The  increase  of  the  factor  of  safety,/)  may  follow  nearly 
as  2 plus  the  fourth  root  of  the  depth,  whence, 

/=  2 + H25 


fpr 

ct 


(7) 


thickness  of  metal  sheet,  in  inches, 
pressure,  for  given  depth  H,  in  pounds  per 
sq.  in. 

radius  of  cylindrical  shell,  in  inches, 
ultimate  cohesion  of  metal  used,  in  lbs.  per 
sq.  in.  and  c the  coef.  of  joint  strength, 
factor  of  safety  adopted. 


(S) 


594 


TANK  STAND-PIPES. 


Several  values  of  f thus  obtained  are  given  in  Table 
No.  119,  (assuming  s — 55000  and  c = .67), 

t — r x --  P . 
cs 


TABLE  No.  119. 

Factors  for  Steel  Stand  Pipes. 


Depth  = H , 
in  feet. 
H 

Pressure  = /, 
in  lbs. 

/ = .434^ 

Factor  = f. 
S=2  + H'*s 

ft 

CS 

20 

8.68 

4.II4 

.000969 

25 

10.85 

4.236 

.001247 

3° 

13.02 

4-340 

.001534 

35 

15.19 

4-432 

.001827 

40 

I7-36 

4-5  r5 

.002127 

5° 

21.70 

4-659 

.002744 

60 

26. 04 

4.783 

.003380 

80 

34-72 

4.99i 

.004702 

100 

43-40 

5.162 

.006080 

120 

52.08 

5-3IQ 

•007504 

140 

60. 76 

5-440 

.008969 

160 

69.44 

5-557 

.010471 

180 

78. 1 2 

5-663 

.012005 

200 

86.80 

5-76i 

.013569 

225 

5-873 

250 

5-976 

The  quotient  of  (fp)  -e  cs  into  the  radius  in  inches 
gives  the  thickness  of  sheet,  in  inches,  for  the  given  depth, 
to  resist  pressure  of  water  only. 

561.  Grades  of  Metals. — Pressure  alone  requires  but 
very  thin  sheets  of  iron  in  the  upper  sections  of  small  pipes, 
mot  enough  to  give  the  required  rigidity.  The  upper  sheets 
are  liable  to  the  most  rapid  deterioration  by  oxidations  of 
any  portion  of  the  pipe,  where  they  are  subject  to  frequent 
alternate  wettings  and  dryings  by  rises  and  falls  of  the 
water,  and  are  most  liable  to  strains  by  ice  expansion,  if 
the  water  surface  is  quiet  during  very  cold  weather. 

For  such  reasons  the  upper  sheets  should,  in  practice, 


LIMITING  DEPTHS  AND  THICKNESSES  OF  METALS.  595 


be  not  less  than  three-sixteenths  inch  thick,  with  a stiffen- 
ing angle-bar  at  the  top,  and  usually  the  top  sheets  are  one- 
quarter  inch  thick. 

When  the  computed  pressure  strain  calls  for  iron  or 
steel  sheets  exceeding  about  one-quarter  inch  thickness,  it 
is  advisable  for  economy  to  use  a good  grade  of  metal, 
having  ultimate  tensile  strengths  of  at  least  45000  or  55000 
pounds  per  square  inch,  for  iron  and  steel  respectively. 

The  upper  sheets,  where  there  is  a large  surplus  of 
thickness,  may  be  of  a lower  grade  of  iron,  or  28000  to 
30000  pounds  tensile  resistance  per  square  inch. 

562.  Limiting-  Depths  and  Thicknesses  of 
Metals. — Transposing  the  formula  of  thickness  for  vary- 
ing pressures  and  diameters. 

, fp  AZXJIfr 

t=rx  • — , 

cs  cs 

we  have  the  formula  for  depth,  //,  to  which  different  thick- 
nesses of  sheets  for  varying  diameters  of  tanks,  may  extend, 
to  sustain  the  internal  pressure,  with  the  given  factor. 

pp  — c^s  — c^s  (91 

.434/r  .217  df  V> 

in  which  t = thickness  of  the  metal  sheet,  in  inches. 

s = ultimate  cohesion  of  metal  used,  in  lbs.,  per 
square  inch 

d — diameter  of  tank,  in  inches. 

II  = depth  from  surface  of  water,  in  feet. 
f = factor  of  safety  used,  and  found  by  interpola- 
tion in  the  above  table,  No.  119,  of  factors. 

Table  No.  120,  based  on  the  above  formula  for  W,  will 
show  at  a glance  the  limiting  depths  below  full  water  sur- 
face, at  which  given  thicknesses  of  sheets  must  be  changed  in 


(When  j = 55000  lbs.  per  sq.  in.)  II 


596 


TANK  STAND-PIPES. 


The  small  figures  give  limiting  heights  of  exposed  stand  pipes.  //  — v")‘ . - and y = a -f-  //  *en;  W = .5  PDII , and  /’  — 40  lbs. 


THICKNESSES  OF  METALS. 


597 


STAND-PIPE  DIAGRAM& 


598 


TANK  STAND-PIPES. 


inclosed  tanks,  for  various  diameters  of  tanks,  when  their 
sheets  vary  in  thickness  by  sixteenths  of  an  inch. 

For  instance,  in  the  ten  feet  diameter  tank  the  -SL"  steel 
must  not  extend  to  more  than  59  feet  below  full  water  sur- 
face; i"  steel  to  79  feet  depth;  " steel  to  96  feet  depth; 
and  so  on,  by  sixteenths,  the  -§"  steel  not  extending  below 
159  feet  depth. 

563.  Thicknesses  of  Metals  Graphically  Shown. 

—The  depths  at  which  the  thicknesses  of  metal  sheets  of 
inclosed  stand-pipes  may  be  most  economically  reduced 
from  the  base  upward,  using  any  assumed  factor  of  safety, 
will  be  shown  graphically,  thus ; plot  the  entire  depth  of 
water  to  scale  in  a vertical  line,  as  an  absciss,  as  in  Figs. 
143  and  144,  on  a scale,  say  of  ten  feet  to  the  inch  ; plot 
the  computed  thickness  of  sheet  at  the  base  as  a horizontal 
ordinate  from  the  foot  of  the  absciss  ; draw  this  ordinate 
on  a large  scale,  say  4 inches  on  a line  equal  1 inch  thick- 
ness of  metal  sheet ; divide  the  portion  of  the  ordinate 
representing  one  inch  into  sixteen  equal  parts ; connect  the 
extreme  of  the  ordinate  with  the  top  of  the  absciss  with  a 
straight  inclined  line  if  the  same  factor  of  safety  is  used 
for  all  depths  of  water ; project  vertical  lines  from  each 
sixteenth  division  on  the  base  ordinate,  cutting  the  inclined 
line ; then  the  depths  from  the  top  by  scale  at  which  the 
sixteenth  divisions  cut  the  inclined  line  will  be  points  of 
change,  subject  to  standard  widths  of  sheets  that  are 
graded  in  thickness  by  sixteenths  of  an  inch.  If  a varying 
factor  of  safety  for  different  depths  is  used,  then  the 
inclined  line  will  be  slightly  curved  to  correspond  with  the 
equation  of  the  factor. 

564.  Exposed  Stand-Pipes. — Considering  the  strains 
upon  the  metals  near  the  bases  of  relatively  tall  uninclosed 
stand-pipes,  by  wind  pressure  leverages  that  tend  to  over- 


TANK  STAND-PIPES. 


598  a 


TANK  STAND-PIPE. 


oez  OZZ  0!Z  00?  OS!  Off/  Oi/  09/  Of/  oh/  OF/ 


5985 


TANK  STAND-PIPES. 


STAND-PIPE  DIAGRAM. 

The  broken  lines  indicate  the  thicknesses  for  exposed,  and  the  solid  lines  for 
inclosed  steel  Stand-pipes. 


EXPOSED  STAND-PIPES. 


599 


turn  the  structures,  we  find  that  these  strains  are  acting 
with  greatest  force  on  the  horizontal  joints  and  their  tend- 
ency is  to  rupture  the  metal  along  horizontal  lines. 

W e found  (§  556,  p.  588)  the  leverage  moment  of  the  wind 

TF77 

TV ; = (.5PA)  x .5IT= 

£ 

and  may  safely  assume  a maximum  pressure  P of  the  wind 
as  40  pounds  per  square  foot. 

Assuming  that  a relatively  tall  stand-pipe,  if  uninclosed, 
will  lack  both  frictional  and  leverage  stability  unless  an- 
chored to  its  foundation,  and  that  the  tank  will  be  bolted 
to  an  ample  weight  of  foundation  to  remain  stable  in 
position,  then  we  may  consider  the  empty  tank  as  a vertical 
cantilever,  and  the  leverage  action  of  the  wind  W1  as  tend- 
ing to  rupture  the  shell  at  the  base  where  its  anchorage 
bolts  take  hold,  or  its  lower  horizontal  joints. 

The  moment  or  resistance  of  the  tank  shell  must  at  least 
equal  the  total  wind  pressure  TV  into  its  leverage  = 
W x .5H. 

In  a vertical  hollow  cylindrical  tank,  secured  at  its  base, 
the  resistance  of  the  metal  at  the  base  equals,  very  nearly, 
one-lialf  the  area  of  the  horizontal  section  of  metal  into 
radius  of  the  cylinder,  into  the  tensile  resistance  per  unit 
of  section  of  riveted  metal,  sr 

If  the  dimensions  of  metal  are  taken  in  inches,  and  ITr 
is  the  total  pressure  in  pounds,  and  is  the  tensile  resist- 
ance of  the  riveted  metal  in  pounds  per  square  inch,  then, 
for  thickness  at  distance  Tt  below  top  of  tank,  neglecting 
factor  of  safety, 

TV  = + x - J-  = 3.1416r£  x -|&  (10) 

(r+\t  ) .oh  .oh 

hTV  hW  II  TV 

6.2832rX  — 1.5708^a51  .1309<$2$ 


and 


t 


(ir 


600 


TANK  STAND-PIPES. 


jrr_  1.5708d2sJi  _ .1309 d*slt1 
—ft  ~ 1T~ 

TF  = total  pressure  force  of  wind,  in  pounds  = 
.5  PDH. 

s — ultimate  cohesion  of  metal,  and  si  of  riveted 
metal,  in  pounds,  per  square  inch. 

D — mean  diameter  of  tank  shell,  in  feet,  and  d in 
inches. 

H = depth  below  top  of  tank,  in  feet,  and  h in 
inches. 

t , = thickness  of  metal  shell,  in  inches,  at  depth 
//,  that  will  just  balance  the  wind  leverage. 

Testing  this  formula  for  coefficients  by  four  experi- 
ments by  Sir  Wm.  Fairbairn,  on  thin  hollow  cylindrical 
beams  supported  at  both  ends  and  loaded  in  the  middle, 
and  taking  breaking  uniform  load  on  a cantilever  as  equal 
.5  IF,  and  s = 18000,  we  have  in  table  JSTo.  121  a mean 
coefficient  equal  .712. 


TABLE  No.  121. 
Experiments  with  Hollow  Cylindrical  Beams. 


Breaking1  Load, 
pounds. 

Diameter. 

inches. 

Thickness. 

inches. 

Span. 

feet. 

Coefficient 

2757- 

12. 

•037 

!7- 

. 700 

1 1 637. 

12.4 

•113 

15-625 

•833 

6S73- 

17.68 

.0631 

23-417 

.621 

14628. 

18.18 

.119 

23-417 

•693 

Mean  .712 

Taking  s as  the  tensile  strength  of  the  plates,  and  affix- 
ing to  the  last  two  formulas  the  coefficient  of  joint  strength, 


c,  and  a factor  of  safety,,  we  have 

, .of it, ir  _ fhw  _ fin v 

' ~ 3.111  Qcr*s  ~ 6.2832 crs  ~ .1309c^ 


(13) 


EXPOSED  STAXD-PIPES. 


601 


_ fH*P  _ .026526/7?'2JP 
tx  _ 37.6992cZ>.s  ~ cWs 


(11) 


H 


.130 9cd2sti  _ /37 ,Q992cI)st1 

~yw  -V'  jp~ 


(!5> 


fIPP  _ .cm526/B3P 
37.6992cs^  cst1 


(16> 


It  will  be  observed  that  this  equation  of  t,  to  resist  wind 

leverage  is  entirely  different  from  the  equation  of  t = V-^ 

cs 

for  static  pressure  of  water.  This,  in  tall  pipes,  increases 
as  diameter  decreases,  while  thickness  for  bursting  pressure 
increases  as  diameter  increases,  so  that  if  a series  of  each 
for  similar  conditions  are  plotted,  their  directions  will  be 
nearly  at  right  angles. 

The  greatest  thickness  given  by  either  formula  for  given 
height  and  diameter  will  be  used,  or  if  computing  for  the 
depth  to  which  a given  thickness  of  sheet  may  be  used  in 
a given  diameter  of  tank,  then  the  least  depth  by  either 
formula  will  be  used  in  the  exposed  tank. 

Rivet  area  must  be  provided  in  horizontal  joints  to  take 
care  of  wind-pressure  shear  stresses  in  exposed  tanks. 

Additional  thickness  may  be  given  the  plate  at  that 
section  over  which  in  tall  tanks  the  water  surface  oscillates, 
and  induces  rapid  destructions  of  paint  and  exposes  the 
metal  to  quicker  corrosions. 

Frequent  inspections  and  paintings  are  necessary  for 
the  long  endurance  of  exposed  tank  stand-pipes,  and 
especial  pains  are  to  be  taken  to  keep  the  cornice  moldings, 
stiffening  angles,  exterior  and  interior  ladder  joints,  and 
other  details  well  protected  with  paint. 

564 a.  Stand-Pipe  Cut-offs. — If  an  independent  force- 
main  extends  from  the  pumps  to  the  stand-pipe  tank,  a 


602 


TANK  STAND-PIPES. 


valve  may  be  placed  in  this  main  within  the  pump-honse, 
for  the  purpose  of  shutting  off  and  preventing  overflow  of 
the  tank  when  an  increased  fire  pressure  is  to  be  put  on  the 
general  system.  If  the  tank  is  on  the  side  of  the  distribution 
opposite  to  the  pumps,  as  is  often  desirable,  and  is  not  suffi- 
ciently elevated  for  direct  fire  pressures,  then  a valve  of 
damper  form  may  be  placed  in  the  inflow-pipe  at  the  tank. 

These  last  devices  may  be  operated  by  the  engineer  at 
the  pump-house,  or  by  the  fire-alarm  electric  circuit. 

565.  Stand-Pipe  Data.  A table  of  data  relating  to 
some  of  the  tank  stand-pipes  constructed  within  a few 
years  past  lias  been  hereto  appended,  and  covers  a large 
range  of  practice. 

Slender  and  tall  stand-pipes  are  generally  inclosed  in  a 
masonry  tower. 

Most  of  the  short  tanks  named  of  large  diameter  are 
mounted  on  masonry  towers  or  iron  trestles  and  are  not 
inclosed. 

Many  villages  in  the  Middle  States  use  tanks  of  wood 
with  three  or  four  inch  staves  hooped  with  iron.  Such 
tanks  are  fifteen  to  thirty  feet  diameter,  and  twelve  to 
twenty  feet  high,  and  are  usually  mounted  on  a wood 
trestle. 

We  have  given  illustrations  of  inclosed  stand-pipes  used 
at  South  Boston,  Mass.,  Milwaukee,  Wis.,  and  Toledo, 
Ohio,  and  of  exposed  stand-pipes  at  South  Abington, 
Mass.,  and  Fremont,  Ohio,  and  other  places. 

In  proportioning  masonry  towers  for  stand-pipes,  the 
wind  leverage  action  on  the  windward  and  resistance  on 
the  lee  side,  and  the  limiting  pressures  in  the  masonry  are 
to  be  considered,  also  the  limiting  pressures  in  the  founda- 
tions, as  affected  by  weight  carried  and  wind  pressure 
leverage. 


STAND-PIPE  DATA. 


60  2a 


Stand-Pipe  Data. 


LOCATION. 

Diameter. 

Feet. 

Height. 

Feet. 

Thickness 
of  base. 
Inches. 

Thickness 
of  top. 
Inches. 

Wichita,  Kan 

2 t 
z 2 

15° 

1 

2 

iV 

Danville,  111  

o.I 
6 2 

200 

5 

T5 

Louisville,  Ky 

4 

170 

1 

2 

TT 

Shelbyville,  111  

5 

I25 

I 

* 

3 

■nr 

Henderson,  Ky 

5 

8o 

2 

T 

Cambridge,  Mass  

S 

54 

3 

■S' 

5 

T5" 

Toledo.  0 

5 

225 

I 

I 

Z 

Catasaqua,  Pa 

5 

IOO 

3 

8 

I 

S 

Erie.  Pa 

5 

233 

Milwaukee.  Wis 

5 

8o 

3 

? 

1 

T 

New  York  City,  N.  Y 

6 

i5° 

1 

2 

I 

T 

Belleville,  N.  J 

6 

I3° 

1 

2 

I 

Z 

Allentown,  Pa 

6 

55 

I 5 

t? 

6 

TZ 

Bristol.  Pa 

6 

140 

7 

IS 

5 

T? 

Joliet,  111 

7 

I05 

5 

S 

I 

Burlington,  Kan  

8 

120 

1 

2 

I 

Carlyle,  111 

IO 

”5 

Mt.  Pleasant,  la 

IO 

80 

3 

8 

3 

T?' 

Arkansas  City,  Kan 

3 o 

I25 

1 

2 

3 

If 

Ottawa,  Kan 

IO 

I25 

1 

2 

3 

TIT 

Marion,  Kan 

IO 

140 

1 

2 

3 

T7T 

Oswego,  Kan 

IO 

140 

1 

2 

3 

TS 

Garden  City,  Kan 

IO 

I25 

1 

2 

3 

TS- 

Landale,  Pa 

IO 

16 

5 

Y 

I 

T 

Lawrenceville,  N.  J 

IO 

8; 

I 

S 

I 

Y 

Sandwich,  111. 

12 

IOO 

1 

2 

3 

TeT 

Caldwell,  Kan 

12 

140 

9 

T 6" 

3 

T7T 

Dodge  City,  Kan 

12 

IOO 

3 

$ 

3 

TY 

El  Dorado,  Kan 

12 

140 

9 

IS 

3 

TS 

Great  Bend,  Kan. 

12 

15° 

9 

TS 

3 

T5 

Hiawatha,  Kan 

12 

140 

1 

2 

3 

TT 

Paola.  Kan  

12 

IOO 

1 

2 

I 

T 

Easton,  Md 

I 2 

IOO 

9 

TS 

5 

TS 

Columbus,  Neb 

12, 

IOO 

5 

s 

I 

T 

St.  Paul,  Neb 

12 

60 

7 

TS 

3 

■g 

Asbury  Park,  N.  J 

12 

I25 

9 

TS 

I 

T 

Lewisburg,  Pa 

12 

130 

1 

2 

I 

4 

Gonzales,  Tex 

I 2 

80 

5 

TS 

T 

T^ 

6026 


TANK  STAND-PIPES. 


Stand-Pipe  Data — Continued. 


LOCATION. 

Diameter. 

Feet. 

Height. 

Feet. 

Thickness 
of  base. 
Inches. 

Thickness 
of  top. 
Inches. 

Orlando  Fla 

1 7 

J25 

IOO 

8o 

IOO 
T /|  O 

1 

I 

Beaumont,  Tex 

I 2 

I 

3 

T7T 

Maquoketa,  la 

I 2i 

I 

I 

% 

Pipe  Stone,  Minn 

X 2 i 

( 'hillicothe,  Mo 

l2i 

Fa  ID  City  Neb 

T 9-1 

t no 

Maquoketa,  Pa 

Splrrm  Ain 

12  j 

I q 

8o 
12  0 

7 

T5' 

i 

I 

Z 

I 

Freeport,  Til 

J5 

*5 

*5 

*5 

J5 

*5 

x5 

*5 

J5 

*5 

*5 

16 

88 

5 

5 

■g" 

Sycamore  111 

*35 

J75 

75 

IOO 

Cravvfordsville,  Ind 

Concord,  Kan 

I 

FTarper,  Kan ... 

Baton  Boncre,  T.a 

IOO 

, , 

Pierre  City,  Mo 

85 

125 

13° 

1 16 

I 

•5^ 

i 

Sedalia,  Mo 

Waterloo,  N.  Y 

rz 

I 

A 

1 

Dallas,  Tex 

Denison,  Tex 

125 

80 

5 

■S' 

3 

1 

Menomonie,  Wis 

1 

T .inroln  TU  . 

IOO 

I 

3 

nr 

1 

Mt  Vernon  Tnd 

16 

130 

120 

I 

Kinsley.  Kan  

16 

I 

1 

Gravesend,  N.  Y 

16 

250 

I40 

IOO 

7 

■g- 

I 

~Z 

I 

3 

TZ 

I 

Middletown,  Pa 

16 

Seguin,  Tex 

16 

3 

TZ 

3 

rz 

1 

Victoria,  Tex 

16 

1 00 

I 

Black  River  Falls,  Wis 

16 

IOO 

5 

Aurora,  111 

i8 

1 5 2 
J52 
75 
148 
1 10 

23 

TZ 

3 

5 

~rz 

5 

ZT 

3 

13- 

3 

TZ 

3 

IZ 

I 

Lansing,  Mich 

18 

Lincoln,  Neb 

18 

I 

Dayton,  0 

18 

3 

Charlotte,  N.  C 

18 

3 

Gloucester  City,  N.  J 

18 

75 

76 

I 

Charleston,  S.  C. . 

18 

I 

I 

Brenham,  Tex 

18 

Lexington,  Mo  

i8S 

I5° 

130 

3 

3 

TZ 

Maryville,  Mo 

i8P 

STAND-PIPE  DATA. 


( 302c 


Stand-Pipe  Data.— Continued. 


LOCATION. 

Diameter. 

Feet. 

Height. 

Feet. 

Thickness 
of  base. 
Inches. 

Thickness 
of  top. 
Inches. 

Yonkers,  N.  Y 

i8i 

21 

1 

2 

3 

n- 

Pensacola,  Fla.  

20 

194 

i 

TS 

Kankakee,  111 

20 

120 

T5' 

tV 

Sterling,  111 

20 

IOO 

IS 

1 

Beloit,  Kan 

20 

3° 

3 

5 

I 

Lawrence,  Kan 

20 

I05 

3 

■S' 

I 

Dedham,  Mass 

20 

103 

5 

■S' 

5 

nr 

Lexington,  Mass 

20 

103 

1 

2 

TS 

Middleboro,  Mass 

20 

103 

1 

2 

TS 

Whitman,  Mass 

20 

i°5 

5 

F 

TS 

Houlton,  Me 

20 

5° 

I 

1 

5 

T<r 

Alliance,  0 

20 

80 

I I 

TiT 

1 

? 

Ashtabula,  0 

20 

IOO 

5 

¥ 

Painesville,  0 

20 

76 

1 

2 

tV 

Salisbury,  N.  C 

20 

IOO 

I I 
T(T 

i 

Wilmington,  N.  C 

20 

90 

TS 

3 

nr 

Perth  Amboy,  N.  J 

20 

71 

5 

F 

1 

Princeton,  N.  J 

20 

18 

3 

F 

3 

■s 

Adams,  N.  Y. 

20 

40 

3 

"nr 

1 

■S' 

Coney  Island.  N.  Y 

20 

74 

tV 

3 

T6" 

Flatbush,  N.  Y 

20 

102 

5 

F 

3 

T6 

Fulton,  N.  Y 

20 

80 

7 

T7T 

3 

T6" 

Newark,  N.  Y 

20 

80 

1 

2 

T 

T6" 

Cleburn,  Tex 

20 

25 

2 

-S' 

2 

Beaver  Dam,  Wis 

20 

80 

13 

T2 

3 

nr 

Manitowoc,  Wis 

20 

1 16 

tV 

A 

Macon,  Ga 

22 

20 

I 

i 

Greencastle,  Ind 

22 

140 

I 0 

nr 

1 

Paducah,  Ky 

22 

G5 

3 

"S' 

1 

* 

Granville,  0 

22 

140 

1 0 

nr 

1 

Warren,  0 

22 

140 

10 

nr 

1 

Nantucket,  Mass 

24 

IS 

1 

1 

Florence,  Kan 

25 

55 

1 

2 

1 

T 

Abington  & Rockland,  Mass. 

25 

IOO 

5 

7 

nr 

Rockland,  Mass  

25 

IOO 

5 

"S' 

s 

T7T 

Rochester,  Mich 

25 

60 

1 

2 

3 

TIT 

Rochester,  Minn 

25 

60 

1 

~z 

3 

T 6 

St.  Cloud,  Minn 

25 

IOO 

602 d 


TANK  STAND-PIPES. 


Stand-Pipe  Data — Continued. 


LOCATION. 

Diameter. 

Feet. 

Height. 

Feet. 

Thickness 
of  base. 
Inches. 

Thicknest 
of  top. 
Inches. 

Fremont',  O 

25 

25 

IOO 

9 

T7T 

3 

TZ 

I 

Massillon  O 

J5° 

56 

229 

122 

Mt  Vernon,  0 

9 

T?T 

7 

3 

T(T 

7 

.Saprfimky  O 

25 

25 

25 

25 

25 

25 

25 

25 

25 

25 

3° 

3° 

?0 

Atlantic  City,  N.  J 

2 9 

3 

nr 

3 

rz 

3 

Ofppnhimh  N".  V 

80 

I I 

nr 

I I 

Orppn  Tslonr^  N\  V 

120 

Homer,  1ST.  V 

40 

IOO 

5 

nr 

3 

tit 

tV 

1 

Chippewa  Falls,  Wis 

Pa  nine  Wis 

90 

80 

1 

Porta  gp  Wis 

5 

3 

Belleville,  Ont 

Rome  Ga 

120 

63 

36 

76 

50 

I 12 

1 

j 

3 

nr 

1 

Savannah  Oa 

3 

1 

Newton,  Kan 

1 

1 

Brookline  Mass 

1 

5 

Springfield,  O 

3° 

'ZO 

7 

3 

White  Plains,  N.  Y.  

52 

70 

5° 

I ^O 

7 . 

3 

Westerly  R.  T 

3° 

3° 

3° 

3° 

3° 

3° 

35 

35 

37  & io 
40 

4° 

40 

40 

40 

40 

40 

40 

40 

40 

40 

5 

1 

Woonsocket  R.  T 

3 

1 

Houston,  Tex. 

3 

1 

Baraboo,  Wis 

Cornwall,  Ont 

J 

52 

120 

7 

TIT 

II 

3 

TT 

3 

Hoboken  N.  J 

30 

35 

60 

3 

I 

Hopkinton,  Mass 

I 

6 v 

Quincy,  Mass 

5 

1 

Augusta,  Ga 

55 

40 

80 

I 

Anniston,  Ala 

3 

I 

Marysville,  Cal 

. . 

Alton,  111 

45 

35 

62 

Franklin,  Mass 

3 

I 

N.  Attleboro,  Mass 

I 

5 

Stoneham,  Mass 

62 

I 

5 

Wakefield,  Mass 

60 

X 

5 

Weymouth,  Mass 

75 

5 

A 

Canandaigua,  N.  Y.  ... 

Cortland,  N.  Y 

40 

46 

I 

3 

Armiston,  Ala 

I 

I 

CHAPTER  XXVI. 


■SYSTEMS  OF  WATER  SUPPLY. 

566.  Permanence  of  Supply  Essential. — Let  the 

projector  of  a public  water  supply  first  make  himself  famil- 
iar with  the  possible  scope  and  objects  of  a good  and  ample 
system  of  water  supply,  and  become  fully  conscious  of  how 
intimately  it  is  to  be  connected  with  the  well-being  of  the 
people  and  their  active  industries  in  all  departments  of  their 
arts,  mechanics,  trade,  and  commerce,  as  well  as  in  them 
culinary  operations,  and  let  him  also  appreciate  the  conse- 
quences of  its  failure,  or  partial  failure  after  a season  of 
success. 

When  the  people  have  become  accustomed  to  the  ready 
flow  from  the  faucets,  at  the  sinks  and  basins,  and  in  the 
shops  and  warehouses,  then,  if  the  pumps  cease  motion  or 
the  valve  is  closed  at  the  reservoir,  the  household  oper- 
ations, from  laundry  to  nursery,  are  brought  to  a stand- 
still— engines  in  the  shops  cease  motion,  hydraulic  hoists 
and  motors  in  the  warehouses  cease  to  handle  goods,  rail- 
way trains,  ocean  steamers,  and  coasters  delay  for  water, 
and  a general  paralysis  checks  the  busy  activity  of  the 
city.  What  a thrill  is  then  given  by  an  alarm  of  fire,  be- 
cause there  is  no  pressure  or  flow  at  the  hydrants ! 

The  precious  waters  of  the  reservoirs  preside  over  cities 
with  protecting  influences,  enhancing  prosperity,  comfort, 
safety  and  health,  and  are  not  myths,  as  were  the  goddesses 
in  ancient  mythology,  presiding  over  harvests,  flowers, 
fruits,  health  and  happiness. 


604 


SYSTEMS  OF  WATER  SUPPLY. 


Let  the  designer  and  builder  of  the  public  water  system 
feel  that  his  work  must  be  complete,  durable,  and  unfail- 
ing, and  let  this  feeling  guide  his  whole  thought  and 
energy,  then  there  is  little  danger  of  his  going  astray  as  to 
system,  whether  it  be  called  “gravitation,”  “reservoir,” 
“stand-pipe,”  or  “direct  pressure,”  or  of  his  being  enam- 
ored with  lauded  but  suspicious  mechanical  pumping  au 
tomatons,  and  uncertain  valve  and  hydrant  fixtures. 

When  the  people  have  learned  to  depend,  or  must  of 
necessity  depend,  upon  the  public  pipes  for  their  indis- 
pensable water,  it  must  flow  unceasingly  as  does  the  blood 
in  our  veins.  All  elements  of  uncertainty  must  be  over- 
come, and  the  safest  and  most  reliable  structures  and  ma- 
chines be  provided. 

Many  times,  in  different  cities,  a neglect,  apparently 
slight,  has  cost,  through  failure,  a fearful  amount,  when 
sacrificed  life  and  treasure  and  a broad  smouldering  swath 
across  the  city  were  the  penalty.  Having  water- works  is 
not  always  having  full  protection,  unless  they  are  fully 
adequate  for  the  most  trying  hour. 

567.  Methods  of  Gathering  and  Delivering  Water. 
— There  is  no  mystery  about  “ systems ” of  water  supply, 
as  they  have  of  late  been  often  classified.  The  problem  is 
simply  to  search  out  the  best  method  of  gathering  or  secur- 
ing an  ample  supply  of  wholesome  water,  and  then  to 
devise  the  best  method  of  delivering  that  supply  to  the 
people. 

Usually  there  is  one  source  whose  merits  and  demerits, 
when  intelligently  examined,  favorably  outweighs  the 
merits  and  demerits  of  each  and  every  other  source,  and 
there  is  usually  one  method  of  delivery  that  is  conspicu- 
ously better  than  all  others,  when  all  the  local  exigencies 
are  seen  and  foreseen. 


TURBINES  AN DiP E 


CHOICE  OF  WATER. 


60.1 


The  usual  methods  of  gathering  the  required  supply  are, 
to  impound  and  store  the  rainfall  or  flow  of  streams  among 
the  hills  ; draw  from  a natural  lake  ; draw  from  a running 
river ; or  draw  from  an  artesian  well. 

The  usual  methods  of  delivering  water  are,  hy  gravita- 
tion from  an  elevated  impounding  hasin  ; elevation  hy 
steam  or  water  power  to  a reservoir  and  from  thence  a flow 
by  gravity ; elevation  to  low  and  high  service  reservoirs, 
and  from  thence  flow  by  gravity  to  respective  districts  ; and 
by  forcing  with  pressure  direct  into  the  distribution-pipes, 
and  cushioning  the  motion  by  a stand-pipe,  or  ample  air- 
vessel  and  relief  valve. 

568.  Choice  of  Water.  — The  pumped  supplies  are 
usually  drawn  from  lake,  river,  or  subterranean  sources. 

The  selection  of  a lake  or  river  water  for  domestic  use  is 
to  be  governed  by  considerations  of  wholesome  purity  ; and 
cautiousness  of  financial  expenditure  must  not  in  this  direc- 
tion exert  too  strong  an  influence  in  opposition  to  inflexible 
sanitary  laws. 

This  selection  involves  an  intelligent  examination  of  the 
origin  and  character  of  the  impregnations  and  suspended 
impurities  of  the  water,  and  the  possibility  of  their  thorough 
clarification. 

None  of  the  waters  of  Nature  are  strictly  pure.  Some 
of  the  impurities  are  really  beneficial,  while  others,  which 
are  often  present,  are  not  to  be  accepted  or  tolerated.  A 
mere  suspicion  that  a water  supply  is  foul  or  unwholesome, 
even  though  not  based  on  substantial  fact,  is  often  a serious 
financial  disadvantage  ; therefore  earnest  effort  to  maintain 
the  purity  of  the  water  must  extend  also  to  the  removal  of 
causes  of  suspicion. 

Chemical  science  and  microscopy  are  valuable  aids  in 
this  portion  of  the  investigation  of  the  qualities  of  waters  : 


606 


SYSTEMS  OF  WATER  SUPPLY. 


but  we  have  detailed  in  the  first  part  of  this  treatise  so 
minutely  the  nature  and  source  of  the  chief  impurities,  and 
so  carefully  pointed  out  those  that  are  comparatively  harm- 
less and  those  that  are  deadly,  that  an  intelligent  opinion 
can  generally  be  readily  formed  of  the  comparative  puri- 
ties and  values  of  different  waters.  We  have  also  pointed 
out  how  waters  may  be  clarified  and  conducted  in  their  best 
condition  to  the  point  of  delivery,  and  distributed  in  the 
most  efficient  manner. 

Predictions  of  any  value  as  to  quantity  and  quality  of  a 
supply  from  a proposed  artesian  well,  demand  a knowledge 
of  the  local  geology  and  subterranean  hydrology,  which  is 
rarely  obtainable  until  the  completion  and  test  of  the  well ; 
nevertheless  we  have  shown  the  conditions  under  which  a 
good  supply  of  water  may  be  anticipated  with  reasonable 
confidence. 

569.  Gravitation. — When  a good  and  abundant  sup- 
ply of  water  can  be  gathered  at  a sufficient  elevation,  and 
within  an  accessible  distance,  the  essential  element  of  con- 
tinuous full-pressure'  delivery  can  then  most  certainly  be 
secured,  and  in  the  matter  of  possible  safety  the  gravitation 
method  will  usually  be  superior  to  all  others. 

The  quality  of  impounded  water,  when  gathered  in  small 
storage  reservoirs  and  from  relatively  limited  watersheds,  is 
subject  to  some  of  those  unpleasant  influences,  heretofore 
referred  to,  which  are  to  be  provided  against ; and  unless  the 
hydrology  and  substructure  of  the  gathering  basin  is  well 
understood,  the  permanence  of  the  supply  may  not  fulfill 
enthusiastic  anticipations. 

The  value  and  importance  of  sufficient  elevation  of  the 
supplying  reservoir,  when  the  delivery  is  by  gravity,  to 
meet  the  most  pressing  needs  of  the  fire-service,  ought  not 
to  be  overlooked,  for  an  efficient  fire-service  is  usually  one 


PUMPING  WITH  RESERVOIR  RESERVE. 


607 


of  the  chief  objects  to  be  attained  in  a complete  water 
supply. 

A water  pressure  of  sixty  to  eighty  pounds  per  square 
inch  in  the  hydrants  in  the  vicinity  of  an  incipient  fire,  has 
a value  which  cannot  be  wholly  replaced  by  a brigade  of 
fire-steamers  in  commission,  for  with  light-hose  carriages 
and  trained  liosemen,  connection  will  usually  be  made 
with  the  hydrants,  streams  be  put  in  motion,  and  the  fire 
overpowered  before  pressure  is  raised  in  the  steamer’s  boil- 
ers ; and  the  fire  will  not  be  suffered  to  assume  unconquer- 
able headway  during  the  delay. 

Constant  liberal  pressures  in  the  hydrants  is  the  first 
element  of  prompt  and  effective  attack  upon  a fire  immedi- 
ately after  an  alarm  is  given.  Each  moment  lost  before  the 
beginning  of  an  energetic  attack  increases  greatly  the  diffi- 
culty of  subduing  the  fire,  and  the  probability  of  a vast 
conflagration. 

The  element  of  distance  of  a gravitation  supply,  as  re- 
gards cost  of  delivery,  is  an  exacting  one,  and  the  lengths 
of  conduit  and  large  main  are  surprisingly  short,  while  the 
balance  of  economy  of  delivery  remains  with  the  side  of  the 
gravitation  scheme  ; for  conduits  and  mains  are  expensive 
constructions,  and  soon  absorb  more  capital  and  interest 
than  would  pay  for  pumps  and  fuel  for  lifting  a nearer 
supply  ; still  an  element  of  safety  is  not  to  be  sacrificed  for 
a moderate  difference  in  first  cost. 

570.  Pumping'  with  Reservoir  Reserve.  — As  re- 
gards safety  and  reliability  of  operation,  we  place  second  the 
method  of  delivery  when  the  supply  is  elevated  by  hydrau- 
lic power,  and  third  when  it  is  elevated  by  steam  power  to 
a liberal-sized  reservoir  holding  in  store  from  six  to  ten 
days  reserve  of  water,  from  whence  the  supply  flows  by 
gravity  into  the  distribution-pipes.  If  in  such  case  there 


608 


SYSTEMS  OF  WATER  SUPPLY. 


are  duplicate  first-class  pumping-machines  whose  combined 
capacity  is  equal  to  the  delivery  of  the  whole  daily  supply 
in  ten  hours,  or  one-half  equal  to  the  delivery  of  the  whole 
daily  supply  in  twenty  hours,  then  this  method  is  scarcely 
inferior  in  safety  to  the  gravitation  method. 

The  elements  of  safety  may  be  equally  secured  in  the 
low  and  high  service  method,  when  the  physical  features  of 
the  town  or  city  make  such  division  desirable.  In  a pre- 
vious chapter  we  have  shown  how  a union  of  the  high  and 
low  service  may  be  made  an  especially  valuable  feature  in 
efficient  fire  service. 

The  records  of  nearly  all  the  water  departments  of  our 
largest  cities,  having  duplicate  pumping  machinery,  show 
how  valuable  and  indispensable  have  been  their  reserve 
stores  of  water,  and  refer  to  the  risks  that  would  have  been 
incurred  had  such  reservoir  storages  been  lacking. 

571.  Pumping’  with  Direct  Pressure. — We  place 
fourth,  as  regards  safety  and  reliability,  the  direct  pressure 
delivery  by  hydraulic  power,  and  fifth,  by  steam  power, 
with  either  stand-pipe  or  air-vessel  cushions  and  safety 
relief-valves. 

The  mechanical  arrangements  that  admit  of  this  method 
of  delivery  are  simple,  and  several  builders  of  pumping 
machinery  have  adapted  their  manufactures  to  its  special 
requirements,  but  in  point  of  continuous  reliability  the 
method  still  remains  inferior  to  gravity  flow. 

Even  when  the  most  substantial  and  most  simple  steam 
pumping  machinery  is  adopted,  if  not  supplemented  by  an 
elevated  small  reserve  of  water,  this  method  of  delivery  is 
accompanied  with  risks  of  hot  bearings,  sudden  strains, 
unexpected  fracture  of  connection,  shaft,  cylinder,  valve- 
chest  or  pipe,  and  occasional  necessary  stoppages. 

The  best  pumping  combinations  are  so  certainly  liable 


PUMPING  WITH  DIRECT  PRESSURE. 


609 


to  such  contingencies  that  cities  may  judiciously  hesitate  to 
rely  entirely  upon  the  infallibility  of  their  boilers,  engines, 
and  pumps,  even  when  so  fortunate  as  to  secure  attendants 
upon  whom  they  can  place  implicit  confidence. 

The  direct  pressure  method,  alone,  necessitates  unceas- 
ing firing  of  the  boiler  and  motion  of  the  pumping-engine, 
and  consequently  double  or  triple  sets  of  hands,  to  whose 
integrity  and  faithfulness,  night  and  day  and  at  all  times, 
the  works  are  committed. 

Hydraulic  power  and  machinery  are  far  more  reliable 
than  steam  machinery,  for  direct  pressure  uses,  and  hy- 
draulic power  presents  the  great  advantage  of  being  able 
to  respond  almost  instantaneously  to  the  extreme  demand 
for  both  water  and  pressure,  while  a dull  fire  under  the 
boiler  may  require  many  minutes  for  revival  so  as  to  raise 
the  steam  to  the  effective  emergency  pressure.  An  example 
of  pumping  machinery  of  live  million  gallons  capacity  per 
diem,  driven  by  hydraulic  power,  is  shown  in  Fig.  143. 
This  set  of  pumping  machinery  was  constructed  for  the  city 
of  Manchester,  N.  H.,  by  the  Geyelin  department  of  Messrs. 
R.  D.  Wood  & Co.,  Philadelphia,  from  general  designs  by 
the  writer,  and  has  operated  very  satisfactorily  since  its 
completion  in  1874.  This  machinery  is  adapted  in  all  re- 
spects to  direct  pressure  service,  and  was  so  used  during  a 
full  season  while  the  reservoir  was  in  process  of  construction, 
and  it  is  equally  well  adapted  to  its  ordinary  work  of  pump- 
ing water  to  the  distributing  reservoir. 

The  direct  forcing  method  does  not  provide  for  the  de- 
position or  removal  of  impurities  after  they  have  passed  the 
engine,  but  the  sediments  that  reach  the  pumps  are  passed 
forward  to  the  consumers  in  all  sections  of  the  pipe  distri- 
bution. 

In  combination  with  a reservoir  sufficient  for  all  the 


610  SYSTEMS  OF  WATER  SUPPLY. 

ordinary  purposes,  and  equalizing  the  ordinary  work  and 
the  ordinary  pressures  at  the  taps,  and  also  in  combination 
with  a very  small  reservoir,  the  direct  pressure  facilities 
may  prove  a most  valuable  auxiliary  in  times  of  emergency, 
and  they  are  then  well  worth  the  insignificant  difference  in 
first  cost  of  pumping  machinery. 

In  the  smaller  works  the  entire  machinery,  and  in  larger 
works  one-half  the  machinery,  ma}T  with  advantage  be 
capable  of  and  adapted  for  direct  pressure  action. 

If,  instead  of  substantial  and  simple  machinery  built 
especially  for  long  and  reliable  sendee,  some  one  of  the 
intricate  and  fragile  machines  freely  offered  in  the  market 
for  direct  pumping  is  substituted,  and  is  not  supplemented 
by  an  ample  reservoir  reserve,  then  a risk  is  assumed  which 
no  city  can  knowingly  afford  to  suffer;  and  if  true  prin- 
ciples of  economy  of  working  are  applied,  it  will  generally 
be  found  that  no  city  can,  upon  well-established  business 
theories,  afford  to  purchase  and  operate  such  machinery. 

Well  designed  and  substantially  constructed  pumping- 
macliines,  such  as  are  now  offered  by  several  reliable  build- 
ers, when  contrasted  with  several  of  the  low-priced  and  low- 
duty  contrivances,  are  most  economical  in  operation,  most 
economical  in  maintenance,  and  infinitely  superior  in  reli- 
ability for  long-continuous  work. 


APPENDIX. 


THE  METRIC  SYSTEM  OF  WEIGHTS  AND  MEASURES. 

The  use  of  the  metric  system  of  measure  and  weights 
was  legalized  in  the  United  States  in  1866  by  the  National 
Government,  and  is  used  in  the  coast  survey  by  the  engineer 
corps,  and  to  considerable  extent  in  the  arts  and  trades. 

Several  of  the  best  treatises  on  theoretical  hydraulics 
give  their  lengths  and  volumes  in  metric  measures,  and  we 
give  their  equivalents  in  United  States  measures  in  the 
following  tables. 

The  metre , which  is  the  unit  of  length , area , and  volume, 
equals  39.87079  inches  or  3.280899  feet  in  length  lineal,  and 
along  each  edge  of  its  cube. 

This  unit  is,  for  measures  of  length,  multiplied  decimally 
into  the  decametre , hectometre , kilometre , and  myriametre , 
and  is  subdivided  decimally  into  the  decimetre , centimetre , 
and  millimetre. 

The  affixes  are  derived  from  the  Greek  for  multiplication 
by  ten,  and  from  the  Latin  for  division  by  ten. 

The  measures  for  surface  and  volume  are  similarly 
divided. 

The  gramme  is  the  unit  of  weight,  and  it  is  equal  to  the 
weight  of  a cubic  centimetre  of  water,  at  its  maximum 
density,  in  vacuo.  = .0022046  lbs. 

A cubic  metre  of  water,  at  its  maximum  density,  weighs 
2204.6  lbs.  avoir. 

38 


612 


APPENDIX. 


Table  of  French  Measures  and  United  States  Equivalents. 


Measures  of  Length. 


No.  of 
Metres. 

I Millimetre 

.OOI 

= .0393708  inch  = .0032809  foot. 

— -393708  inch  = .032809  foot. 

= 3-93708  inches  = .3280899  ft.  = .1093633  yd. 
= 39  3708  inches  = 3.2808992  ft.  = .198842  rod 

i Centimetre 

i Decimetre 

.01 
. I 

I Metre 

I i 

t 

10 

= .0006214  mile. 

= 32.808992  ft.  = 1.98842  rods  = .0062138  mile. 
= 328.08992  ft.  = 19.88424  rods  = .062138  mile. 
= 3280.8992  ft.  = 198.8424  rods  = .621383  mile. 
= 32808.992  ft.  = 1988.424  rods  = 6.21383  miles. 

I Hectometre 

100 

1000 

I Myriametre 

10000 

Measures  of  Area. 


No.  of  sq. 
Metres. 

I Centiare 

H 

10 

100 

1000 

10000 

= 10. 7643  sq.  ft.  = 1.196033  sq.  yds.  = .039538 
sq.  rod. 

= 107.643  sq.  ft.  = .39538  sq.  rd.  = .002471  acre. 
= 1076.43  sq.  ft.  = 3.95383  sq.  rds.  = .02471  acre. 
= 10764.3  sq.  ft.  = 39.5383  sq.  rds.  = .2471  acre. 
= 107643  sq.  ft.  = 395.383  sq.  rds.  = 2.471  acres. 

I Deciare 

1 Are 

1 Decare  (not  used) 
1 Hectare 

Measures  of  Volume. 


No.  of  cu. 
Metres. 

I Millilitre 

.OOOOOI 

.OOOOI 

.OOOI 

.OOI  -J 

.01  -J 

. 1 -j 

I ] 

= .0610279  cubic  inch. 

= .610279  cubic  inch. 

= 6.10279  cu.  ins.  = .00353  cu.  ft.  = .0264165  gal. 

= 61.0279  cu.  'ns-  = cu.  ft.  = .264165 

gallon. 

= 610.279  cu.  ins.  = .353136  cu.  ft.  = .0130791 
cu.  yard. 

= 26.4165  gallons  = 3.53136  cu.  ft.  = .130791  cu. 
yard. 

= 264.1651  gallons  — 35-3I3  cu.  ft.  = 1.30791 
cubic  yards. 

I Centilitre 

1 Decilitre 

1 Litre 

1 Decalitre 

I Hectolitre 

1 Kilolitre 

APPENDIX. 


613 


Table  of  French  Measures  and  United  States  Equivalents 

( Continued ). 


Measures  of  Solidity. 


No.  of  cu. 
Metres. 

I Millistere 

.OOI 

.01  -j 
.1 

1 1 
10 
100 
1000 

= 61.0279  cubic  inches  = .03532  cubic  foot. 

= 610.279  cu.  ins.  = 353166  cu.  ft.  = .013079  cu. 
yard. 

6102.79  cu.  ins.  = 3.53166  cu.  ft.  = .130791  cubic 
yard. 

= 61027.9  cu.  ins.  = 35.3166  cu.  ft.  = 1. 30791  cu. 
yards. 

= 353. 166. cu.  ft.  = 13.0791  cu.  3’ards. 

= 3531.66  cu.  ft.  = 130. 791  cu.  yards. 

= 35316.6  cu.  ft.  = 1307.91  cu.  yards. 

t Centistere 

t Decistere 

I Stere 

I Decastere 

1 Kilostere . . 

Measures  of  Weight. 


No.  of 
Grammes. 

X Milligramme 

.001 

= .015432  grain. 

1 Centigramme. . . . 

.OI 

= .I5432  grain. 

1 Decigramme 

. I 

= I.5432  grains  = .0035274  oz.  Avoir. 

1 Gramme 

I 

= 15.432  grs.  = .035274  oz.  Av.  = 002205  lb.  Av. 

x Decagramme 

10 

= 154.32  grs.  = .35274  oz.  Av.  = .02205  lb-  Av. 

1 Hectogramme  . . . 

IOO 

= 1543.2  grs.  = 3.5274  oz.  Av.  = .2205  lb  Av. 

I Kilogramme 

IOOO 

= 15432  grs.  = .35.274  oz.  Av.  = 2.205  lbs.  Av. 

I Tonne 

— 

= 2204.737  lbs. 

A cubic  inch  is  equal  to 

.004329  gallon;  or  .0005787  cu.  ft;  or  16.3890T  millilitres;  or  1.638901 
centilitres ; or  .1638901  decilitre  ; or  .016389  litre ; or  .016389  millistere ; or 
•0016389  centistere. 

A gallon  is  equal  to 

231  cubic  inches,  .13368  cubic  foot ; or  .031746  liquid  barrel ; or  3785.513 
millilitres  ; or  378.551  centilitres  ; or  37.8551  decilitres  ; or  3.785513  litres  ; or 
.378551:3  decalitre  ; or  .037855  hectolitre  ; or  .0037855  kilolitre. 

A cubic  foot  is  equal  to 

1728  cubic  inches;  or  7.48052  liquid  gallons;  or  6.2321  imperial  gallons; 
or  3.21426  U.  S.  pecks  ; or  .803564  U.  S.  struck  bushel ; or  .23748  liquid  bar- 


614 


APPENDIX. 


rel  of  31 J gallons;  or  2831.77  centilitres;  or  283.177  decilitres:  or  28.3177 
litres  ; or  2.83177  decalitres  ; or  .283177  hectolitre  ; or  .0283177  kilolitre  ; or 
28.3177  millisteres ; or  2.83177  centisteres  ; or  .283177  decistere ; or  .0283177 
stere. 

The  imperial  gallon  is  equal  to 

.16046  cu.  feet  ; or  1.20032  U.  S.  liquid  gallons. 

A cubic  yard  is  equal  to 

46656  cu.  inches  ; or  201.97404  liquid  gallons  ; or  27  cu.  feet ; or  21.69623 
struck  bushels  ; or  764.578  litres  ; or  76.4578  decalitres  ; or  7.64578  hectolitres  ; 
or  .764578  kilolitre  ; or  764.578  milisteres  ; or  76.4578  centisteres  ; or  7.64578 
decisteres  ; or  .764578  stere;  or  .0764578  decastere  ; or  .0076458  hectostere ; 
or  .00076458  kilostere. 


Comparative  Heads,  Pressures,  and  Volumes. 


One  cubic  foot  per  minute 

= 

rate  of  1,440. 

cubic  feet  per  24  hours. 

44  44  “ 44 

= 

10,771.9488 

gallons  per  24  hours. 

“ 44  “ 44 

= 

44  448.8312 

44  per  hour. 

44  44  44  second 

= 

44  26,929.872 

44  44 

44  t.  tt  a 

= 

646,316.928 

44  per  24  hours. 

One  gallon  per  minute 

= 

1,440.0 

44  44  24  ,4 

“ 44  44 

= 

44  8.02083 

cubic  feet  per  hour. 

“ “ 44 

= 

44  192.49992 

44  44  24  hours. 

One  U.  S.  gallon 

= 

0.13368 

cubic  foot. 

One  million  gallons 

= 

133,680.5462 

cubic  feet. 

“ 44  per  24  hours 

= 

rate  of  92.83371 

cubic  feet  per  minute. 

“ “ “ 24  “ 

= 

1.5472285 

44  4 4 second. 

“ 24  44 

= 

694.44444 

gallons  per  minute. 

One  foot  per  second,  velocity 

= 

44  0.68182 

miles  per  hour. 

One  mile  per  hour,  44 

= 

44  1.46667 

feet  per  second. 

One  inch  of  rain  per  hour 

= 

volume  of  3630.0 

cu.  ft.  per  hour  per  acre. 

a a a a 

= 

44  2,323,200.0 

44  44  4 * sq.  mile. 

44  44  44  24  hours 

= 

44  151-25 

44  44  44  acre. 

“ “ “ 24  44 

= 

4*  96,800.0 

44  44  “ sq.  mile. 

“ “ " 24  “ 

= 

44  3,630.0 

44  per  24  hours  per  acre. 

“ “ 44  24  44 

= 

44  2,323,200.0 

44  per  24  hours  per  sq.  mile. 

One  foot  of  water  at  52°.3  Fah. 

= 

62.4 

lbs.  on  the  square  foot 

44  44  44  *f 

= 

•433 

44  44  44  inch. 

a a a a 

= 

.0295 

atmosphere. 

tt  a a a 

= 

.8823 

inch  of  mercury  at  320. 

One  ib.  on  the  square  foot 

= 

.016026 

foot  of  water. 

“ “ “ inch 

= 

2.308 

feet  of  water. 

One  atmosphere  (=  29.922  in.  mercury) 

= 

33-9 

44  44 

One  inch  of  mercury,  at  320 

= 

I-I334 

44  44 

One  cubic  foot  of  average  sea-water 

= 

1.026 

cu.  ft.  of  pure  water  in  weight 

One  Fahrenheit  degree 

= 

•55555 

Centigrade  degree. 

One  Centigrade  degree 

= 

x.8 

Fahrenheit  degrees. 

Temperature  of  melting  ice 

1 32° 

on  Fahrenheit’s  scale. 

44  44  44 

=3 

© 

44  Centigrade  scale. 

APPENDIX. 


615 


Table  of  Average  Weights,  Strengths,  and  Elasticities  of 
Materials. — (From  Trautvvine,  Neville,  and  Rankine.) 


Materials. 

Weight 
per 
cu.  in. 

Weight 
per 
cu.  ft. 

Specific 

Grav. 

Tenacity 
per 
sq. in. 

Resist- 
ance per 
sq.  in.  tc 
crush- 
ing force. 

Woods  (seasoned,  and  dry). 

Lbs. 

Lbs. 

48.0 

38 

48 

47 

56.8 
41 

36.8 
35 

O.77 
. 61 

Lbs. 

I7OOO 

Lbs. 

“ American  white 

Beech 

• 77 
•75 

16000 

8500 

Cedar,  American 

“ “ green 

1 1400 
12000 
13500 

5600 

.66 

.56 

. J.O 

53 

.85 

•79 

CQ  . 2 

I3COO 

6400 

6500 

6000 

51.8 
40.0 
2s  . 0 

• 83 

10250 

.40 

• 55 

• 72 
.40 
.61 

34-3 

45-o 

25.0 

38 

162 

7800 

12400 

5500 

7200 

Metals. 

2.6 

525 

524 

533 

529 

538 

549 

560 

153 

444 

443 

485 

474 

717 

713 

846 

644 

490 

456 

437 

Cu.  yd. 

2357 

3375 

2700 

4050 

1512 

1339 

8.40 

8.40 

8.54 

8.5 

8.61 

18000 

10300 

49OOO 

36000 

I9OOO 

30000 

60000 

Bronze  (copper  8 parts,  tin  I part). . . . 

. .3062 

“ sheet 

8.80 

S.88 

Glass 

2.45 

9400 

16700 

13500 

50000 

48000 

1800 

33000 

106000 

“ “ hot  blast  

7.04 

7-77 

7.60 

108000 

“ “ wrought,  sheet  or  plate 

“ “ “ large  bars 

11.44 

11.40 

1358 

10.31 

7.85 

7-30 

7.00 

“ milled 

33°° 

40900 

120000 

Mercury  (at  320  Fah.,  849  lbs.)  (at  212  , 1 
836  lbs.),  at  6o° \ 

. .4896 

— 

Tin,  cast 

5300 

7500 

Earth  and  Stones  (dry). 

Cu.  ft. 

87.3 

125 

100 

1 .4 

Brick,  common  hard 

“ sofr  inferior 

280 

800 

ci  best  pressed 

150 

56 

49.6 

Cement,  American  Rosendale,  loose. . . . 
“ “ Louisville 

616 


APPENDIX. 


Table  of  Average  Weights,  Strengths,  Etc. — ( Continued ). 


Materials. 

Weight 
per 
cu.  ft. 

Weight 
per 
cu.  yd. 

Specific 

Gray. 

Tenacity 
per 
sq.  in. 

Resist- 
ance per 
sq.  in.  to 
crush- 
ing force. 

Lbs. 

Lbs. 

Lbs. 

Lbs . 

Cement,  English  Portland 

90 

2430 

280 

“ French  Boulogne 

80 

2160 

Clay,  potter’s 

119 

3213 

1.9 

“ dry,  in  lump,  loose 

63 

1701 

Concrete 

556 

Coal,  bituminous 

84 

2268 

i-35 

“ broken,  loose 

50 

1350 

“ a ton  occupies  43  to  48  cu.  ft 

Earth,  loam,  loose 

75 

2025 

“ “ moderately  rammed 

95 

2565 

“ “ as  a mud 

no 

2970 

Granite 

168 

4536 

2.69 

10000 

“ quarried,  in  loose  piles 

96 

2592 

Gneiss 

168 

4536 

2.69 

“ quarried,  in  loose  piles 

100 

2700 

Greenstone 

187 

5049 

“ auarried,  in  loose  piles 

107 

2889 

Gravel.  . . 

100 

2700 

“ moderately  rammed,  dry 

120 

3240 

1.90 

“ “ “ moist 

130 

3510 

Limestone 

168 

4536 

2.7 

8333 

Lime,  ground,  loose 

53 

1431 

Marble 

165 

4455 

2.64 

5500 

Masonry,  dressed  granite,  or  limestone. . 

165 

4455 

“ well-scabbled  mortar  rubble  of  do. 

154 

4153 

.... 

“ “ “ dry  “ “ do. 

138 

3726 

• • • • 

“ roughly  “ . “ “ “ do. 

125 

3375 

“ dressed  sandstone 

144 

3388 

“ dry  rubble  “ 

no 

2970 

“ brickwork,  medium 

125 

3375 

345 

“ “ coarse 

100 

2700 

“ “ press’d  bricks,  close  joints 

140 

373o 

.... 

Marl 

no 

2970 

i-75 

Mortar,  cement 

103 

2781 

1.65 

50 

Peat,  unpressed 

25 

675 

Sand,  loose 

100 

2700 

‘‘  shaken 

no 

2970 

1.76 

“ wet 

125 

3375 

.... 

Sandstone 

150 

4050 

5000 

“ quarried,  in  loose  pile 

86 

2322 

Slate  

180 

4373 

2.89 

12000 

Soapstone,  or  steatite 

170 

4590 

2-73 

.... 

Miscellaneous  Materials. 

58.7 

1585 

0.94 

200 

Leather 

4200 

Oil,  linseed 

58. 6S 

•94 

Petroleum . 

54.81 

.878 

Powder,  slightly  shaken 

62.3 

1.0 

Snow,  loose 

12 

324 

“ wet  and  compact 

50 

1350 

Water 

62.334 

1693 

1.0 

APPENDIX. 


61? 


Formulas  for  Shafts. — (Francis.) 
Wrought-iron  prime  movers,  with  gears : 

d = ^1(^P,  and  P = .01  Nd\ 

Wronght-iron  transmitting  shaft : 

d = -y and  P - .02 Nd\ 

Steel  prime  mover,  with  gears : 

d = and  P - .016iVP. 

Steel  transmitting  shaft : 

d = and  P = .032m5. 

In  which  ^ = diameter  of  shaft  in  inches. 

iV  = number  of  revolutions  per  minute 
P = horse  powers. 

Trigonometrical  Expressions. 


Radius  = AC. 
Sine  = Cd. 
Cosine  = Ce. 
Tangent  = Bf. 
Cotangent  = lig. 
Secant  = Af. 
Cosecant  = A g. 
Versed  sine  = Bd. 
Co-versin  — lie. 


618 


APPENDIX. 


Trigonometrical  Equivalents,  when  Radius  = i. 


Sine  = 

1 -r-  Cosec. 

U _ 

Cosin.  -4-  Cotan. 

U _ 

V(1  — Cosin2.) 

Cosine  = 

1 -4-  Sec. 

a __ 

Sin.  -4-  Tan. 

u _ 

Sin.  x Cotan. 

u 

Sin2. 

Tangent  = 

1 -4-  Cotan. 

U 

Sin.  -4-  Cosin. 

Cotangent  = 

1 -4-  Tan. 

CC  

Cosin.  -4-  Sin. 

Secant  = 

1 -4-  Cosin. 

6C  

Vl  + Tan2. 

Cosecant  = 

1 -4-  Sin. 

a 

Vl  + Cotan2. 

Versine  = 

Rad.  — Cosin. 

Coversine  = 

Rad.  — Sin. 

Complement  = 

90°  — Angle. 

Supphmient  = 

180°  — Angle. 

If  radius  of  an  arc  of  any  angle  is  multiplied  or  divided 
by  any  given  number,  then  its  several  correspondent  trigo- 
nometrical functions  are  increased  or  diminished  in  like 
ratio. 

Diameter  = Rad.  x 2. 

• Circumference  = Rad.  x 6.2882. 

“ = Diam.  x 3.1416. 

Area  of  circle  = Diana2,  x .7854. 

Surface  of  a sphere  = Diam3.  x 3.1416. 

Volume  of  a sphere  = Diam3.  x .5236. 

Length  of  one  second  of  arc  = Rad.  x .0000048. 

“ “ “ minute  “ “ = Rad.  x .0002909. 


degree 


= Rad.  x .0174533. 


U U 


APPENDIX. 


619 


Values*  of  Sines,  Tangents,  Etc.,  when  Radius  = 1. 


Deg. 

Sine. 

Cover. 

Cosec. 

Tang’t. 

Cotan. 

Secant. 

Versine. 

Cosine. 

Deg. 

O 

.OO 

I.  OOOOO 

Infinite. 

.O 

Infinite. 

I.  OOOOO 

0. 

I.  OOOOO 

90 

I 

•01745 

.98254 

57.2986 

.01745 

1 57-2899 

1. 00015 

.0001 

•99984 

8q 

2 

.O3480 

.96510 

28.6537 

.O3492 

28.6362 

1.00060 

.0006 

•99939 

88 

3 

•05234 

.94766 

19.1073 

.05241 

19.0811 

1-00137 

.0013 

.99863 

87 

4 

.06976 

.93024 

14-3355 

.06993 

14.3007 

1.00244 

.0024 

.99756 

86 

5 

.08716 

.91284 

n-4737 

.08749 

11.4300 

1.00381 

.0038 

.99619 

8.5 

6 

.IO453 

.89547 

9-5667 

.IO5IO 

9.5144 

1.00550 

.0054 

.99452 

84 

7 

.12187 

•87813 

8.2055 

.12278 

8.1443 

1.00750 

.0074 

•99255 

83 

8 

•I39I7 

,86o32 

7.1852 

.14054 

7-II54 

1.00982 

■0097 

•QQ027 

82 

9 

•15643 

.84356 

6.3924 

.15838 

6.3137 

1.01246 

.0123 

.98769 

81 

IO 

■1736s 

.82035 

5-7587 

•17633 

5.6712 

1.01542 

.0151 

.98481 

80 

II 

.19081 

.80919 

5.2408 

.19438 

5.1446 

1.01871 

.0183 

.98x63 

79 

12 

.20791 

.79208 

4.8097 

.21255 

4.7046 

1.02234 

.0218 

.97815 

78 

13 

.22495 

•775°4 

4.4454 

.23087 

4.3315 

1.02630 

.0256 

•97437 

77 

14 

.24192 

.75807 

4-1335 

•24933 

4.0108 

1.03061 

.0297 

•97°3° 

76 

IS 

.25882 

.74118 

3.8637 

■26795 

3.7320 

i-°3527 

.0340 

•96593 

75 

l6 

.27504 

■ 72436 

3.6279 

.28674 

3.4874 

1.04029 

.0387 

.96126 

74 

17 

.29237 

.7O762 

3.4203 

•30573 

3.2708 

1.04569 

.0436 

•95630 

73 

18 

.30902 

.69O98 

3-2360 

■32492 

3-o  777 

1.05146 

.0489 

.95106 

72 

19 

•32557 

•67443 

3-07i5 

•34433 

2.9042 

1.05762 

•0544 

■94552 

71 

20 

.34202 

■65797 

2.9238 

•36397 

2*7475 

I.064I7 

.0603 

.93969 

70 

21 

35337 

.64163 

2.7904 

.38^86 

2.6051 

I.O7II4 

.0664 

•93358 

69 

22 

.37461 

.62539 

2.6694 

.40403 

2.4751 

1.07853 

.0728 

.92718 

68 

23 

•39173 

.60926 

2 5593 

.42447 

2.3558 

I.08636 

.0794 

.92050 

67 

24 

.40674 

•59325 

2 4585 

•44523 

2.2460 

1.09463 

.0864 

•91355 

66 

25 

.42262 

•57738 

2.3662 

•46631 

2.1445 

1.10337 

.0936 

.90630 

65 

26 

•43837 

.56162 

2.2811 

•48773 

2.0503 

I.II26o 

.1012 

.89879 

64 

27 

•45399 

.54600 

2.2026 

.50952 

I.9626 

I. 12232 

.1089 

.89IOI 

63 

28 

.46947 

.53052 

2.1300 

•53171 

1.8807 

1-13257 

.1170 

.88295 

62 

29 

.48481 

•5I5I9 

2.0626 

•55431 

1.8040 

1-14335 

•1253 

.87462 

6l 

3° 

.50000 

.50000 

2.0000 

•57735 

1.7320 

1.15470 

•T339 

.86603 

60 

31 

•51504 

.48496 

1.9416 

.60086 

1.6643 

I.16663 

.1428 

•85717 

59 

32 

.52992 

.47008 

1.8870 

.62487 

1.6003 

I*I7917 

•1519 

.84805 

58 

33 

•54464 

•45536 

1.8360 

.64941 

I-5398 

1.19236 

.1613 

.83867 

57 

34 

•55919 

.44080 

1.7882 

•67451 

I.4826 

1.20621 

.1709 

.82904 

56 

35 

•57358 

.42642 

1-7434 

.70020 

I.428l 

1.22077 

.1808 

.81915 

55 

36 

.58778 

.41221 

1-7013 

.72654 

1-3764 

1.23606 

.1909 

.80902 

54 

37 

.60181 

.39818 

I.  66l6 

•75355 

1.3270 

1. 25213 

.2013 

.79864 

53 

3« 

.61566 

•38433 

1.6242 

.78128 

1.2799 

1.26901 

.2119 

.7880I 

52 

39 

.62932 

.37067 

1.5890 

.80978 

1.2349 

1.28675 

.2228 

•77715 

SI 

40 

.64279 

•35721 

1-5557 

.83970 

I.I9l8 

1.30540 

•2339 

.76604 

50 

41 

.65606 

•34394 

1.5242 

.86929 

I.I504 

1.32501 

.2452 

.75471 

49 

42 

•66913 

.33086 

1.4944 

.90040 

I.  1 106 

1.34563 

.2568 

•743I4 

48 

43 

.68200 

.31800 

I.4662 

•93251 

1.0724 

1-36732 

.2686 

-73135 

47 

44 

.69465 

•30534 

1-4395 

96569 

1-0355 

1.39016 

.2808 

•7T934 

46 

45 

.70711 

.29289 

1 4142 

1. 

I. 

1.41421 

.2928 

.70711 

45 

Cosine. 

Versine. 

Secant. 

Cotan. 

Tang’t. 

Cosec. 

Cover. 

Sine. 

* When  the  angle  exceeds  450,  read  upward  ; the  number  of  degrees  will  then  be  found  in 
"he  right-hand  column,  and  the  namts  of  columns  at  the  bottom. 


620 


APPENDIX. 


In  Right-Angled  Triangles. 

Base  = PHyp\  — Perp2. 

“ = V (Hyp.  + Perp.)  x (Hyp.  — Perp.) 

Perpendicular  = PHyp.2  — Base2. 

“ — P(Hyp.  + Base)  x (Hyp.  — Base.) 

Hypotlienuse  = PBase2  + Perp2. 


What  constitutes  a car  load  (30,000  lbs.  weight) : 

70  bbls.  lime  ; 70  bbls.  cement ; 90  bbls.  flour ; 6 cords 
of  hard  wood  ; 7 cords  of  soft  wood  ; 18  to  20  head  of  cattle ; 
9000  feet  board  measure  of  plank  or  joists ; 17,000  feet 
siding ; 13,000  feet  of  flooring  ; 40,000  shingles  ; 340  bushels 
of  wheat ; 360  bushels  of  corn ; 680  bushels  of  oats ; 360 
bushels  of  Irish  potatoes  ; 121  cu.  ft.  of  granite ; 133  cu.  ft. 
sandstone ; 6000  bricks  ; 6 perch  rubble  stone ; 10  tons  of 
coal ; 10  tons  of  cast-iron  pipes  or  special  castings. 

Lubricator , for  slushing  heavy  gears: 

10  gallons,  or  31  pails  of  tallow ; 1 gallon,  or  ^ pail  of 
Neat’s  foot-oil ; 1 quart  of  black-lead.  Melt  the  tallow, 
and  as  it  cools,  stir  in  the  other  ingredients. 

For  cleaning  brass : 

Use  a mixture  of  one  ounce  of  muriatic  acid  and  one- 
half  pint  of  water.  Clean  with  a brush  ; dry  with  a piece 
of  linen  ; and  polish  with  fine  wash  leather  and  prepared 
hartshorn. 

Iron  cement , for  repairing  cracks  in  castings : 

Mix  l lb.  of  flour  of  sulphur  and  j lb.  of  powdered  sal 
ammoniac  with  25  lbs.  of  clean  dry  and  fine  iron-borings, 
then  moisten  to  a paste  with  water  and  mix  thoroughly. 


APPENDIX. 


621 


Calk  the  cement  into  the  joint  from  both  sides  until  the 
crack  is  entirely  tilled.  In  heavy  castings  to  be  subjected 
to  a great  pressure  of  water,  a groove  may  be  cut  along  a 
transverse  crack,  on  the  side  next  the  pressure,  about  one- 
quarter  inch  deep,  with  a chisel  32  -inch  wide,  to  facilitate 
the  calking  in  of  the  cement. 

Alloys. — The  chemical  equivalents  of  copper,  tin,  zinc, 
and  lead  bear  to  each  other  the  following  proportions,  ac- 
cording to  Rankine : 

Copper.  Tin.  Zinc.  Lead. 

31-5  59-  32-5  103.5 

When  these  metals  are  united  in  alloys  their  atomic  pro- 
portions should  be  maintained  in  multiples  of  their  respec- 
tive proportional  numbers  ; otherwise  the  mixture  will  lack 
uniformity  and  appear  mottled  in  the  fracture,  and  its 
irregular  masses  will  differ  in  expansibility  and  elasticity, 
and  tend  to  disintegration  under  the  influence  of  heat  and 
motion. 


Materials. 

Composition. 

By  Equivalents. 

By  Weight 

Very  hard  bronze 

Copper. 

12 

Tin. 

I 

Copper. 

6.401 

Tin. 

I 

Hard  bronze,  for  machinery  bearings 

Bronze  or  gun-metal,  contracts  in  cooling 

14 

I 

6.966 

I 

16 

I 

8.542 

I 

Bronze,  somewhat  softer  

18 

I 

9.610 

I 

Soft  bronze,  for  toothed  wheels 

20 

I 

10.678 

I 

Malleable  brass 

Copper. 

4 

Zinc. 

I 

Copper. 

3-877 

Zinc. 

I 

Ordinary  brass,  contracts  ^ in  cooling 

2 

I 

1.938 

I 

Yellow  metal,  for  sheathing  ships 

3 

2 

1-454 

I 

Spelter  solder,  for  brazing  copper  and  iron.. 

4 

3 

I.292 

I 

Babbitt’s  metal  consists  of  50  parts  of  tin,  1 of  copper,  and  5 of  antimony. 


623 


APPENDIX. 


Aluminum  bronze,  containing  95  to  90  parts  of  copper 
and  5 to  10  parts  of  aluminum,  is  an  alloy  much  stronger 
tlian  common  bronze,  and  has  a tenacity  of  about  22.6 
tons  per  square  inch,  while  the  tenacity  of  common  bronze, 
or  gun-metal,  is  but  about  16  tons. 

Manganese  bronze  is  made  by  incorporating  a small 
proportion  of  maugauese  with  common  bronze.  This  alloy 
can  be  cast,  and  also  can  be  forged  at  a red-heat. 

A specimen  cast  at  the  Royal  Gun  Factory,  Woolwich, 
in  1876,  showed  an  ultimate  strength  of  24. i'  tons  per  square 
inch,  an  elastic  limit  of  14  tons,  and  an  elongation  of  8.75 
per  cent.  The  same  quality  forged  had  an  ultimate  resist- 
ance of  29  tons  per  square  iucli,  an  elastic  limit  of  12  tons, 
and  an  elongation  of  31.8  per  cent.  A still  harder  forged 
specimen  had  an  ultimate  strength  of  30.3  tons  per  square 
inch,  elastic  limit  of  12  tons,  and  elongation  of  20.75  per 
cent. 

The  tough  alloy,  introduced  by  Mr.  M.  P.  Parsons,  will 
prove  a desirable  substitute  for  the  common  bronze  in  hy- 
draulic apparatus,  where  its  superior  strength  and  greater 
reliability  will  be  especially  valuable. 

Approximate  Bottom  Velocities  of  flow  in  Channels  at 

WHICH  THE  FOLLOWING  MATERIALS  BEGIN  TO  MOVE. 

.25  feet  per  second,  microscopic  sand  and  clay. 


•5° 

cc 

cc 

CC 

fine  sand. 

1. 00 

cc 

cc 

cc 

coarse  sand. 

cc 

cc 

cc 

pea  gravel. 

3 

cc 

cc 

cc 

• smooth  nut  gravoi. 

4 

cc 

c; 

cc 

ij-inch  pebbles. 

5 

<6 

* • 

2-inch  square  brick- 

APPENDIX. 


623 


Tensile  Strength  of  Cements  and  Cement  Mortars,  when 
7 Days  old,  6 of  which  the  Cements  were  in  Water. 

(Compiled  from  Gillmore.*) 


How  Mixed. 

By  Weight. 

By  Volume, 
Loosely  Measur’d 

By  Volume, 

WELL  SHAKEN. 

C/5 

JO 

O 

_bJ0 

‘53 

£ 

a £ 

,5  s 

u S 

O <u 
DhU 

| Rosendale  Cement. 

| Sand. 
1 

Portland  J Weight  per  U.  S.  bu., 
Cement  1 loos,?1>'  measured, 

( 120  lbs. 

Rosendale  I W.^h‘  Per  U-  S-  b.u- 
Cement  ] j^ly  measured, 

Sand. 

Portland  Cement. 

| Rosendale  Cement. 

Sand. 

Tensile  strength  per  square  inch. 

Crushing  ) ( 3.5  in.  wide, 

wt.  per  V Blocks-!  5.5  in.  long, 
sq.  in.  j ( 3.0  in.  thick. 

Lbs. 

Lbs. 

Like  beton  agglomere. 

t 

— 

■25 

I 

— 

.21 

I 

— 

•25 

377 

— 

common  mortar. . 

1 

— 

■25 

44 

— 

44 

44 

— 

44 

289 

— 

44 

beton  agglomere. 

1 

— 

■5 

I 

— 

.42 

I 

— 

320 

— 

R 

common  mor.tar. . 

1 

— 

•5 

44 

— 

44 

44 

— 

222 

— 

beton  agglomere. 

i 

— 

1 

I 

— 

•8S 

I 

— 

■?? 

244 

— 

common  mortar. . 

1 

— 

1 

44 

— 

44 

44 

— 

197 

— 

“ 

beton  agglomere. 

1 

— 

i-33 

I 

— 

I 

— 

\3 

179 

— 

common  mortar. . 

1 

— 

i-33 

44 



44 

— 

44 

129 

— 

U 

beton  agglomere. 

1 

— 

2 

I 

— 

1-7 

I 

— 

1.9 

138 

2804.4 

common  mortar.. 

1 

— 

2 

44 

— 

44 

— 

109 

IO38.O 

U 

beton  agglomere. 

1 

— 

6 

I 

— 

5 

I 

— 

5 9 

66 

259-5 

common  mortar.. 

1 

— 

6 

44 

— 

44 

44 

— 

35 

— 

44 

beton  agglomere. 

1 

— 

8 

I 

— 

6.8 

I 

— 

bo 

39 

259-5 

R 

common  mortar.. 

1 

— 

8 

44 

— 

44 

44 

— 

24 

104.7 

44 

beton  agglomere. 

1 

8 

— 

1 

— 

11. 6 

— 

— 

— 

96 

44 

common  mortar.. 

1 

8 

— 

44 

— 

44 

— 

— 

— 

40 

— 

44 

beton  agglomere. 

1 

2 

— 

I 

— 

2;P 

— 

— 

— 

129 

T 

R 

common  mortar. . 

1 

2 

— 

44 

— 

— 

— 

— 

44 

— 

44 

beton  agglomere. 

— 

I 

I 

— 

— 

— 

— 

— 

— 

51 

— 

n 

— 

I 

2 

— 

1 

1.2 

— 

I 

1.4 

40 

310.7 

— 

I 

3 

— 

I 

1.8 

— 

I 

2 

33 

116.4 

R 

_ 

I 

4 

— 

I 

2.4 

— 

I 

2.8 

22 

156.0 

j 

Less  than 

— 

I 

6 

I 

3-6 

4 i 

10  lbs. 

52.4 

— 

I 

8 

— 

— 

— " 

— 

— 

— 

— 

46.5 

1 

400 

2846.7 

41 

common  mortar.. 

I 

2579.2 

44 

beton  agglomere. 

— 

I 

— 

— 

— 

— 

— 

— 

— 

72 

727  3 

common  mortar.. 

' I 

- 

IO4.7 

* Vide  Treatise  on  Coignet  Beton,  p.  28,  et  seq.  New  Y ork,  1871, 


624 


APPENDIX 


Standard  Dimensions  of  Bolts,  with  Hexagonal  Heads 

and  Nuts. 


Diameter 
of  bolt 
‘*i  inches. 

No.  of 
V threads 
per  in.  of 
length. 

Breadth 
of  head, 
in  inches. 

Thickn’ss 
of  head 
in  inches. 

Breadth 
of  nut 
in  inches. 

Thickness 
of  nut 
in  inches. 

Weight 
of  round  rod 
a per  foot 
in  pounds. 

Weight  of 
head  and  nu. 
in  pounds. 

I 

20 

3 

¥ 

I 

¥ 

3 

¥ 

5 

T¥ 

• 1653 

.017 

5 

T6 

l8 

I 

5 

nr 

I 

~2 

3 

¥ 

•2583 

•°33 

3 

¥ 

l6 

5 

¥ 

3 

¥ 

5 

¥ 

7 

T¥ 

.3720 

•°57 

7 

T¥ 

14 

fs 

7 

T¥ 

1 1 
TS 

I 

¥ 

•5°63 

.087 

1 

2 

13 

3 

* 

1 

2 

3 

.6613 

.128 

9 

T6 

12 

7 

¥ 

9 

7¥ 

7 

¥ 

5 

¥ 

•837o 

. I90 

5 

¥ 

II 

i 

5 

¥ 

I 

1 1 
T¥ 

1 -°33 

. 267 

3 

IO 

if 

3 

Jf 

I 3 
T¥ 

1 .488 

•43 

7 

¥ 

9 

Xt 

7 

¥ 

if 

I 5 
T¥ 

2.025 

•73 

i 

8 

if 

i 

if 

ITS 

2.645 

1 . 10 

if 

7 

if 

if 

if 

I A 

3-348 

1 .60 

ii 

7 

if 

if 

if 

lA 

4-133 

2.14 

if 

6 

2f 

if 

2f 

it? 

5.001 

2-95 

if 

6 

-7  I 

2T 

4 

2f 

iA 

5-952 

3-78 

T S 

5f 

^ 2 

if- 

,i 

Tn 

its 

6.985 

4.70 

if 

5 

oS 

2* 

if 

2¥ 

T 13 

irs 

8. 101 

5.60 

if 

5 

,7 

2-g- 

if 

~7 

2¥ 

iff 

9.300 

7.00 

2 

4| 

3 

2 

3 

2tV 

10.58 

8-75 

*i 

4i 

3l 

2f 

3f 

2A 

13-39 

12.40 

2f 

4 

3l 

,1 

3f 

2ff 

16.53 

17.00 

2f 

4 

4f 

2? 

4f 

2ff 

20.01 

22.30 

3 

3i 

4f 

3 

4i 

3iV 

23.81 

28 . 80 

APPENDIX. 


625 


General  Water-works,  Statistics,  1880. 


Cities. 

Population  in 
1880. 

Average  daily 
Consumption. 

Annual 

Revenue. 

Miles  of  Pipe. 

| No.  of  Meters. 

Albany,  N.  Y 

90.903 

6,363,210 

$145,404 

77 

12 

Alleghany,  Pa 

78,682 

10,000,000 

168,000 

60 

I 

Brooklyn,  N.  Y 

566,577 

30,674,761 

977,703 

352 

1,085 

Boston,  Mass 

362,535 

35.900,000 

1,044,780 

500 

1,219 

Baltimore,  Md 

332,190 

23,000,000 

606,879 

277 

524 

Buffalo,  N.  Y 

154765 

16,369,802 

216,214 

102 

► . . 

Cambridge,  Mass 

52,669 

2,474,616 

177.430 

85 

156 

Cincinnati,  Ohio 

255-708 

19,476,739 

499,857 

189 

545 

Cleveland,  Ohio 

155.946 

10,180,000 

203.379 

125 

402 

Chicago,  111 

503.304 

57,384.376 

961,051 

461 

2,113 

Columbus,  Ohio 

51.644 

2,159,327 

44,572 

44 

534 

Detroit,  Mich 

116,027 

15,170,000 

380,684 

209 

29 

Hartford,  Conn 

42,569 

4,000,000 

121,281 

72 

99 

Indianapolis,  Ind 

75.056 

4,000,000 

70,940 

43 

25 

Jersey  City,  N.  J 

120,728 

14,916,825 

249,641 

153 

41 

Louisville,  Ky 

126,566 

6,567,141 

187,708 

no 

228 

Lawrence,  Mass 

3Q.068 

1.861,363 

62.670 

42 

272 

Lowell,  “ 

59.340 

2,252,197 

n8,8oo 

63 

708 

Lynn,  “ 

38,376 

1,238,290 

79,899 

57 

121 

Milwaukee,  Wis 

115,578 

10,604,000 

129.505 

86 

Minneapolis,  Minn 

48,323 

3,010,591 

20,819 

19 

Manchester,  N.  H 

32,458 

1,180,930 

57.264 

33 

280 

Montreal,  Canada 

145,000 

9,691,901 

364,475 

133 

305 

New  Orleans,  La 

216,090 

9,000,000 

100,000 

69 

New  York,  N.  Y 

1,206,577 

95,000.000 

1,560,599 

503 

4,002 

Newark,  N.  J 

136,400 

9,390,000 

312,649 

136 

New  Haven,  Conn 

62,861 

5,100,000 

131,580 

98 

13 

Philadelphia,  Pa 

874,542 

57,707,082 

1,415.477 

746 

Pittsburgh,  Pa 

156,389 

16,021,624 

302,000 

III 

Poughkeepsie,  N.  Y 

20,207 

1,403,292 

19.379 

l6 

122 

Providence,  R.  I 

104,760 

3,547.264 

247,705 

155 

4,401 

Quebec,  P.  Q 

50,000 

2,500,000 

91,000 

2 

Richmond,  Va 

63.243 

5,718.053 

74.909 

53 

Rochester,  N.  Y 

87,057 

5,607,000 

72,659 

113 

San  Francisco,  Cal 

233  959 

13,824.000 

1,300,000 

178 

5,180 

St.  Louis,  Mo 

333,577 

25,124.000 

660,280 

212 

573 

Syracuse,  N.  Y 

52,210 

4,000,000 

68,000 

42 

Troy,  N.  Y 

56.747 

5,000,000 

61,080 

40 

. . . 

Toledo,  Ohio 

53,635 

3,270,873 

26,124 

47 

Toronto,  Canada 

86,445 

4,787,000 

169,245 

113 

50 

Washington,  D.  C 

147,307 

26,000.000 

69,459 

175 

Worcester,  Mass 

58,040 

3,000,000 

84.326 

80 

3,791 

Wilmington,  Del 

42,499 

3,564,856 

67,638 

52 

Yonkers,  N.  Y 

18,892 

860,000 

22,162 

23 

402 

626 


APPENDIX. 


Comparative  Water-works  Statistics,  1880. 


Cities. 

Average  daily  con- 
sumption per  cap- 
ita. 

Annual  receipts  per 
capita. 

Annual  receipts  for 
each  million  gal- 
lons daily  water- 
age. 

Miles  of  pipe  for 
each  thousand  in- 
habitants. 

Meters  for  each 
thousand  inhabi- 
tants. 

a 0 
0 

jfg 

v.  5-- 

6 = £ 
0 

Albany,  N.  Y 

Galls. 

70. 

$1.59 

£22,850 

.847 

•13 

$... 

Alleghany,  Pa 

127. 

2.14 

16,800 

.762 

.0127 

Brooklyn,  N.  Y 

54.14 

1.72 

31.873 

.621 

I.92 

6.38 

Boston,  Mass 

99.02 

2.88 

29,102 

1-37 

3-36 

Baltimore,  Md 

69.24 

1.83 

26,386 

■833 

i-57 

Buffalo,  N.  Y 

105.77 

1 ■ 39 

13,208 

• 659 

Cambridge,  Mass 

47- 

3.18 

71,700 

1.613 

2.960 

Cincinnati,  Ohio 

76.16 

i-95 

25,664 

•739 

2.13 

5.58 

Cleveland,  Ohio 

65.28 

I .29 

19,880 

.800 

2-57 

4.64 

Chicago,  111 

II4.0I 

1. 91 

16,747 

.915 

4.19 

5.42 

Columbus,  Ohio 

41 . 81 

0.86 

20,641 

.852 

1.03 

8.00 

Detroit,  Mich 

130.74 

3.28 

25.094 

1.80 

Hartford,  Conn 

93  -9b 

2.84 

30,320 

1.69 

2.32 

Indianapolis,  Ind 

53-3 

0.94 

17-735 

•573 

■332 

Jersey  City,  N.  J . ... 

123-55 

2.07 

16,802 

1.26 

•339 

7.84 

Louisville,  Ky 

51.88 

i. 48 

28.583 

.869 

1 S 

5.76 

Lawrence,  Mass 

47.65 

1.60 

33,669 

1.07 

6.94 

4.71 

Lowell  “ 

37-95 

2.00 

52.752 

1.06 

11.9 

5-25 

Lynn,  “ 

32.26 

2.08 

64,524 

1.47 

3-15 

5.36 

Milwaukee,  Wis 

91-74 

I . 12 

12,213 

■745 

Minneapolis,  Minn 

62.30 

0.43 

6,915 

3-93 

Manchester,  N.  H 

36-38 

1.76 

48,491 

I .OI 

8.62 

Montreal,  Canada 

65-53 

2.51 

37.607 

.916 

2.09 

12.30 

New  Orleans.  La ... 

41.6 

0.45 

II, III 

•319 

New  York,  N.  Y 

78.73 

I .29 

16,427 

.416 

3-31 

Newark,  N.  1 

68.63 

2.28 

33.306 

■997 

New  Haven,  Conn 

81.13 

2 09 

25,800 

1.56 

.206 

Philadelphia,  Pa 

65.9 

I .6l 

24.528 

.868 

5-51 

Pittsburgh,  Pa 

104.5 

i-93 

18,854 

•709 

Poughkeepsie,  N.  Y 

69.47 

0.95 

13,810 

.791 

6.03 

5.85 

Providence,  R.  I 

33-86 

2.36 

69,830 

1 . 4S 

42. 

Ouebec,  P.  O 

50. 

1.82 

36400 

•04 

Richmond,  Va 

90.41 

I . l8 

13,100 

.838 

Rochester,  N.  Y 

64.40 

0.83 

12,957 

1.29 

San  Francisco,  Cal 

59- 

5-56 

94.047 

.761 

24-833 

St.  Louis,  Mo 

75-31 

1.97 

26,281 

•635 

i-7 

5-35 

Syracuse,  N.  Y. . . . 

76.61 

1.30 

17,000 

.804 

Troy,  N.  Y 

88.11 

1.07 

12,216 

•704 

Toledo,  Ohio 

60.98 

0.48 

7.987 

.878 

5 77 

Toronto,  Canada 

55  30 

i-95 

35,342 

1.30 

. 57 

Washington,  D.  C 

176-50 

0-47 

2.671 

I . 12 

Worcester,  Mass 

51.68 

1.45 

28,107 

i-37 

6.53 

Wilmington,  Del 

83.88 

1.59 

18,974 

1.22 

4.8s 

Yonkers,  N.  Y 

45-52 

1. 17 

25,770 

1 . 21 

21.2 

6.39 

APPENDIX. 


627 


General  Water  works  Statistics,  1882. 


Cities. 

Number  of 
Fire  Hydrants. 

Number  of 
Meters  in  use. 

Annual  Reve- 
nue from  Meters. 

Per  cent,  of  con- 
sumption 
through  Meters. 

Price  of  Water, 
per 

1,000  gallons. 

Number  of  Taps 
in  use. 

Percentage  of 
Taps  metered. 

DOLL. 

CENTS. 

Attleboro,  Mass 

73 

108 

2,000 

40 

380 

28. 

Boston,  Mass 

5,032 

2,650 

383,628 

13.06 

20  to  30 

60,000 

4.04 

Baltimore,  Md 

S92 

677 

62,708 

IO.42 

Spcl. 

Brooklyn,  N.  Y .... 

2,970 

I,5l6 

198,178 

n.46 

10.33 

64,177 

2.36 

Buffalo,  N.  Y 

1,400 

140 

80.000 

13,400 

Binghamton,  M.  Y 

175 

80 

5 ,024 

3- 

6 to  25 

1,935 

4- 

Chicago,  111 

3>&25 

2,310 

363,000 

II  . 

8 to  40 

78,840 

3- 

Cambridge,  Mass 

596 

156 

42.466 

26. 

20 

7.725 

2. 

Cleveland,  Ohio 

1,264 

702 

101,192 

20.57 

6.66  to  13. 33 

12,923 

5-9 

Cincinnati,  Ohio 

QOO 

780 

75,000 

11 . 18 

9 

24.500 

3-2 

Columbus  Ohio 

363 

546 

27,969 

•25 

7 to  20 

2,288 

•25 

Detroit,  Mich. 

872 

27 

7,000 

IO 

26,000 

Elmira,  N.  Y 

146 

183 

10  to  50 

900 

.20 

Fall  River,  Mass 

655 

1,966 

49,018 

23.06 

30 

3.120 

63.08 

Fitchburg,  Mass 

203 

150 

5-940 

10  to  50 

1,442 

10. 

Grand  Rapids,  Mich 

1,296 

352 

J J ,000 

15  to  30 

1,032 

32. 

Holyoke.  Mass 

177 

105 

9,839 

5 to  15 

1.493 

Hoboken,  N.  J 

42 

23,OCO 

10 . 

12  tO  15 

3 OOO 

I . 5 

Jacksonville,  Fla 

102 

160 

3115 

20. 

15  to  30 

250 

6.4 

Jersey  City,  N.  J. . 

1,415 

28l 

194,737 

25- 

Kansas  City,  Mo 

393 

141 

20,640 

7-5 

r5  to  35 

2,788 

• 5 

Louisville,  Kv 

365 

273 

84,390 

6 to  15 

7,947 

3-5 

Lowell,  Mass 

727 

1,090 

43  OOO 

24. 

6,200 

21  . 

Lawrence,  Mass 

470 

421 

19,750 

20  to  25 

3.653 

1 1 - 5 

Lynn,  Mass 

498 

156 

13.358 

9.07 

25  and  Spcl. 

5,441 

3- 

Meriden,  Conn 

180 

64 

10,862 

10  to  25 

2,000 

Manchester,  N.  H 

339 

400 

1,333 

14. 

26.66 

2,140 

18. 

Milwaukee,  Wis 

794 

102 

44,273 

10. 

4.6  to  20 

7,974 

New  Haven,  Conn 

650 

20 

4,500 

15  to  30 

7,000 

3- 

Newton,  Mass 

344 

664 

13,000 

17.07 

35 

2,371 

28. 

New  York,  N.  Y 

6,944 

6,817 

186,600 

14- 

13-33 

85,000 

8. 

Newark,  N.  ( 

1,197 

252 

36,021 

8.9 

12,676 

§4-5 

New  Brunswick,  N.  J . . . . 

166 

68 

13-724 

24. 

1,330 

5- 

poughkeepsie,  N.  Y 

286 

176 

4,682 

6. 

10  to  20 

1,436 

.12.2 

Providence,  R.  I 

1,186 

5,279 

15  to  30 

10,357 

51- 

Pawtucket,  R.  I 

965 

1,600 

6 to  30 

3,000 

5°. 

Rochester,  N.  Y 

1,050 

639 

46,000 

30- 

12.5  to  30 

12,000 

5-3 

San  Francisco,  Cal 

1,396 

5,846 

464,400 

23,000 

20. 

Salem.  Mass 

154 

134 

9,237 

13.5  to  20 

4,700 

2.03 

Springfield,  Mass 

424 

no 

2,870 

2. 

30  and  Spcl. 

3,500 

3- 

St.  Louis,  Mo 

1,980 

1,218 

222,400 

12.5  to  30 

28,000 

Toledo,  Ohio 

361 

no 

2,000 

8.7 

8 to  20 

1,853 

20. 

Taunton,  Mass  ....  . . . . 

367 

401 

12,139 

38. 

12.5  to  25 

2,062 

19. 

Waterbury,  Conn 

180 

84 

9,000 

5 to  30 

2,217 

Worcester,  Mass 

690 

4,709 

82,914 

.07 

15  to  25 

6,061 

77. 

Yonkers,  N.  Y 

263 

605 

14-945 

48. 

16  to  40 

1,133 

628 


APPEKDIX. 


Stand  Pipe  Data. 
(See  new  table,  page  603.) 


LOCATION. 

Diameter. 

Feet. 

Height. 

Feet. 

Thickness 
of  base. 
Inches. 

Thickness 
<•:  top. 
lnci.cs. 

Wichita,  Kan 

z 2 

15° 

1 

2 

6 

ITT 

Milwaukee,  Wis 

5 

80 

I 

1 

T 

Henderson,  Ky 

5 

80 

1 

2 

I 

¥ 

Catasauqua,  Pa 

5 

IOO 

3 

¥ 

I 

T 

Toledo,  Ohio 

5 

224 

1 

2 

I 

3: 

Erie,  Pa 

5 

233 

3 

T 

I 

T 

Allentown,  Pa 

6 

58 

3 

¥ 

I 

T 

Bristol,  Pa 

6 

140 

7 

"nr 

5 

T¥ 

New  York  City,  High  Service 

6 

!5° 

1 

2 

I 

T 

Joliet,  111 

7 

I05 

5 

¥ 

I 

T 

Mt  Pleasant,  la. 

10 

80 

5 

8 

3 

¥ 

Sandwich,  111. ...  

12 

IOO 

1 

2 

3 

T¥ 

Lewisburgh,  Pa 

12 

130 

I 

1 

T 

Maquoketa,  la 

12  J 

80 

tV 

I 

T 

Freeport,  111 

*5 

88 

5 

■S’ 

Lincoln,  Neb 

18 

75 

I 

3 

T¥ 

Charleston,  S.  C . . 

18 

76 

I 

Y 

Yonkers,  N.  Y 

18} 

21 

I 

■j 

3 

TST 

Princeton,  N.  J 

20 

60 

3 

¥ 

T 

T 

Perth  Amboy,  N.  J. . 

20 

71 

5 

¥ 

I 

-f 

Alliance,  0 

20 

80 

5 

¥ 

3 

¥ 

Wilmington,  N.  C.  

20 

90 

tV 

3 

TIT 

Dedham,  Mass ... 

20 

I03 

5 

¥ 

5 

TIT 

South  Abington,  Mass 

20 

105 

5 

5 

Nantucket,  Mass 

25 

15 

I 

% 

Fremont,  O 

25 

IOO 

5 

■g; 

3 

T(T 

Atlantic  City,  N.  J 

25 

132 

5 

¥ 

3 

T¥ 

Sandusky,  0 

{*! 

IOO  j 

229  j 

3 

T¥ 

Newton  Kan  

30 

76 

5 

¥ 

T 

Springfield,  0 

30 

1 12 

i 

A 

Franklin,  Mass 

40 

35 

3 

¥ 

i 

Wakefield,  Mass 

40 

60 

I 

¥ 

5 

T¥ 

N.  Attleborough,  Mass 

40 

62 

I 

¥ 

5 

T¥ 

APPENDIX. 


629 


Weights  of  Lead  and  Tin  Lined  Service-Pipes. 


Calibre. 

AAA. 
Weight 
per  ft. 

A A 
W eight 
per  ft. 

A. 

Weight 
per  ft. 

B. 

Weight 
per  ft. 

C. 

Weight 
per  ft. 

D. 

Weight 
per  ft. 

D.  Light. 
Weight 
per  ft. 

E. 

Weight 
per  ft. 

E.  Light. 
W eight 
per  ft. 

Inches. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs 

Lbs. 

Lbs. 

Lbs. 

3 

¥ 

i-5 

1-3 

I . 12 

I 

I.06 

0.62 

— 

0-5 

— 

1 

¥ 

3 

2 

i-75 

1.25 

I 

0.81 

— 

0.7 

O.56 

5 

¥ 

3-5 

2-75 

2-5 

2 

i-75 

i-5 

1.25 

I 

0-75 

3 

¥ 

4-5 

3-5 

3 

2.25 

2 

i-75 

i-5 

I.25 

I 

I 

6 

4-75 

4 

3-25 

2.5 

2 

— 

1-5 

— 

6 75 

5-75 

4-75 

3-75 

3 

2.5 

— 

2 

— 

it 

9 

8 

6.25 

5 

4.25 

3-5 

— 

3-25 

— 

2 

10.75 

9 

7 

6 

5-25 

4 

— 

— 

— 

A manufacturer’ s circular  states  that  the  following  quanti- 
ties of  water  will  he  delivered  through  500  feet  of  their  pipes, 
of  the  respective  sizes  named,  when  the  fall  is  ten  feet : 


Calibre 

Gallons  per  minute. . . 
Gallons  per  24  hours. . 


| inch. 

inch. 

| inch. 

f inch. 

r inch. 

ij  inch. 

•348 

.798 

1 .416 

2.222 

4.600 

6-944 

576 

1150 

2040 

3200 

6624 

I OOOO 

A f-inch  clean  service-pipe  connected  to  a 4-inch  tap 
under  a hundred  feet  head,  will  deliver  at.  the  sink,  through 
a common  compression  bib,  ordinarily  about  three  pails  of 
water,  or  say  8.25  gallons,  or  1.1  cu.  ft.  of  water  per  minute. 

Lead  is  more  generally  used  for  service-pipes  than  any 
other  material,  but  wrought-iron  pipe,  lined  and  coated 
with  cement,  or  with  a vulcanized  rubber  composition  or 
sundry  coal-tar  compositions  and  enamels,  have  been  used 
to  a nearly  equal  extent  within  a few  years  past.  Block- 
tin  pipe,  tin-lined  pipe,  and  galvanized  iron  pipe,  have  been 
used  also  to  a limited  extent. 


630 


APPENDIX. 


Safe  Weights  of  Lead  Service  Pipes. 

Good  lead  pipes  have  an  ultimate  cohesion  of  about 
2000  lbs.  per  square  inch.  The  effect  of  the  water  ram 
when  the  house  faucets  are  suddenly  shut  is  not  quite  as 
severe  on  services  as  it  is  on  the  risers  and  fixtures  in  the 
house.  Fifty  per  cent,  of  the  pressure  is  a fair  allowance 
for  the  ram  on  services,  if  an  additional  coefficient  of  safety 
of  5 or  .2s  is  taken  to  cover  the  limit  of  elasticity  and  ordi- 
nary weaknesses. 

On  this  basis  we  have  formulas  for  thickness  t and 
weight  w, 

4 _ 1 .5pr  _ 7.5pr 
1 ~ ~72 ~s~  ~ '~s~  ’ 

w — ((Z+f)  x ^ x tt  x 12”  x .411, 

in  which  p = pressure  in  lbs.  per  sq.  inch. 

= .434  head  in  ft. 

r = internal  radius  of  pipe,  in  inches. 

d = internal  diameter  of  pipe,  in  inches. 

t = thickness  of  pipe  shell,  in  inches. 

77  = 3.1416. 

s — ultimate  cohesion  of  lead,  mean,  2000  lbs.  per 
sq.  in. 


APPENDIX', 


631 


Weights  for  given  Pressures  of  Water. 


Head  of  Water  in  Feet. 

75  | joo  | 125  | 150  | 175  | 200  [ 225  | 250  | 275  | 300 

Pressure  of  Water  in  Pounds. 

32-55  I 43-4°  I 54-25  I 65-1°  I 75  95  I 86.80  | 97.65  | 108.50  1 119.35  I 130.20 
Weights  of  Lead.  Pipes  per  foot,  in  Pounds. 


Diameter,  y2" 

X 

% 

14 

% 

% 

X 

X 

X 

I 

iX 

“ X" 

X 

X 

% 

X 

% 

I 

*/4 

ll4 

IX 

“ 34" 

X 

X 

% 

T 

■ 

1% 

*X 

2 

2^4 

“ 1"  

% 

x/4 

1 14 

ik 

2 

2% 

2/4 

3 

3% 

354 

“ IX" 

i5£ 

2 14 

254 

3X 

3X 

4/4 

4/4 

5 X 

s?4 

I Zt"..  •• 

2 

2/2 

3% 

3 % 

4 % 

5 H 

6 

6X 

7/4 

814 

These  weights  should  be  increased  somewhat  in  the 
house  plumbing. 


632 


APPENDIX. 


RESUSCITATION  FROM  DEATH  BY  DROWNING. 

“ Persons  may  be  restored  from  apparent  death  by 
drowning,  if  proper  means  are  employed,  sometimes  when 
they  have  been  under  water,  and  are  apparently  dead,  for 
fifteen  or  even  thirty  minutes.  To  this  end— 

1.  Treat  the  patient  instantly,  on  the  spot,  in  the  open 
air,  freely  exposing  the  face,  neck,  and  chest  to  the  breeze, 
except  in  severe  weather. 

2.  Send  with  all  speed  for  medical  aid,  and  for  articles 
of  clothing,  blankets,  etc. 

I.  To  Clear  the  Throat. 

3.  Place  the  patient  gently  en  the  face,  with  one  wrist 
under  the  forehead. 

(All  fluids,  and  the  tongue  itself,  then  fall  forwards,  and 
leave  the  entrance  into  the  windpipe  free. 

II.  To  Excite  Respiration. 

4.  Turn  the  patient  slightly  on  his  side,  and 

(I.)  Apply  snuff,  or  other  irritant,  to  the  nostrils  ; and 

(II.)  Dash  cold  water  on  the  face,  previously  rubbed 
briskly  until  it  is  warm. 

If  there  be  no  success,  lose  no  time,  but 

III.  To  Imitate  Respiration. 

5.  Replace  the  patient  on  the  face. 

6.  Turn  the  body  gently  but  completely  on  the  side,  and 
a little  beyond,  and  then  on  the  face  alternately,  repeating 
these  measures  deliberately,  efficiently,  and  perse* 
Veringly,  fifteen  times  in  the  minute  ouly. 

(When  the  patient  reposes  on  the  chest,  this  cavity  is 


APPENDIX. 


633 


compressed  by  the  weight  of  the  body,  and  expiration 
takes  place  ; when  it  is  turned  on  the  side,  this  pressure  is 
removed,  and  inspiration  occurs.) 

7.  When  the  prone  position  is  resumed,  make  equable 
but  efficient  pressure  along  the  spine,  removing  it  immedi- 
ately before  rotation  on  the  side. 

(The  first  measure  augments  the  expiration,  and  the 
second  commences  inspiration.) 

IV.  To  Induce  Circulation  and  Warmth,  continue 
these  Measures. 

8.  Rub  the  limbs  upwards,  with  firm  pressure  and 
energy,  using  handkerchiefs,  etc. 

9.  Replace  the  patient’s  wet  covering  by  such  other  cov- 
ering as  can  be  instantly  procured,  each  bystander  supply- 
ing a coat  or  a waistcoat.  Meantime,  and  from  time  to  time, 

V.  Again,  to  Excite  Inspiration, 

10.  Let  the  surface  of  the  body  be  slapped  briskly  with 
the  hand ; or 

11.  Let  cold  water  be  dashed  briskly  on  the  surface, 
previously  rubbed  dry  and  warm. 

Avoid  all  rough  usage.  Never  hold  up  the  body  by  the 
feet.  Do  not  roll  the  body  on  casks.  Do  not  rub  the  body 
with  salts  or  spirits.  Do  not  inject  smoke  or  infusion  of 
tobacco,  though  clysters  of  spirits  and  water  may  be  used. 

The  means  employed  should  be  persisted  in  for  several 
hours,  till  there  are  signs  of  death.” 


INDEX 


The  figures  refer  to  the  pages. 


A. 

Acceleration  of  motion,  185. 

Adirondack  watershed,  101. 

Adjustable  effluent  pipe,  364. 

Advantages  of  water  supples,  29. 

Air,  resistance  of,  to  a jet,  190. 

Air  valves,  523. 

“ vessels,  564,  565. 

Ajutage,  an,  213. 

“ inward  projecting,  218. 

“ vacuum,  214. 

Algae,  fresh  water,  129. 

Analyses  of  lake,  spring,  and  well  waters,  117. 
^ “■  mineral  waters,  143. 

“ u potable  waters,  table.  117, 138. 
u “ river  and  brook  waters,  118,  120. 

Analysis  of  impure  ice,  136. 

Anchoring  stand-pipes,  588,  589,  599. 

Angles  of  repose  of  masonry,  396. 

Angular  force  graphically  represented,  175. 

Apertures,  sluice,  201,  202,  203. 

Aquatic  life,  purifying  office  of,  132. 

“ organisms,  131. 

Arago’s  prediction  at  Grenelle,  106. 

Arjas  of  sluice  valves,  360. 

Artesian  wells,  105,  106,  108. 

“ “ temperature  of,  table,  127. 

Artificial  clarification  of  water,  159. 

“ gathering  areas,  100. 

“ pollution  of  water,  152. 

“ storage  “ “ 84,93,95,98,99. 

Asphaltum  batn  for  pipes,  475,  487,  490. 

Atlantic  coast  rainfall,  53. 

Atomic  theory,  162.  - 

Attraction,  capillary,  296. 

Atmospheric  impurities  of  water,  122. 

“ pressure,  182. 

Averag:  consumption  of  water,  44. 

B. 

Bacteria,  128,  130,  556^,  556^. 

Basins,  clear  water,  550. 

“ filter,  536,  537,  548,  551,  553,  555- 
infiltration,  537. 
tk  settling,  550. 

Batters,  front  of  masonry,  283,  385,  387,  424. 

Beams,  cylindrical,  strength  of,  600. 

Bends  and  branches,  272,  275,  478,  485. 
lk  coefficients  for,  table  of,  274. 

Blow-off  valves,  513. 

Boiler  at  Newport  water  works.  580. 

Boilers,  577,  578,  580. 

Bolts  and  nuts,  standard  dimensions,  624. 

Bolts  in  flang.s,  table  of,  462. 

Bolt-holes,  templet  for,  460. 

Boyden’s  hook  gauge,  297. 

Branches  and  bends,  272,  478,  484. 
composite  pipe,  484. 

“ formula  for  flow  through,  275. 

British  water  supplies,  37. 


Bucket-plunger  pump,  557,  567. 

Building  stones,  strength  of,  404. 

Bursting  pressure,  232. 

C. 

Caloric,  influence  of,  163. 

Canal  banks,  370. 

“ in  side  hill,  370. 

“ miner’s,  375. 

“ open,  370. 

*•  revetments  and  pavings,  371,  374. 

“ slopes,  371,  374. 

“ stop  gates,  373,  374. 

Canals  and  channels,  velocities  in,  302,  303,  304 
3°7,  3°8>  3IO>  3I2>  3x4j  3i8i  32°»  325»  3z6i  33^ 
373- 

Canals  and  rivers,  observed  flows  in,  table  o£ 
3°7»  373- 

Canals  and  rivers,  coefficients  for  flow  in,  308. 

“ irrigation,  370,  372,  373,  375,  3 76a. 

“ noted,  3735376a. 

“ water  supply,  370,  373,  375- 
Cantilever.  strength  of  cylindrical,  599,600,601. 
Capacity  for  filter  beds.  552,  554. 

Capillary  attraction,  296. 

Cast-iron  pipes,  451. 

kk  “ weights  of,  465,  468,  469. 

Cast  socket  on  wrought  pipe,  483. 

Casting  of  pipes,  452. 

Cement  joints  of  pipes,  482. 

,k  lined  pipe  , 479. 

“ lining  of  pipes  with,  481. 

“ mortar  for  lining  and  covering  pipes, 
487. 

“ tensile  strength,  623. 

Census  statistics,  31. 

Central  rain  system,  49. 

Chamber,  effluent,  358. 

influent.  366. 
walls,  369. 

Chandler’s.  Prof.,  remarks  on  wells,  140. 
Channels,  coefficients  for.  308,  308^,  373,  444. 
tk  depths  and  relative  volumes  and 
velocities,  328,  443,  444. 

“ experimental  flow  in,  307.  309,  312, 
314.  315  317,  321.  323-  326,  326a- 
“ flow  in,  experimental  data,  306,308. 

‘‘  “ open,  299,  370.  373,  375. 

“ formulas  lor  flow,  table,  309,  310. 

“ inclination  in.  304. 

“ influences  affecting  flow  in,3oS£, 316. 

“ mean  velocities,  312,  314.  316,  318^ 
319. 

“ ratios  of  surface  to  mean  velocity 
3*5,  443- 

“ surface  velocities,  313. 

“ velocity  of  flow  in,  303,  304,  307,  308, 
310.  314,  31S.  321,  328,  444- 
kk  velocities  of  given  films,  311. 

“ water  supph*,  protection  of,  431. 


INDEX. 


635 


Characteristics  of  pipe  metals,  470. 

Charcoal  clarification  ot  water,  535,  537. 

44  filters.  536. 

Check  valve,  367,  525. 

Chemical  clarification,  532. 

Choice  of  water,  587. 

Cities,  families  in  various,  32. 

“ persons  per  family  in  various,  32. 

“ population  of  various,  32. 

“ wjLter  supplied  to,  35,  36,  37. 
Clarification  of  water,  artificial,  159,  532,  535, 
537'  547- 

Clarification  of  water,  charcoal,  535,  537. 

4*  chemical,  532. 

44  44  natural,  149,  530,  532. 

Cleaning  of  filter  beds,  553. 

Clear  water  basins,  550. 

Climate  effects,  rainfall.  47. 

Coal  required  for  pumping,  581. 

Coating  (asphaltum)  pipes,  475,  487,  490. 
Cochituate  basin,  rain  upon,  72. 

Coefficients,  compound  tubes,  219,  220. 

“ convergent  tubes,  217. 

“ c\  table  of,  271. 

44  experimental,  198,  269^. 

44  “ table  of,  237. 

“ for  channelsdCutter’ 5,305,308^,373. 

44  “ circular  orifices,  196,  199,  203. 

44  44  current  meters,  325,  326,  32 6a. 

44  4t  flow  in  conduits,  444. 

44  44  hydrometers,  325. 

44  44  pipes,  table  of,  242,  268,  269#. 

44  44  rectangular  orifices,  198,  200, 

201,  202,  205,  206. 

44  “ service  pipes,  528. 

44  44  short  tubes,  214,  217,  218,  219, 

220,  227,  228. 

44  44  sluice  apertures,  201,  202,  203, 

205,  206. 

44  44  various  forms  of  tubes,  215, 

2l8,  219,  220,  221. 

44  44  weir  formulas.  287,  288. 

44  44  wide  crested  weirs,  294. 

44  formulas  for  pipes,  236,  242,  267, 

268,  269^,  269^/,  271. 

44  from  Castel,  200. 

44  44  Eytelwein  and  d’Aubuis- 

son,  256. 

44  44  General  Ellis.  201. 

44  4 4 L’Abbe  Bossut,  199. 

44  44  Lespinasse,  201. 

44  44  Michelotti,  198. 

44  44  Prony,  225. 

44  44  Rennie,  199. 

44  increase  of  in  short  tubes,  213. 

“ mi  234.  247- 

mean,  for  smooth  and  foul  pipes, 
248,  249.  267. 

44  of  efflux,  factors  of,  197,  208. 

44  table  of,  227. 

44  of  entrance  of  jet,  267. 

44  44  flow  from  channels,  305,  307, 

..  £ „ 3°8,  329'  373- 

4>  flow  in  pipes,  236,  242,  248,  495. 
4*  friction  of  earth-work,  345. 

44  44  44  table  of,  495. 

44  44  issue  from  short  tubes,  218. 

44  masonry  friction,  396. 

44  44  velocity  and  contraction  of 

orifice  jets,  208. 
practical  application  of,  197. 

44  range  of,  222. 

resistance  in  bends,  274. 
tables  of,  for  pipes,  236.  242,  248, 
495- 

variable  values  of,  210. 
Coffer-dams,  430 

Combined  reservoir  and  direct  svstems,  525. 
Commercial  use  of  water,  34. 


Compensation  flow,  86. 

“ to  riparian  owners,  94. 

Composite  branches,  pipe,  484. 

Composition  of  water,  the,  112. 

Compound  tubes,  218.  220. 

44  coefficients  for,  220. 
Compressibility  and  elasticity  of  water,  167. 
Concrete  conduit,  a.  438. 

44  foundations,  368. 

44  44  for  pipes,  487. 

“ paving,  355. 

44  proportions  of,  368. 

44  revetments.  429,  430. 

44  wall,  338,  348. 

Conduit  arch,  thrust  of,  437. 

44  data,  443,  444,  445. 

44  masonry  to  be  self-sustaining,  437. 

“ of  concrete,  438. 

44  “ wood,  439,  441. 

44  shells,  434 
Conduits  and  pipes.  223. 

44  backing  of,  438. 

44  capacities  of  noted,  445. 

44  coefficients  for,  444. 

14  examples  of,  74,  431,  435,  438,439,445. 
‘4  exposure  to  frost,  437. 

44  formulas  for  flow  in,  442,  443,  445* 

44  foundations  for,  433. 

44  locked  bricks  for,  435. 

44  masonry.  431. 

*4  mean  radii  of.  441,  442. 

44  protection  from  frost,  436. 

44  stop-gates  in.  436. 

44  transmission  of  pressure  in,  436. 

44  under  pressure,  435,  439. 

44  ventilation  of,  434. 

Confervae,  129. 

Construction  of  embankments,  348. 

4 4 44  filter  beds,  548. 

Consumption  of  water,  34,  43,  503. 

Contents  of  pipes.  504. 

Core  of  an  embankment,  348. 

Cornish  pump,  557,  563. 

Costs  of  pumping  water.  574,  575. 

Crib-work  foundations,  385. 

44  weir,  384. 

Croton  basin,  rainfall  upon,  72. 

44  Dam,  94. 

44  Aqueduct,  74,  431,  444,  445, 

Curbs,  stop- valve.  515. 

Current  meters,  322,  325.  326,  32 6a. 

44  meter  rating.  325,  325^,  326. 
Curved-face  wall,  421. 

Cut-off  wall  embankment,  338,  348. 

Cycle,  low,  rainfalls.  69,  77,  78. 

Cylindrical  cantilevers,  strength  of,  599,  600. 

44  penstock,  440. 

44  pressures  in,  593. 

44  thickness  of,  448,  450,  486,  488,  489. 

“ tubes,  222. 

D. 

Dams,  aprons  of.  383,  387,  388. 

44  caps,  .386. 

‘4  discharges  over,  290;  298^,  378,  380,  38$ 
388. 

44  forms  of.  94,  382,  384,  391. 

44  ice  thrust  on,  386. 

44  thickness  of,  387. 

Darcy-Pitot  tube  gauge,  322. 

Data  from  existing  conduits,  445. 

Debris,  floating,  530. 

Decimal  parts  of  an  inch  and  foot,  457. 
Decomposing  organic  impurities,  127. . 
Densities  and  volumes  of  water,  relative,  164- 
Depths  of  pipes,  501,  502. 

44  on  weirs,  228.  290,  298a. 

Desmids,  in  fresh  ponds,  129. 


636 


INDEX. 


Details  of  stop-valves,  513. 

Diagonal  force,  175. 

Diagrams  of  pumping,  42. 

“ “ rainfall,  55,  57,  59. 

“ “ stand-pipe  stabilities,  597. 

Diameter  of  sub-mains,  507. 

44  4*  supply-main,  500. 

Dimensions  of  existing  canals,  373. 

44  44  filter-beds,  554. 

44  44  retaining  walls,  420. 

Direct  pressure  system,  525,  590. 

Discharges  of  pipes,  498,  500. 

“ over  waste-weirs,  378,  381, 

44  “ weirs,  288,  290,  298#. 

Distribution  pipes,  493,  495,  503,  505,  506,  508. 
Domestic  draught  of  water,  34,  508. 
Drainage  from  given  areas,  67,  75. 

Draught,  variations  in,  41. 

Drowning,  resuscitation,  632. 

Duplicate  pumping  machinery,  590. 
Duplication  in  pipe  systems,  510. 

Duty  of  pumping-engines,  574,  576,  580,  583. 
Dwellings  in  various  cities,  32,  33 a. 

Dykes,  canal  and  river,  372. 


E. 


Earth  and  rock,  porosity  of,  102. 

“ embankments,  333,  347,  348,  353,  370. 

41  evaporation  from,  89,  90. 
pressures  against  walls,  408. 

Eastern  coast  rain  system,  50. 

Economy  of  high  duty  of  pumping-engines, 
t 579.1  581. 

“ 44  skillful  workmanship,  369. 

Eddies,  in  weir  channels,  292. 

Effect,  mechanical,  of  the  efflux,  225. 

Effluent  chambers,  358. 

44  pipe,  adjustable,  364. 

“ u ice  thrust  upon,  358. 

Efflux,  equation  of,  211. 

44  factors  of  the  coefficient,  197. 

44  from  pipes,  coefficients  of,  196,  227. 

“ sluices,  201,  203,  205,  206,  207. 

“ mechanical  effect  of,  225. 

peculiarities  of  jet,  207. 

“ volume  from  short  tubes,  194,  210,  214. 
Elasticity  and  compressibility  of  water,  167. 
Electric  current  meters,  326,  326^. 

41  meter  register,  325^; 

Elementary  dimensions  of  pipes,  504. 
Elements,  the  vapory,  45. 

Embankment,  a light,  353. 

“ core  materials,  339, 342,  348, 354, 


41 


*4 

(4 

<4 


359* 

cut-off-  walls,  330,  338,  348. 
example  of,  347. 
failures,  334. 
fine  sand  in,  353. 
foundations,  335,  337,  338. 
frost  covering,  350. 
gate  chambers,  357, 358. 
masonry  faced,  354. 
materials,  coefs.  of  friction,  345. 
44  frictional  angle  of, 
345- 

4 proportions  of,  340, 


349- 

weights  of,  341. 
pressures  in,  343. 
puddle  wall,  351,  354. 
puddled  slopes,  352,  356,  370. 
revetted,  149,  354,  370. 
sheet-piling  under,  339. 
site,  reconnaissance  for,  347. 
slope-paving,  350,  333. 
slopes,  344,  345,  350,  355. 
sluices,  355,  356,  358. 
soils  beneath,  337. 


Embankment,  springs  under  foundation,  337, 

4‘  substructure,  336. 

44  siphon  waste-pipe,  358. 

44  test  borings  at  site,  336. 

treacherous  strata  under,  338. 
Embankments,  canal,  370. 

4‘  effect  ot  waves  on,  388. 

44  Indian,  334. 

44  reservoir,  333. 

Energy  of  jet,  225,  276. 

England,  supply  per  capita,  37. 

Equation  of  motion,  186. 

“ 44  resistance  to  flow,  233. 

Equilibrium  destroyed,  r7o,  300. 

Equivalent  heads  and  pressures  of  water,  614. 
Errors  in  application  of  formulae,  252,  257. 

44  44  weir  measurements,  296. 

Estimates  of  flow  of  streams,  78,  94. 

European  infiltration,  544. 

“ water  supplies,  36. 

Evaporation,  effect  upon  storage,  93. 

44  examples  of,  90. 

44  from  earth,  89,  no. 

*4  “ reservoirs,  94. 

4*  44  water,  88,  89. 

“ phenomena,  87. 

44  ratios  of  table,  92. 

Evaporative  power  of  boilers,  578,  580. 
Examples  of  conduits.  431,  438,  439. 

Expansion  of  water,  164,  166. 

Expansions  of  pipe  metal,  458. 

Experimental  channel  data,  306. 

coefs.  for  hydrometers,  325. 

44  44  pipes,  236,  241. 

“ flow  in  channels,  306,  307,  309, 

3I2i  3>4i  3*5*  3i7»  321,  323,  32? 
326a. 

44  hose  streams,  520. 

Experiments  with  weirs,  284,  288,  291,  294. 

44  by  Fairbairn  on  cylindrical 

beams,  600. 

44  by  Bailey,  240. 

44  4 * Bossut,  199. 

44  44  Eytelwein,  220,  222. 

44  4 4 Eytelwein’s  coefs.,  222. 

44  4>  Castel,  200,  217. 

44  41  Couplet,  239. 

44  4 4 Darcy,  237,  240. 

44  44  Du  Buat,  238. 

44  4 4 Ellis,  201. 

44  44  Fanning,  238. 

44  4‘  Lespinasse,  201. 

44  4*  Micnelotti,  198. 

44  44  Provis,  198. 

44  44  Rennie,  199,  239. 

44  44  Smith,  236. 

44  with  compound  tubes,  220. 

44  44  current  meter,  325a. 

44  44  cylindrical  beams.  600. 

44  orifices,  198,  199,  200,  201, 

44  short  tubes,  217,  219,  220, 
Exposed  stand-pipes,  598. 

Exponents,  271^,  271  d,  309. 


F. 

Faced  revetments,  429. 

Factors  of  safety,  449.  451,  453,  485,  486,  593 
Failures  of  embankments,  334. 

44  44  walls,  427. 

Falling  bodies,  187,  190. 

Families  in  various  cities,  32. 

Fascine  revetments,  371. 

Filter-beds,  547,  548,  551,  553,  554. 

44  capacity  of,  552,  554,  556^. 

“ cleaning  of,  553,  5565. 

“ construction  of,  548,  551,  554. 

“ ice  upon,  556. 

“ protection  of,  548,  555. 

“ temperature  of,  555. 


INDEX. 


637 


Filter-beds,  vegetable  growth  in,  555. 

Filters,  Atkin’s,  536. 

Fire  draught  of  water,  34,  506,  508.  510. 

44  extinguishment,  reserve  for,  44. 

44  hydrants,  510,  516.  519,  521,  5*2. 

44  losses,  effect  of  water  upon,  26. 

44  service,  493,  588,  589,  591. 

“ 44  head  desirable  lor,  493. 

44  supplies,  diameters  of  pipes  for,  510. 
f*  ish  screens,  365. 

Flanges,  diameters  of  valve;  462. 

44  of  cast-iron  pipes,  462. 

V 'ash-boards,  378. 

flashy  and  steady  streams,  71. 

Flexible  pipe-joints,  463. 

Floats,  double,  gauge,  326. 

*4  maximum  velocity,  328. 

44  mid-depth.  326. 

Flood  flow,  65,  98. 

44  volumes,  62,  65,  66,  67,  75,  380,  381. 

44  ratios  of,  to  rainfalls,  62. 

44  seasons  of,  68. 

Flow,  available  for  consumption,  94. 

44  coefficients  of,  in  pipes,  230,  236,  242, 
248,  495. 

“ compensation,  86. 

44  equivalent  to  given  depths  of  rain,  81. 

44  from  Croton  and  Cochituate  basins,  73. 
44  4*  different  surfaces,  77. 

44  44  Sudbury  basin,  83^. 

44  gauged  volumes  of,  277. 

44  gravity  the  cause  of,  299. 

44  in  channels,  experimental,  306,  307,  309, 
312,  314,  315,  317,  321,  323,  326,  326a. 

44  in  pipes,  frictional  head,  225.  233,  250, 
252,  253,  254,  255,  266,  268,  270,  495, 
508,  528. 

in  pipes,  velocity  formulas,  249,  250,  252, 
254,  259.  263,  266,  267,  268,  270,  273. 
in  seasons  of  minimum  rain,  69. 
increase  and  decrease  of,  86. 
influence  of  absorption  and  evaporation 
upon,  68. 

minimum,  mean  and  flood,  75. 
of  streams  and  channels,  65,  299. 

44  water,  184. 
over  a weir,  280. 

per  acre  and  per  mile  from  given  rains, 
82. 

periodic  available,  69,  101. 
resistance  to,  in  channels,  232,  300. 
sub-surface  equalizers  of,  70. 
summaries  of  monthly  statistics  of,  71. 
through  orifices,  194. 

44  pipes,  223,  495,  508,  560. 

*4  short  tubes,  213. 

44  sluices,  pipes  and  channels,  161. 
Fluctuations  of  streams,  73,  83^,  101,  319. 
Flush  hydrants,  519,  521. 

Foot  and  inch,  equivalent  decimal  parts  of,  457. 
Force,  loss  of,  in  pipes,  224. 

44  percussive,  of  particles,  221. 

Forces,  angular  176. 

44  equivalent.  172. 

44  graphically  represented,  175. 

Formula,  efflux  from  an  orifice,  196,  209,  211. 

44  44  44  short  pipes,  215. 

44  for  area  of  sluices,  361. 

44  44  capacity  of  air  vessel,  566. 

44  44  coal  tor  pumping,  581. 

44  “ current  meter  coefficient,  326. 

44  44  curved-face  walls,  421. 

44  44  depth  upon  a weir.  286. 

44  44  duty  of  pumping-engines,  576. 

44  44  earth  pressures  upon  walls,  410, 

412,413.415,416. 

44  energy  of  jets,  226. 

u 44  hydraulic  mean  depth,  235,  303, 
441- 


Formula  for  inclination  in  channels,  304. 

44  4*  pipe  coefficients,  236,  242,  267, 

271,  271  d. 

44  k4  power  consumed  in  pumps,  560, 
561. 

44  44  power  to  produce  flow  in  pipes, 

561. 

pressure  in  pipes,  447. 

44  44  44  on  submerged  walls, 

393-  394- 

44  44  relative  volumes  and  tempera- 

tures of  water,  166,  167. 

44  44  resistance  in  channels,  301,  303. 

44  44  submerged  orifice,  209. 

44  44  surcharged  pressure  walls,  414, 

416,  423. 

44  44  thickness  of  walls,  399,  413,  421. 

44  44  triangular  notch  w'eir,  294. 

44  44  velocity  in  channels,  303,  304, 307, 

308,  314,  320,  325,  326. 

44  44  volume  at  given  temperature, 

165. 

44  44  weight  of  cast  pipes,  460,  465, 

467. 

44  gravity  and  motion  due  to,  186,  187, 
190. 

44  heights  and  times  of  falling  bodies, 
186,  187,  190. 

44  of  factor  of  safety,  593. 

44  44  M.  Chezy,  pipes.  252,  270. 

44  44  power  to  open  sluices,  363,  364. 

44  44  pressure  in  cylinders,  448,  593. 

44  4“  resistance  of  tanks,  589. 

44  44  weight  of  anchorage  of  tanks,  589. 

44  44  Weisbach,  257. 

44  44  wind  and  force  on  tanks,  588. 

Formulas,  coefficients  for  weir,  284,  287,  288, 
289,  291,  293,  294. 

44  for  aiameters  of  pipes,  251,  266,  269, 
270,271,  498, 

44  for  flood  volumes,  66,  67,  320,  380. 

44  44  flow  in  conduits,  442.  443. 

“ “ u “ pipes,  254,  257,  271,  4Q8. 

44  44  44  origin  of.  229. 

44  44  4 * through  bends,  272. 

44  44  44  *4  branches,  275. 

44  44  44  44  channels,  303,  304. 

307,  308,  310,  314, 
320,  325,  326. 

44  44  gauging  streams,  320. 

44  44  head,  pipes,  233,  250,  2 66,  268, 

270  271,  404. 

44  44  lengths  of  pipes.  269,  270. 

44  44  pipes,  various  compared,  274. 

44  44  resistance  to  flow.  230,  233,  234, 

250,  254,  256,  266,  268,  270,  272, 
271,  275,  528. 

44  44  shafts,  617. 

44  44  thickness  of  pipes,  table,  4 66, 

486,  487. 

44  44  thickness  of  cast  pipes,  453,  454. 

44  44  44  44  wTOught  pipes,  448, 

450,  486. 

44  44  velocity,  pipes,  248,  249,  250, 

259,  266,  267,  268,  270,  272,  498. 
44  44  velocities  in  channels,  302,  303, 

304,  307,  308,  310,  312,  314,  320, 
325,  326,  330. 

44  44  volume,  pipes,  250,  254,  266,  498. 

44  44  water  ram,  449 

44  44  44  storage  ratios,  95. 97. 

44  44  weir  volumes.  282,  283,  284,  286, 

287,  293,  298^.  379,  380. 

44  44  wide-crested  weirs,  293. 

44  manv  incomplete.  252. 

44  misapplication  of,  316. 

44  of  thickness  o:  stand-pipes,  593,  595, 

509,  600. 

u stability  of  masonry,  395,  -97,  398. 


638 


INDEX. 


Formulas,  velocities  and  times  of  falling  bod- 
ies,  186,  187,  190. 

Foundation,  concrete,  386. 

44  embankment,  335. 

44  for  pipes,  487. 

44  of  conduits,  433. 

44  44  gate-chambers,  367. 

“ 44  walls,  395,  406,  407. 

44  under  water,  430. 

Foundations,  angles.  396,  423. 

“ frictions  on,  396. 

“ of  stand-pipes,  586. 

Fountain,  use  of  water,  34. 

Francis,  Jas.  B.,  experiments  with  weirs,  284. 

“ tubes.  517. 

Frankland’s  deh  .ition  of  polluted  water,  137. 
Friction,  coefficient  of  masonry,  396,  444,  495. 
44  in  pipes,  230,  234,  250,  269,  495,  508,  528. 
“ of  ice  on  canals,  372. 

“ 44  pumping  machinery,  578. 

Frictional  head,  formulas  for,  225,  233,  250,  252, 
253,  254,  255,  266,  268,  270,  495,  508,  528. 
Frost  curtain.  367. 

“ disintegration  o mortar  by,  436. 

4‘  protection  of  conduits  from,  436. 

Fuel,  expense  for  pumping,  581. 

“ required  for  pumping,  575. 

Fungi,  microscopic,  129. 


a. 

Galleries,  infiltration,  539,  540. 

Gate  chambers,  357,  367. 

“ hydrants,  522. 

Gates,  stop,  canals,  374. 

Gauge,  Darcy-Pitot  tube,  322. 

“ Darcy’s  double  lube,  322. 

“ double  float,  326. 

44  formulas,  319. 

“ hook,  Boyden’s,  296,  297. 

44  maximum  velocity  float,  328. 

44  mid-depth  float,  326. 

44  Pitot  tube,  320. 

“ rain,  63. 

44  rule,  for  weirs,  298. 

44  tube,  317. 

44  tube  and  scale,  weirs,  298. 

44  Woltman’s,  322. 

Gauges  and  weights  of  plate  iron,  487,  488. 
Gauging,  hydrometer,  316,  321. 

4'  of  mountain  streams,  296. 

4 4 4 4 rainfall,  62. 

44  44  rivers,  318,  319. 

Gears  for  sluice-gates,  359. 

General  rainfall,  46. 

Geological  science,  application,  106,  108. 
Granular  stability  of  masonry,  402. 
Graphical  representation  of  force,  175,  402. 
Gravitation  system,  588,  590. 

Gravity,  185,  187,  189,  190,  230,  299. 

44  centre  of,  177,  391,  402. 

Great  rain-storms,  61. 

Grouped  rainfall  statistics,  52. 

Grouting,  353,  369. 


H. 

Hardening  impurities,  125. 

Hardness  of  water,  125. 

Head,  desirable  for  fire-service,  493. 
4 4 effective  in  pipe-system,  493. 

44  how  to  economize,  276. 

44  loss  by  friction,  493. 

44  subdivisions  of,  225. 

44  value  of,  493. 

Heat,  units  of,  utilized,  578. 
Heights,  falling  bodies,  187,  190. 

44  of  waves,  388. 


Hirsch’s  sugar  test  of  water,  150. 

Helpful  influence  of  water  supplies,  27. 
Hook  gauge,  Boyden’s,  296. 

44  44  use  to  detect  fluctuations,  319 

Horse-power  of  effluent  jet.  225. 

44  44  to  produce  flow,  561. 

Hose  streams,  510,  520. 

44  use  of  water,  34. 

Hudson  river  basin,  roi. 

44  valley  rainfall  in.  53. 

Hydrants,  516,  517,  519,  522. 

44  high  pressures,  522. 

44  streams,  520,  585. 

Hydraulic,  excavation,  376. 

44  masonry,  369. 

44  mean  depth,  235,  303,  441. 

44  44  radius,  236,  445. 

44  power  pumping,  589,  591. 

44  proof  of  pipes,  477. 

Hydrometers,  Castellis’  and  others,  326. 

44  coefficients,  325,  326,  326a. 

44  gauging  with,  316,  325,  326. 


I. 

Ice  covering  of  canals,  372,  386. 

44  impure,  in  drinking  water,  135, 

44  thrust,  358,  386. 

Impounders,  flow  to,  86. 

Impounding  of  water.  144. 

Impregnation  of  water,  141.  152. 

Impurities  of  water,  112, 138. 

44  44  4 agricultural,  134. 

“ *4  44  atmospheric,  122. 

“ 44  4*  manufacturing,  134* 

44  4 4 44  mineral,  115,  133. 

4 4 4 4 “ organic,  116,  127,  130. 

44  44  44  sewage,  134. 

44  44  44  sub-surface,  123. 

44  44  deep  wells,  125. 

Inch  and  foot,  decimal  parts  of,  457. 
Incidental  advantages  of  water  supplies,  29. 
Inclination  in  channels,  235,  304.  371,  372,  373 
Increase  in  use  of  water,  39. 

Indian  embankments,  334. 

Indicator,  stop-valve,  361. 

Infiltration,  537.  540,  543,  544,  546. 

Influent  chamber,  366. 

Infusoria,  130. 

Inhabitant,  supply  per.  40. 

Inspections  of  stand-pipe  materials,  590,  601. 
Intercepting  well,  102,  546. 

Interchangeable  pipe-joints,  469. 

Introduction  of  filters,  551. 

Insurance  schedule,  29. 

Investment,  value  of  water  supplies  as  an,  3^ 
Iron,  gauges  and  weights,  488. 

44  sluice  valves,  360. 

44  work,  varnishes  for,  474,  476,  489. 
Irrigation  canals,  370,  372,  373,  376a. 

Isolated  weirs,  383. 


J. 

Jets,  21 1,  267. 

44  coefficients  of  velocity  and  contraction 
196,  198.  208. 

44  'contraction,  208. 

44  varying  forms  of.  211. 

44  velocity,  208. 

Joints,  mortar  for  pipes.  487. 

44  of  cast  pipes,  457,  461,  463,  469. 


K. 

Rutter’s  coefficients  for  channels,  305,  306 


INDEX. 


639 


L. 

Lake  waters,  142. 

Lakes,  150. 

Laying  of  wrought-pipes,  482. 

Lead,  joint,  468. 

Lead-pipes,  629,  630,  631. 

Lengths  ot  waste-weirs,  381. 

Level,  use  of,  in  gauging,  319. 
Leverage  of  water-pressure,  397. 

“ resistance  of  walls,  402. 

44  stability  of  masonry,  39 7. 

Life  of  dams,  388. 

Limiting  pressure  in  masonry,  686. 
Lining  of  pipes,  cement,  481. 
Logarithms  of  ratios,  121. 

Loss  by  evaporation,  87. 

44  from  reservoirs.  84. 

44  of  head  by  friction,  276,  493. 


M. 

Mains  and  distribution  pipes,  446. 

44  power  to  produce  flow  in,  561. 
Masonry,  angles  of  repose,  396. 

44  coefficients  of  friction,  396. 

41  concrete,  429,  430. 

44  conduits,  431,  437. 

44  coverings  of  waste  pipes,  357. 

44  examples  of  pressure  in,  392,  397, 
403,  406,  412. 

“ faced  embankment,  354,  409, 418,  423, 

425- 

*•  frictional  stability  of,  402. 

44  granular  stability  of,  402. 

44  hydraulic.  369. 

44  limiting  pressures  in,  403,  404,  586. 

44  step  and  curve  batters,  383,  385,  387, 
424. 

44  weight  leverage  of,  398. 

44  44  of,  395,  397,  404,  420. 

Materials,  embankment,  339,  341,  342,  345,  348, 
35^  354- 

44  cf  stand-pipes,  590. 

Maximum  velocities  of  flow,  508. 

Mechanical  energy  of  effluent  water,  225. 
Metal  plates,  tests  of,  590,  591. 

Metals  for  stand-pipes  thickness,  595,  596,  597, 
598,  601. 

44  pipe,  470,  472. 

44  tenacities  ot  wrought,  451,454,  486,  491. 
Meters,  current,  322,  325,  326,  32 6a. 

Metric  weights  and  measures.  611. 
Microscopical  examinations,  138,  471. 

Mineral  impurities,  115,  138,  530. 

44  springs,  142,  143. 

Miners1  canals,  375. 

Misapplication  of  formulae,  316. 

Mississippi  valley,  rainfall  in,  54. 

.Molecular  theories,  162,  296. 

Molecules,  185. 

Moment  of  earth  leverage,  412. 

Monads,  130^,  556c. 

Monthly  and  hourly  variations  in  the  draught, 
n 41- 

44  fluctuations  in  rainfall,  56. 

Mortar  for  lining  and  covering  pipes,  487. 
Motion,  acceleration  of,  185. 

44  equations  of,  186. 

44  of  a piston,  562. 

44  of  water,  184,  194. 

44  parabolic,  of  a jet,  187. 

Moulding  of  pipes,  451. 

Moulinets,  323,  326. 

Municipal  control  of  water  supplies,  28. 


N. 


Natural  clarification,  149,  532. 

44  laws,  uniform  effects  of,  61. 


Necessity  of  water  supplies,  25. 
Noctos,  129. 


O. 

Ohio  river  valley,  rainfall  in,  54. 

Open  canals.  370. 

Ordinary  flow  of  streams,  80. 

Organic  impurities,  80,  113,  116,  531,  532, 
Organisms,  129,  131,  133. 

Orifice,  submerged,  209. 

44  volume  of  efflux,  211. 

Orifices,  classes  of,  194. 

44  coefficients  for  circular,  196,  198,  199, 
203. 

44  coefficients  for  rectangular,  198,  2oor 
201,  202,  205,  206. 

44  convergent,  212. 

44  44  path  toward,  194. 

44  cylindrical  and  divergent,  212. 

44  experiments  with,  198,  199,  200,  201. 

44  flow  of  water  through,  194,  210. 
Orifice-jet,  form  of  submerged,  195. 

44  peculiarities,  207. 

4‘  ratios  of  minimum  section,  195. 

44  variations,  204. 

44  velocity,  196,  208,  209. 


P. 


Pacific  coast  rainfall.  54. 

Painting  iron  work.  476.  478  489. 

Parabolic  path  of  jet,  187. 

44  segment,  application  to  weir  vol- 
umes. 282. 

Partitions  and  retaining  walls,  390. 

Paving,  concrete,  355. 

44  embankment  slope,  348,  350,  354,  355 
356,  358. 

Peculiar  water  sheds,'7i. 

Penstock,  cylindrical  wood,  439,  441. 
Percentages  of  rainfall  on  river  basin,  73,  83^. 
Percolation  from  reservoirs.  85.  94. 

ot  rain,  10^,  105,  111. 

44  under  retaining  walls.  406. 
Permanence  of  water  supply  essential,  585. 
Persons  per  famil}\  32,  33^. 

Physiological  effects  of  the  impurities  of  water, 


114. 

i4  office  of  water,  25. 

Pipe,  adjustable  effluent,  364. 

44  and  conduit,  223. 

44  branches,  composite.  484. 

44  coverings,  481,  487,  489,  501,  502. 

44  distribution,  493,  495,  503,  505,  506,  508. 
44  joints,  cast,  457,  461,  463,  460,  483. 

44  44  44  hub,  on  WTOugnt,  483. 


44  dimensions  of,  451,  459,  462. 

44  flexible,  463,  464. 

44  interchangeable,  469. 
metals,  470,  472. 

44  wrought  strength  of,  451,  454, 
<68,  490,  491. 

resistance  at  entrance  to,  226. 
shells,  wrought,  thickness  of,  448,  485, 
486. 

systems,  duplication  in,  510. 

“ illustrations,  493,  510. 
testing  press,  477. 
walls,  resistances  of.  227,  228. 

Pipes  and  sluices,  embankment,  355. 
casting  of,  452. 
cast-iron,  447,  451,  452. 

4*  thickness  of,  453,  454,  455,  466. 
44  weights  of,  465,  468,  469. 
cement-ioints,  482. 

44  lined.  479,  481. 

coefficients  of  friction,  236,  242,  248,  495. 


640 


INDEX 


Pipes 

u 

u 


, concrete  foundations  for,  487. 
contents  of,  504. 
direct  pressure  systems,  525. 
depths  ot,  501,  502. 

“ sockets,  459,  461. 
diameters  for  fire  supplies,  510. 
elementary  dimensions  of,  504. 
expansions  of,  458. 
flanges,  table  of,  462. 
formulas  for  thickness  of  cast,  453,  466. 

" *•  velocity,  head,  volume  and 


diameter,  224,  266,  268,  270,  271  d,  498. 

“ formulas  for  weights  of  cast,  465. 

“ friction  in,  222,  495,  508. 

“ hydraulic,  proof  of,  477. 

“ lead  in  joints,  468. 

“ mains  and  distribution,  446. 

“ molding  of  cast-iron,  451. 

“ plan  of  a system,  505. 

“ preservation  of  surfaces,  473,  480,  489, 
491- 

“ proof  tests,  476. 

“ relative  capacities  of,  498,  500. 

“ service,  527,  528. 

“ short,  223. 

“ square  roots  of  fifth  powers  of  diam- 
eters, 499,  500. 

“ static  pressure  in,  446. 

“ sub-coefficients  of  flow  (1/),  271. 

“ temperatures  of  water  in,  50-2. 

“ thickness  of  cast,  453,  455,  456. 

“ “ wrought,  447. 450, 486, 488. 

“ tuberculated,  247,  248. 

^ volumes  of  flow  from,  223,  225,  495. 

“ water-ram  in,  448,  449. 

“ wood,  491. 

“ wrought-iron,  479. 

“ “ plates  for,  490. 

Piping  and  water  supplied,  38. 

“ ratio  to  population,  35. 

Piston  motion,  562. 

“ pump,  557,  558. 

Pitot  tube  gauge,  320. 

Plant  and  insect  agencies,  147. 

“ growth  in  reservoirs,  145. 

Plates  for  wrought  pipes,  490. 

Plunger  pump,  557,  563. 

Pluviometer,  63. 

Polluted  water,  definition  of,  137. 

Polluting  liquids,  inadmissible,  154. 

Pollution  question,  156. 

“ of  water,  artificial,  152. 

Population,  and  relation  of  supply  per  capita. 


4°. 

*•  of  various  cities,  32,  33 a,  33 o. 
Portland  cement  for  joint  mortar,  487. 

Porosity  of  earths  and  rocks,  102. 

Post  hydrants,  517. 

Power  consumed  by  variable  flow  in  a main, 
560. 

“ consumed  in  pumps,  560,  561. 

“ required  to  open  a valve,  361,  364. 
Practical  construction  of  water-works,  333. 
Precautions  for  triangular  weirs,  295. 
Precipitation,  influence  of  elevation  upon,  50. 
Preservation  of  pipe  surfaces,  473,  480,  489, 


491. 

Press  for  testing  pipes,  477. 

Pressure,  a line  a measure  of,  174. 

“ conduits  under,  435,  439,  440. 

“ conversion  into  mechanical  effect, 

230. 

“ conversion  of  velocity  into.  227. 

“ direction  of  maximum  effect,  176. 

“ in  stand-piDes,  593. 

“ leverage  of  water,  397. 

“ of  earth  against  walls,  408,  410,  413, 
415,  416. 

**  of  water,  168,  172,  446. 


Pressure  of  water  in  a conduit.  437. 

proportional  to  depth,  169,  172. 
resultants,  391,  400,  41 1.  418,  423. 
sustaining  upon  floating  bodies,  179 
transmission  o£  183. 
upon  a unit  of  surface,  171. 
upon  surfaces,  391,  393. 
weight  a measure  ot,  173. 

Pressures,  artificial,  171. 

at  given  depths,  table,  172. 
atmospheric,  182. 
centres  of,  177. 
convertible  into  motion,  184. 
examples  in  walls,  403,  404. 
from  inclined  columns  of  watei 
170. 

freat,  in  hydrants,  522. 

orizontal  and  vertical  effects,  177. 
in  embankments,  343. 
limiting  in  masonry,  403,  404. 
static  in  pipes,  446,  448. 
total  of  water,  176. 
upon  circular  areas,  179,  446. 

“ curved  surfaces,  178,  446. 
upward  upon  submerged  lintela. 
181. 

Prism  of  weir  volumes,  282. 

Processes  for  preserving  iron,  474.  476,  489. 
Profile  across  the  United  States,  48. 

‘ of  retaining  walls,  407. 

Properties  of  water.  113. 

“ “ embankment  materials,  343. 

Proportions  of  ‘ “ 349. 

Protection  of  filter  beds,  548,  555. 

“ water  supply  channels,  431. 
Protective  value  of  stand-pipes,  586. 

Pronv’s  analysis  of  experiments,  *55. 

Proving  press,  hydraulic,  477. 

Puddled  canal  bank,  370. 

Puddle-walL,  351,  354. 

“ slope,  352,  356,  370. 

Pump,  bucket-plunger,  557,  567,  603. 

“ Cornish.  557.  563. 

“ piston,  557.  558. 

“ plunger  557,  563. 

“ rotary.  558, 

'■  valves.  558,  563,  566,  568,  S69,  570,  57*. 
Pumping  ot  water.  557. 

“ “ diagram  of,  42. 

engines,  557.  567,  573,  577. 

“ adaptability  of,  584. 

“ cost  of  supplies,  575,  582. 

“ “ attendance,  575, 589. 

duties,  574,  579, 580, 581, 583. 
“ fuel  expenses.  581,  5S2. 

“ principal  divisions,  577. 

“ special  trial  duties.  580. 

“ values  compared,  583. 
machinery.  591,  392.  603. 

“ contingencies,  586. 

'•  duplicate,  608. 

“ for  direct  pressure,  590 
591. 

“ Manchester,  603,  609. 
system.  607,  608. 
water,  cost  of,  574,  575. 

Pumps,  power  consumed  in,  560,  561. 
types  of,  557. 

variable  flow  through,  559. 

Purity  of  water,  chief  requisites  tor.  144. 

*■  “ preservation  of,  148. 

Purification  of  water,  natural,  134.  157,  158. 

Q. 

Quality  of  water,  sugar  test  of,  159. 


Radii,  mean  of  conduits.  441.  442. 


INDEX. 


641 


Rainfall  along  river  courses,  51. 

“ and  equivalent  flow.  8a. 

“ diagrams  01,  55,  57,  59. 

“ gauging,  62. 

“ general,  46 

“ in  the  U nited  States,  53. 

“ influences  affecting,  60. 

“ low  cycle.  69,  77.  78. 

“ monthly  fluctuations  in,  56. 

“ on  Cochituate  Basin,  72,  73. 

“ “ Croton  Basin,  83a. 

“ ratio  of  floods  to,  62. 

*l  ratios,  72,  100,  101. 

“ secular  fluctuations  in,  60. 

“ sections  of  maximum.  47. 

“ statistics,  review  of.  46,  72,  83a. 

“ volumes  of  given,  62,  83a. 

Rainfalls,  flow  from  given,  per  acre  and  per 
mile,  82. 

Rain-gauge,  63. 

Rains,  river  basin,  50,  72. 

Rain,  water  in  pipes,  449. 

Rates  of  fire  supplies.  506. 

Rating  of  current  meters,  32s,  326,  328a. 

Ratios  of  evaporation,  91. 

'■  “ monthly  consumption,  43. 

“ “ “ flow  in  streams,  76,  101. 

“ “ qualification  of  deduced,  99. 

“ “ rainfall,  flow,  etc.,  table,  72,  100, 101. 

“ “ standard  gallons,  120. 

“ surface  to  mean  velocities  in  chan- 
nels, 315. 

“ “ variable  delivery  of  water,  564. 

“ “ water  storage,  95,  97. 

Reaction  and  gravity,  opposition  of,  230. 
Reconnaissance  for  embankment  site,  346. 

“ of  a water-shed,  78. 

Rectangular  and  trapezoidal  walls,  moments 
of,  399. 

Rectangular  weirs.  277. 

Reducer,  pipe,  478. 

Register,  electric  current  meter,  325a. 

Relation  of  supply  per  capita  to  total  popula- 
tion, 40. 

Relative  values  of  h,  k\  h" x 253. 

“ discharging  capacities  of  pipes,  498, 
500. 

“ rates  of  domestic  and  fire  draughts, 
508. 

Repulsion,  molecular,  296. 

Reserve  for  fire  service,  44. 

Reservoir,  coverings,  556, 

" distributing,  334,  353,  354,  356,  358. 
embankments,  333, 335, 341, 345,  348, 
353- 

“ storage,  surveys  for,  347. 

44  strata  conditions  in,  146. 

“ system,  598. 

“ revetments,  354. 

Reservoirs,  failure  of,  334. 

44  Indian,  334. 

11  storage,  84,  87,  93,  95,  97,  101,  347. 

44  subterranean,  105. 

“ waves  upon,  388. 

Resistance  of  the  air  to  a jet,  190. 

44  at  entrance  to  a pipe,  266. 

44  of  maso  ;ry  revetments,  417. 

44  to  flow,  measure  of,  230,  231. 

Resistances  to  flow  within  a pipe,  227,  229,  230, 
233,  248,  254,  256,  266,  272,  403. 

Resistances  to  flow  in  channels,  300,  304,  307, 
310,  312. 

Resultant  effect  of  rain  and  evaporation,  92. 
Retaining  wall  , 390.  395,  397,  399,  406,  417,  420, 
42^,  426. 

' 44  effect  of  traffic  on.  425. 

44  41  for  earth,  table.  420. 

44  4;  front  batters,  424. 

44  percolation  under,  406. 


Retaining  walls,  sections  of.  354,  407, 

44  44  top  breadths,  424. 

Resultants  in  stand-pipes,  597, 

44  of  pressure,  391,  400,  41 1,  418,  433* 
Revetted  conduits,  431. 

44  embankment,  149,  354,  370,  429, 
Revetments,  faced  and  concrete,  429. 

*4  final  resultants,  418. 

“ resistance  of,  417. 

44  trapezoidal,  table  of,  420. 

Riparian  rights,  85,  86. 

Rip-rap,  slope,  371. 

River  basin  rains,  50. 

44  basins  of  Maine,  84. 

44  courses,  rainfall  along,  51. 

“ pollution  committee,  154. 

44  waters,  15 1. 

Rivers  and  canals,  table  of  flows,  307. 

Rivets,  joints,  591,  592. 

44  table  of,  592. 

Riveting,  591,  592. 

Roof  for  filter  beds  and  reservoirs,  548,  555, 
Rotary  pump,  558. 

Rubble,  grouted,  353. 

44  masonry,  252. 

44  priming  walls,  352. 

S. 

Safety,  factors  of,  449,  451,  453,  485,  486,  593, 
594,  595,  598,  600. 

Sand  in  embankments,  353. 

Sanitary  discussions,  152. 

44  improvements,  26. 

44  office  of  water,  26. 

44  views,  precautionary,  154. 

Schussler’s  process  of  coating  pipes,  489. 
Screens,  fish,  365. 

Seasons  of  floods,  68. 

Sections  of  maximum  rainfall,  47. 

Secular  fluctuations  in  rainfall,  60. 

Sediments,  530,  531. 

Service  pipes,  frictions  in,  table.  528. 

Services,  high  and  low,  524. 

Settling  basins,  550. 

Sewage  impurities,  130^,  134. 

44  44  dilution  of,  153, 155. 

Shells  of  conduits,  434. 

Sheet-iron,  gauges  and  weights,  488. 
Sheet-piles,  371. 

44  under  embankment,  339. 
Short-tubes,  215,  216. 

Showers,  source  of,  45. 

Sines  of  slopes,  table,  259. 

Siphon,  182,  184. 

Site  for  embankment,  reconnoissance  for,  346 
Skillful  workmanship  required,  369. 

Sleeves,  pipe,  479,  482. 

Slope,  earthwork,  344,  345. 

4‘  of  channels,  302,  307,  308,  310,  329. 

44  paving,  348,  354,  355,  356,  358. 

44  puddled,  352. 

44  44  embankment.  356. 

Slopes,  velocities  for  given,  258. 

Sluice  areas,  360. 

44  apertures,  coefficients  for,  201,  202,  203, 
205,  206. 

44  gate  areas,  359. 

44  temporary  stop-gate,  359. 

“ tunneled,  embankment,  356,  358. 

44  valves,  iron,  360.  364. 

Sluices,  flow  through,  200,  201,  203,  205,  206. 

44  high  and  low,  204. 

44  varying  head  on,  204. 

Smith’s  (A.  F.)  adjustable  pipe,  364. 

Soils  beneath  embankments,  337. 

44  evaporation  from,  no. 

Solutions,  organic,  532. 

44  in  water,  112= 


642 


INDEX. 


Springs  and  wells,  102. 

44  44  supplying  capacity  oi  no. 

44  mineral,  141. 

44  under  embankments,  337. 

“ 44  waters,  141. 

Stable  use  of  water,  34. 

Stand-pipe  foundations,  586. 

“ materials,  590,  594,  595,  596,  597,  601. 
Stand-pipes,  526,  564,  585,  602,  628. 

44  exposed,  ix.,  585,  598,  599,  628. 

44  moments  of  resistance,  588,  589. 

“ overturning  tendency,  588. 

“ pressures  in,  593. 

“ “ on,  599. 

“ stabilities,  589,  597. 

“ Tank,  ix.t  585,  628. 

44  wind  strains  on,  587. 

Static  pressures  in  pipes,  446. 

Stones,  building,  strengths  of,  404. 

Stop-gates  in  conduits,  374*  436. 

Stop-valve,  Coffin’s,  493. 

“ curbs,  515. 

44  Eddy’s,  511. 

44  Flower’s,  493. 

44  Ludlow’s,  514. 

“ system,  511. 

Stop-valves,  360,  374,  436,  493,  511,  513,  514. 
Storage,  additional,  required,  98. 

basins,  percolation  from,  85. 

“ substratas  of,  85. 
losses  of  water,  84. 
of  water,  84. 

effect  of  evaporation  on,  93. 
influence  upon  continuous 
supply,  99. 
required,  95. 

voir,  84,  87,  03,  95,  97,  101,  338. 
embankment,  553. 
substrata,  85. 

supply  to,  and  draught  from, 
table,  96. 

Storms,  great  rain.  61. 

Strata,  conditions,  146. 

Strains  on  stand-pipes,  590,  593,  599. 

Streams,  annual  flow  of,  77. 

“ available  annual  flow,  94. 

44  estimates  of  flow,  65,  78. 

44  flashy  and  steady,  71. 

“ gauging,  296,  316,  320,  322,  326. 

44  mean  monthly  flow  of,  79. 

“ minimum,  mean,  and  flood  flow,  75. 

4‘  ordinary  flow  of,  80. 

44  ratio  of  monthly  flow,  76. 

Strength  of  cylindrical  cantilevers,  599,  600. 

44  44  hollow  cylindrical  beams,  600. 

Strengths  of  building*  stones,  404. 

“ “ cylinders,  448,  593. 

44  44  metals,  451,  454. 

44  “ riveted  joints,  591. 

44  44  wrought  pipe  metals,  451,  486,  491. 

Sub-heads  compared,  253. 

Sub-mains,  diameters  of,  507. 

Submerged  orifices,  209. 

Subterranean  reservoirs,  105. 

‘‘  waters,  102. 

“ watershed.  109. 

“ waters,  temperatures  of,  126. 

44  “ uncertainties  or  search 


for,  106. 

Substrata  of  a storage  basin.  85. 

Sudbury  river  rainfall  and  flow,  83 a. 

Supply  main,  diameter  of,  506. 

4*  to  and  draught  from  a reservoir,  table, 

96,  97- 

Supplying  capacity  of  watersheds,  94. 
Surcharged  pressure,  earth,  414,  416,  423. 
Surfaces,  pressure  of  water  upon,  391,  393. 
Surveys  for  storage  reservoir,  347. 

Sources  of  water  supplies,  587. 


Symbols,  definitions  of,  235. 

Systems,  combined  reservoir  and  direct,  525 
44  of  water  supply,  603,  604. 

• “ 44  44  distribution,  493,  505. 

“ “ rainfall,  47,  49,  50, 

T. 

(See  List  of  Tables,  page  xix.) 

Tank  materials.  590. 

44  stand-pipes,  ix.,  585. 

44  44  lack  of  stability  of,  587.  =;83 

598,  600. 

Temperatures,  artesian  well,  127. 

44  of  deep  sub-surface  waters.  1 

44  ‘‘  filter  beds,  555. 

“ “ water  in  pipes,  502. 

Templets,  for  flange  bolt-holes,  460. 
Tenacities  of  wrought-pipe  metals,  431, 

_ 49I# 

Tests  of  metal  plates,  590,  591. 

44  44  pipe  metals,  472,  590,  591. 

Testing  of  nydrometers,  325,  326. 

Theory  of  flow  over  a weir,  278,  280. 
Thicknesses  of  a curved-face  wall,  422. 

44  44  dams,  table,  387. 

44  44  pipes,  lormulas,  448,  450,  4^ 

485,  486,  487. 

44  44  stand-pipe  sheets,  595,  596,  597 

60  T. 

44  4*  w’alls  for  water-pressure.  399. 

44  44  wrought-pipe  shells,  447,  486 

488,  495,  597,  601. 

Thompson  s molecular  estimate,  162. 

Thrusts  of  a conduit  arch,  437. 

Timber  weirs,  384. 

Transit,  use  in  gauging,  313,  318,  319. 
Transmission  of  pressures,  1S3. 

Traffic,  effect  upon  retaining  walls,  425. 
Trapezoidal  revetments,  table,  420. 
Treacherous  strata  beneath  embankments. 
Trial  shafts,  at  embankment  sites,  336. 
Trigonometrical  equivalents,  618. 

Tube  gauge,  317.  32T. 

Tubes,  coefficients  of  flow,  217,  219,  220 
44  compound,-  220. 

44  experiments  with  short,  217,  219,  220. 

44  short,  213.  215,  218,  220. 

Tubercles,  in  pipes,  247,  248. 

Turbine  water-wheels,  559,  585.  593,  597 
Turned  pipe-joints,  458. 

Type  curves  of  rainfall,  55,  57,  59. 

U. 

Uniform  effect  of  natural  laws.  61. 

Union  of  high  and  low  services,  524. 

Units  of  heat  utilized.  578. 

Use  of  water  increasing,  39. 

V. 

Vacuum,  ajutage,  214. 

44  imperfect,  short  tubes,  215. 

44  rise  of  water  into,  182. 

44  tendency  to  in  compound  tubes, 

44  under  a weir  crest,  292. 

Values  of  c\  271. 

44  44  h and  h\  table,  264. 

44  4 4 pumping  engines  compared,  583. 

44  44  water  supplies  as  investments,  29 

Valves,  air,  523. 

44  blow-off,  513. 

4‘  Cornish,  569,  570. 

44  check,  525. 

44  curbs.  515. 

44  disk.  571. 

“ double  beat,  569.  570. 

44  flap,  568. 


INDEX. 


643 


Valves,  iron  sluice,  360,  364. 

“ pis.on,  569. 

“ power  required  to  open,  361,  364. 

“ pump,  558,  563,  566,  568,  569,  570,  571. 

“ ^°P,  364.  493,  5“.  5i3i  5i4- 

“ indicator,  361. 

“ “ system,  511. 

“ “ waste,  513. 

Vanne  conduit,  438. 

Vapor}'  elements,  the,  43,  87. 

Variable  flow  through  pumps,  559. 

Varnishes  for  iron,  474,  476,  489. 

Vegetal  growth  in  filter  beds,  555. 

Vegetable  organic  impurities,  128. 

Velocity,  conversion  into  pressure,  227. 

“ equation,  modification  of,  270. 

“ formula  for,  249,  250. 

“ formulas  for  pipes,  249,  250,  252,  254, 
259,  263,  266,  267,  268,  270,  273. 

Velocities  in  canals  and  channels,  302,  307, 308, 
310,  312,  314,  n8,  320,  325,  326,  330.  371,  373. 

Velocities  for  given  slopes,  table,  259. 

“ of  falling  bodies,  table,  190. 

“ u flow  in  pipes,  236,  243,  249,  254. 

“ “ given  films  in  channels,  311,  443. 

“ ratios  of  surface  to  mean,  315,  443. 

" relative,  due  to  different  depths  in 
channels,  328. 

“ surface  in  channels,  313,  443. 

“ theoretical  table,  190. 

Vermin  in  canal  banks,  371. 

Vertical  shifting  of  water,  365. 

Virginia  City,  wrought-iron  pipe,  489. 

Voids  of  earths  and  rocks,  103. 

Volume  delivered  by  pipes,  table,  495. 

“ of  efflux  from  an  orifice,  194,  209. 

“ “ “ formula  for,  196. 

“ “ hydrant  streams.  585. 

“ flood  inversely  as  the  area  of  the 
basin,  65. 

Volumes,  formulas,  for  flood,  65 

“ flood,  from  watersheds,  381. 

“ relative,  due  to  different  depths  In 
channels,  328. 

“ of  given  rainfalls,  62. 

“ for  given  depth  upon  weirs,  290. 

“ from  waste  weirs,  table,  380. 

W. 

Walls,  back  batters  of,  422. 

“ chamber,  369. 

M counterforted,  427. 

“ curved  face,  table,  422. 

“ earth  pressure  against,  408, 410, 412,413, 
415,  416. 

eiem  ;nts  of  failure,  427. 

“ end  supports  of,  429. 

“ front  batters  of,  424. 

“ formula  of  thickness  for  water  pressure, 

, 399; 

foundations  of,  395,  406,  407. 

“ leverage  resistance  of,  402. 

“ limiting  pressures  in,  404. 

“ of  concrete.  429,  430. 

“ profiles  of,  407. 

“ retaining,  390,  393,  397,  399, 406,  417,  420, 
425,  426. 

**  to  retain  water,  table,  400. 

u “ sustain  traffic,  425. 

“ top  breadths,  424. 

“ wharf,  426. 

Waste  pipes,  embankment,  357. 

“ sluice,  “ 356. 

“ valves,  5^3. 

“ weir  aprons,  383. 

“ “ ballast,  385. 

“ “ caps,  387. 

**  “ formulas,  379. 


Waste  weir  volumes,  table,  380. 

“ weirs,  377,  381.  386,  387. 

“ “ discharges  over,  378. 

“ “ effect  of  ice  on,  386. 

“ “ forms  of,  382. 

“ “ lengths  forgiven  watersheds, 381 

“ “ thickness,  table,  387. 

Water,  analyses  of  potable,  117, 138. 

“ characteristics  r , 113,  159,  161. 

“ choice  of,  605, 

“ clarification  of,  530,  556^. 

“ commercial  use  of,  34. 

“ compressibility  and  elasticity  of,  167. 

“ consumption  of,  34,  503. 

“ crystalline  forms  of,  165. 

“ domestic  use,  34. 

“ engine,  569. 

“ evaporation  from,  88,  89. 

“ expansion  of,  164,  166. 

“ flow  of,  184.  194. 

“ force  of  falling,  388. 

“ hose,  use  of,  34. 

“ impregnations.  112,  141. 

“ impunties,  112,138,  141. 

“ molecular  actions,  168,  169. 

“ physiological  office  of,  25. 

“ “ effect  of  the  impurities  ot 

1 14. 

Water  pipes,  organisms  in,  129,  133. 

“ plant  and  insect  agencies  in, 130,147,55615. 
“ pressure  leverage  ot,  397. 

“ “ upon  surfaces,  168,  176,  391 

393- 

“ pumping  of,  557. 

“ rarity  of  clear,  530 

“ ratios  of  variable  flow,  564. 

“ relative  volumes  and  temperatures,  166, 
“ river,  151. 

“ sanitary  office  of,  26. 

“ solvent  powers  of,  113. 

“ spring,  141. 

“ storage  oi,  84. 

“ subterranean,  102. 

“ sugar  test  :f  quality,  159. 

“ supplied,  31,  35,  36,  37,  38.  40. 

“ supplies,  gathering  and  delivery,  586. 

‘‘  supplies,  incidental  advantages  of;  29. 

“ “ necessities  Of,  25. 

“ supply,  gravity,  606. 

“ “ permanence  of,  603. 

“ “ systems  of,  603. 

“ the  composition  of,  112,  138. 

“ vertical  changes  in,  365. 

“ volumes  and  weights,  table,  161,  164. 

166. 

“ waste,  34. 

“ weight  of  constituents,  164. 

“ “ pressure  and  motion  of,  i6r. 

“ well,  139. 

“ wheels.  559,  379. 

“ works,  construction  of,  333. 

“ ram  in  pipes,  449. 

“ sheds,  71,  100. 

“ “ flood  volumes,  62,  67,  63,  75, 98, 

380,  381. 

“ “ flow  from,  96. 

“ “ supplying  capacity  of,  94. 

“ “ waste  weirs  required,  381. 

Weights  and  measures,  metric,  611. 

Weir  apron,  279. 

“ benches,  384. 

“ caps,  bre  dths,  386,  387. 

“ coefficients.  288,  289,  291. 

“ crests,  278,  292,  293. 

“ gauging,  77. 

“ over  'alls,  377. 

Weirs,  crest  contractions,  280. 

“ dimensions  of,  278,  279,  386,  387. 

“ discharges  over,  table,  289,  289a,  290 


644 


INDEX. 


Weirs,  experiments  with  large,  284. 

“ forms  of,  277,  386,  387. 

44  formula  lor  wide-crested,  293. 

“ “ *‘  depth  upon,  286, 287. 

“ formulas,  282,  283,  284,  286. 

“ gratings  in  iront  ot,  292. 

14  nook-gauge  for,  297. 

44  initial  velocity  ot  approach  to,  285,  292. 
44  isolated  waste,  383. 

4-  measuring,  277,  295. 

44  rule  gauge  for,  298. 

44  stability  of,  279,  386,  387. 

44  tail-water  of,  292. 

44  thickness  of  waste,  386,  387. 

41  triangular  notch,  294,  295. 

44  tube  and  scale-gauge  for,  298. 

44  timber,  384. 

44  varying  lengths,  279, 

44  volumes,  formulas  for,  282,  283,  284, 
286,  287,  293. 

44  waste,  337,  383,  386,  387. 

“ wide-crested,  293. 

ht,  a line  a measure  of,  173. 
a measure  of  pressure,  173. 
and  volume  of  water,  table,  166 
leverage  of  masonry,  398. 
of  pond-water,  167. 

Weights  of  cast  pipes,  465,  468,  469. 


Weights  of  embankment  materials,  341,  342, 
411. 

4 4 44  molecules,  168. 

Well,  intercepting,  546. 

“ water,  139. 

44  waters,  anal  ses  of,  121. 

Wells  and  springs,  102,  no. 

44  condition  ot  overflowing,  107. 

louling  ol  old,  140. 

44  influence  upon  each  other,  107. 

4*  impurities  ot  deep,  125. 

44  location  lor,  139. 

44  water-sheds  of,  ic8. 

Western  rain  system,  47. 

Wharf,  cap-log,  426. 

4*  fender  and  belay  piles,  427. 

44  walls,  426. 

Wind  leverage  on  tanks,  588,  589,  598,  599. 

44  strains  on  stand-pipes,  587. 

Winds,  destructive  actions,  586,  587. 

4*  resultant  on  curved  surtace,  587. 
Wood  pipes,  491. 

Woltmann's  tachometer,  322. 

Workmanship,  skilful,  369. 

Wrought-iron  pipes;  479. 

44  “ pipe-joint,  cast,  483. 

44  44  plates,  gauges  and  weights,  488, 

WyckofF’s  wood-pipe,  491. 


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Camm,  a.-.  Aeroplane  Construction i2mo,  3 00 

Carhart,  H.  S.  Thermo  Electromotive  Force  in  Electric  Cells. ..  i2mo,  2 00 

Carey,  A.  E.,  and  Oliver,  F.  W.  Tidal  Lands 8vo,  5 00 

Carpenter,  P.  D.  Geographical  Surveying i6mo, 

Carpenter,  R.  C.,  and  Diederichs, H.  Internal  Combustion  Engines. 8vo,  5 50 

Carpmaei,  H.  Electric  Welding  and  Welding  Appliances 4to,  5 00 

Carter,  B.  A.  Ramie  (Rhea),  China  Grass i2mo,  *3  00 

Carter,  H.  R.  Modern  Flax,  Hemp,  and  Jute  Spinning 8vo,  *5  50 

Bleaching,  Dyeing  and  Finishing  of  Fabrics 8vo,  *1  25 

Cary,  E.  R.  Solution  of  Railroad  Problems  with  the  Slide  Rule.i6mo,  1 25 
Casler,  M.  D.  Simplified  Reinforced  Concrete  Mathematics. ..  .12010,  1 25 

Cathcart,  W.  L.  Machine  Design.  Part  I.  Fastenings 8vo,  *350 

Cathcart,  W.  L.,  and  Chaffee,  J.  I.  Elements  of  Graphic  Statics . . .8vo,  *3  00 

— — Short  Course  in  Graphics i2mo,  1 50 

Caven,  R.  M.,  and  Lander,  G.  D.  Systematic  Inorganic  Chemistry . i2mo,  2 25 

Chalkley,  A.  P.  Diesel  Engines 8vo,  5 00 

Chalmers,  T.  W.  The  Production  and  Treatment  of  Vegetable  Oils, 

4to,  7 50 

Paper  Making  and  its  Machinery 4to,  8 00 

The  Gyroscopic  Compass 8vo,  5 00 

Chambers’  Mathematical  Tables 8vo,  2 50 

Chambers,  G.  F.  Astronomy i6mo  2 50 

Chappel,  E.  Five  Figure  Mathematical  Tables 8vo,  2 50 

Charnock,  Mechanical  Technology 8vo,  3 50 

Charpentier,  P.  Timber 8vo,  *6  co 

Chatley,  H.  Principles  and  Designs  of  Aeroplanes i6mo,  o 75 

-How  to  Use  Water  Power i2mo,  *1  5c 

-Gyrostatic  Balancing  8vo,  *1  25 

Child,  C.  D.  Electric  Arc 8vo,  *2  oc 

Christian,  M.  Disinfection  and  Disinfectants nmo,  2 50 

Christie,  W.  W.  Boiler-waters,  Scale,  Corrosion,  Foaming 8vo,  *3  00 

■ Chimney  Design  and  Theory 8vo,  *3  00 

Furnace  Draft  i6mo,  o 75 

Water:  Its  Purification  and  Use  in  the  Industries 8vo,  3 oc 

Church’s  Laboratory  Guide 8vo,  2 50 


D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG 


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Clapham,  J.  H.  Woolen  and  Worsted  Industries.. 8vo,  2 00 

Clapperton,  G.  Practical  Papermaking. 8vo  ( Reprinting .) 

Clark,  A.  G.  Motor  Car  Engineering.  ; 

Vol.  L Construction i *4  00 

Vol.  II.  Design  8vo,  *3  50 

Clark,  C.  H.  Marine  Gas  Engines.  New  Edition 2 00 

Clarke,  J.  W.,  and  Scott,  W.  Plumbing  Practice. 

Vol.  I.  Lead  Working  and  Plumbers’  Materials 8vo,  00 

Vol.  II.  Sanitary  Plumbing  and  Fittings {In  Press.) 

Vol.  III.  Practical  Lead  Working  on  Roofs {In  Press.) 

Clarkson,  R.  P.  Elementary  Electrical  Engineering i2mo,  2 00 

Clerk,  D.,  and  Idell,  F.  E.  Theory  of  the  Gas  Engine i6mo,  o 75 

Clevenger,  S.  R.  Treatise  on  the  Method  of  Government  Surveying. 

i6mo,  morocco,  2 5c 

Clouth,  F.  Rubber,  Gutta-Percha,  and  Balata 8vo,  *6  00 

Cochran,  J.  Concrete  and  Reinforced  Concrete  Specifications 8vo,  *2  50 

Treatise  on  Cement  Specifications 8vo,  *1  00 

Cocking,  W.  C.  Calculations 1 for  Steel-Frame  Structures 12010,  *2  50 

Coffin,  J.  H.  C.  Navigation  and  Nautical  Astronomy 12010,  3 00 

Colburn,  Z.,  and  Thurston,  R.  H.  Steam  Boiler  Explosions. ..  .i6mo,  o 75 

Cole,  R.  S.  Treatise  on  Photographic  Optics 12100,  2 00 

Coles-Finch,  W.  Water,  Its  Origin  and  Use 8vo,  3 50 

Collins,  C.  D.  Drafting  Room  Methods,  Standards  and  Forms Svo,  2 00 

Collins,  S.  Hoare.  Plant  Products  and  Chemical  Fertilizers 8vo,  3 00 

Chemical  Fertilizers ' 8vo,  3 50 

Collis,  A.  G.  High  and  Low  Tension  Switch-Gear  Design 8vo,  *3  50 

Switchgear  12010,  o 50 

Colver,  E.  D.  S.  High  Explosives 8vo,  12  50 

Comstock,  D.  F.,  and  Troland,  L.  T.  The  Nature  of  Electricity  and 

Matter  8vo,  2 50 

Coombs,  H.  A.  Gear  Teeth i6mo,  o 75 

Cooper,  W.  R.  Primary  Batteries 8vo,  *6  00 

Copperthwaite,  W.  C.  Tunnel  Shields 4to,  *900 

Corfield,  W.  H.  Dwelling  Houses i6mo,  o 75 

Water  and  Water-Supply i6mo,  o 75 

Cornwall,  H.  B.  Manual  of  Blow-pipe  Analysis 8vo.  *250 

Couch,  J.  F.  Dictionary  of  Chemical  Terms i2mo,  fabrikoid,  2 50 

Cowee,  G.  A.  Practical  Safety  Methods  and  Devices 8vo,  4 00 

Cowell,  W.  B.  Pure  Air,  Ozone,  and  Water 12010,  *2  50 

Craig,  J.  W.,  and  Woodward,  W.  P.  Questions  and  Answers  About 

Electrical  Apparatus 12010,  leather,  1 50 

Craiu,  T.  Motion  of  a Solid  in  a Fuel i6mo,  o 75 

-Wave  and  Vortex  Motion i6mo,  o 75 

Crehore,  A.  C.  Mystery  of  Matter  and  Energy 8vo,  1 00 

The  Atom nmo,  2 00 

Crocker,  F.  B.,  and  Arendt,  M.  Electric  Motors 8vo,  3 co 

Crocker,  F.  B.,  and  Wheeler,  S.  S.  The  Management  of  Electrical  Ma- 
chinery  12010,  *1  00 

Crosby,  E.  U.,  Fiske,  H.  A.,  and  Forster,  H.  W.  Handbook  of  Fire 

Protection 12010,  4 00 

Cross,  C.  F.,  Bevan,  E.  J.,  and  Sindall,  R.  W.  Wood  Pulp  and  Its 

Uses  8vo,  3 50 

Crosskey,  L.  R.  Elementary  Perspective 8vo,  1 50 


8 D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG 


Culley,  J.  L. 


Dadourian,  H.  M. 


Davies,  F.  H.  Ele< 
Davis,  A.  M.  Int 
— • — Foundations  a 
Deerr,  N.  Sugar 
Deite,  C.  Manual 
De  la  Coux,  H.  T1 
Del  Mar,  W.  A.  E 
Denny,  G.  A.  Dee 
De  Roos,  J.  D.  C. 
Derr,  W.  L.  Block 
Desaint,  A.  Three 
De  Varona,  A.  S( 
Devey,  R.  G.  Mill 


Linkages. 


2 

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. i2mo, 

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7 

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OO 

. i2mo, 

*3 

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Dixon,  D.  B.  Machinist’s  and  Steam  Engineer’s  Practical  Calculator. 


i6mo,  morocco, 

1 25 

Dommett, 

W.  E Motor  Car  Mechanism,  . 

I2HL0, 

*2  00 

Dorr,  B.  F. 

The  Surveyor’s  Guide  and  Pocket  Table-book. 

i6mo,  morocco, 

2 00 

Draper,  C. 

H.  Heat  and  the  Principles  of 

Thermo-Dynamics,  .nmo, 

2 25 

Draper,  E. 

G.  Navigating  the  Ship 

2 OO 

Dubbel,  H. 

High  Power  Gas  Engines 

*5  00 

Dumesny,  P.,  and  Noyer,  J.  Wood  Products,  Distillates,  and  Extracts. 

8vo, 

Duncan,  W.  G.,  and  Penman,  D.  The  Electrical  Equipment  of  Collieries. 

Svo, 

Dunkley,  W.  G.  Design  of  Machine  Elements.  Two  volumes.  .8vo,each, 

Dunstan,  A.  E.,  and  Thole,  F.  B.  T.  Textbook  of  Practical  Chemistry. 

1 2 mo, 

Durham,  H.  W.  Saws Svo, 

Duthie,  A.  L.  Decorative  Glass  Processes Svo, 


'5  oo 

*5  oo 

2 oo 

3 oo 
2 50 
2 50 


Dwight,  H.  B.  Transmission  Line  Formulas Svo,  *200 

Dyke,  A.  L.  Dyke’s  Automobile  and  Gasoline  Engine  Encyclopedia, 

8vo,  6 00 

Dyson,  S.  S.  A Manual  of  Chemical  Plant.  12  parts.  ..  .4to,  paper,  7 50 

Dyson,  S.  S.,  and  Clarkson,  S.  S.  Chemical  Works. . 8vo,  *9  00 

Eccles,  W.  H.  Wireless  Telegraphy  and  Telephony umo,  700 


D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG 


9 


Eck,  J.  Light,  Radiation  and  Illumination 8vo,  2 50 

Eddy,  L.  C.  Laboratory  Manual  of  Alternating  Currents nmo,  o 50 

Edelman,  P.  Inventions  and  Patents i2mo,  2 00 

Edgcumbe,  K.  Industrial  Electrical  Measuring  Instruments 8vo,  5 00 

Edler,  R.  Switches  and  Switchgear 8vo,  4 oc 

Eissler,  M.  The  Metallurgy  of  Gold 8vo,  9 00 

The  Metallurgy  of  Silver 8vo,  4 00 

The  Metallurgy  of  Argentiferous  Lead 8vo,  6 25 

A Handbook  on  Modem  Explosives 8vo,  5 00 

Ekin,  T.  C.  Water  Pipe  and  Sewage  Discharge  Diagrams folio,  *3  00 

Electric  Light  Carbons,  Manufacture  of 8vo,  1 00 

Eliot,  C.  W.,  and  Storer,  F.  H.  Compendious  Manual  of  Qualitative 

Chemical  Analysis i2mo,  1 50 

Eliott,  A.  W.  M.  Rectangular  Areas i2mo,  3 00 

Ellis,  C.  Hydrogenation  of  Oils 8vo,  7 50 

Ultraviolet  Light,  Its  Applications  in  Chemical  Arts 12110, 

(In  Press ) 

and  Meigs,  J.  V.  Gasolene  and  Other  Motor  Fuels. . (In  Press.) 

Ellis,  G.  Modern  Technical  Drawing 8vo,  *2  00 

Ennis,  Wm.  D.  Linseed  Oil  and  Other  Seed  Oils 8vo,  5 00 

Applied  Thermodynamics 8vo,  5 00 

Vapors  for  Heat  Engines i2mo,  *1  00 

Ennen,  W.  F.  A.  Materials  Used  in  Sizing 8vo,  *2  00 

Erwin,  M.  The  Universe  and  the  Atom i2mo  (Reprinting.) 

Ewing,  A.  J.  Magnetic  Induction  in  Iron 8vo,  5 00 

Fage,  A.  Airscrews  in  Theory  and  Practice 4to,  10  00 

Fairchild,  J.  F.  Graphical  Compass  Conversion  Chart  and  Tables...  o 50 

Fairie,  J.  Notes  on  Lead  Ores nmo,  *0  50 

Notes  on  Pottery  Clays i2ino,  *2  00 

Fairley,  W.,  and  Andre,  Geo.  J.  Ventilation  of  Coal  Mines. ..  . i6mo,  o 75 

Fairweather,  W.  C.  Foreign  and  Colonial  Patent  Laws 8vo,  *3  00 

Falk,  K.  G.  Chemical  Reactions:  Their  Supply  and  Mechanism,  .nmo,  2 50 

Farming,  J.  T.  Hydraulic  and  Water-supply  Engineering 8vo,  *5  00 

Farnsworth,  P.  V.  Shop  Mathematics...  i2mo  (In  Press.) 

Fay,  I.  W.  The  Coal-tar  Dyes 8vo,  5 00 

Fembach,  R.  L.  Glue  and  Gelatine 8vo,  *3  00 

Findlay,  A.  The  Treasures  of  Coal  Tar i2mo,  2 00 

Firth,  J.  B.  Practical  Physical  Chemistry i2mo,  1 25 

Fischer,  E.  The  Preparation  of  Organic  Compounds i2mo,  2 oc 

Fisher,  H.  K.  C.,  and  Darby,  W.  C.  Submarine  Cable  Testing.  .. 8vo,  4 00 

Fleischmann,  W.  The  Book  of  the  Dairy 8vo,  4 50 

Fleming,  J.  A.  The  Alternate-current  Transformer.  Two  Volumes.  8vo. 

Vol.  I.  The  Induction  of  Electric  Currents *6  50 

Vol,  II.  The  Utilization  of  Induced  Currents 6 50 

Propagation  of  Electric  Currents 8vo,  5 00 

A Handbook  for  the  Electrical  Laboratory  and  Testing  Room.  Two 

Volumes 8vo,  each,  *6  50 

Fleury,  P.  Preparation  and  Uses  of  White  Zinc  Paints 8vo,  3 00 

Flynn,  P.  J.  Flow  of  Water i2mo,  o 75 

Hydraulic  Tables  i6mo,  o 75 


IO 


D.  ViJN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG 


Foster,  H.  A.  Electrical  Engineers’  Pocket-book.  ( Seventh  Edition.) 


i2mo,  leather,  5 00 

Engineering  Valuation  of  Public  Utilities  and  Factories 8vo,  *3  00 

Fowle,  F.  F.  Overhead  Transmission  Line  Crossings nmo,  *1  50 

The  Solution  of  Alternating  Current  Problems £vo  {In  Press.) 

Fox,  W.  G.  Transition  Curves i6mo,  o 75 

Fox,  W.,  and  Thomas,  C.  W.  Practical  Course  in  Mechanical  Draw- 
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Foye,  J.  C.  Chemical  Problems r6mo,  o 75 

1 Handbook  of  Mineralogy i6mo,  o 75 

Francis,  J.  B.  Lowell  Hydraulic  Experiments 4to,  15  00 

Franzen,  H.  Exercises  in  Gas  Analysis nmo,  *1  00 

Fraser,  E.  S.,  and  Jones,  R.  B.  Motor  Vehicles  and  Their  Motors, 

Svo,  fabrikoid,  2 00 

Freudemacher,  P.  W„  Electric  Mining  Installations i2mo,  1 00 

Friend,  J.  N.  The  Chemistry  of  Linseed  Oil i2mo,  1 00 

Fritsch,  J.  Manufacture  of  Chemical  Manures 8vo,  5 00 

Frye,  A.  I.  Civil  Engineers’ Pocket-book i2mo,  leather,  *5  00 

Fuller,  G.  W.  Investigations  into  the  Purification  of  the  Ohio  River. 

4to,  *10  00 

Furnell,  J.  Paints,  Colors,  Oils,  and  Varnishes 8vo. 

Gant,  L.  W.  Elements  of  Electric  Traction 8vo,  *250 

Garcia,  A.  J.  R.  V.  Spanish-English  Railway  Terms 8vo,  3 00 

Gardner,  H.  A.  Paint  Researches,  and  Their  Practical  Applications, 

8vo,  *5  00 

Garforth,  W.  E.  Rules  for  Recovering  Coal  Mines  after  Explosions  and 

Fires i2mo,  leather,  1 50 

Garrard,  C.  C.  Electric  Switch  and  Controlling  Gear 8vo,  *6  00 

Gaudard,  J.  Foundations i6mo,  o 75 

Gear,  H.  B.,  and  Williams,  P.  F.  Electric  Central  Station  Distribution 

Systems  Svo,  *3  50 

Geerligs,  II.  Cj  P.  Cane  Sugar  and  Its  Manufacture 8vo,  *6  00 

— — Chemical  Control  in  Cane  Sugar  Factories 4to,  5 00 

Geikie,  J.  Structural  and  Field  Geology Svo,  7 50 

Mountains.  Their  Growth,  Origin  and  Decay 8vo,  4 50 

The  Antiquity  of  Man  in  Europe 8vo,  *3  00 

Georgi,  F.,  and  Schubert,  A.  Sheet  Metal  Working Svo,  3 50 

Gerhard,  W.  P.  Sanitation,  Watersupply  and  Sewage  Disposal  of  Country 

Houses  i2mo,  2 50 

Gas  Lighting  i6mo,  o 75 

Household  Wastes  r6mo,  o 75 

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Gerhardi,  C.  W.  H.  Electricity  Meters Svo,  *7  20 

Geschwind,  L.  Manufacture  of  Alum  and  Sulphates Svo,  5 00 

Gibbings,  A.  H.  Oil  Fuel  Equipment  for  Locomotives.  8vo. 

(Reprinting.) 

Gibbs,  W.  E.  Lighting  by  Acetylene i2mo,  *r  50 

Gibson,  A.  H.  Hydraulics  and  Its  Application Svo,  6 00 

■ Water  Hammer  in  Hydraulic  Pipe  Lines i2mo,  2 50 

Gibson,  A.  H.,  and  Ritchie,  E.  G.  Circular  Arc  Bow  Girder 4to,  *3  50 


D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG  n 


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Primer  of  Scientific  Management i2mo,  1 25 

Gill,  A.  H.  Gas  Analysis  for  Chemists 8vo,  1 25 

Gillmore,  Gen.  Q.  A.  Roads,  Streets,  and  Pavements i2mo,  1 25 

Godfrey,  E.  Tables  for  Structural  Engineers i6mo,  leather,  *2  50 

Golding,  H.  A.  The  Theta-Phi  Diagram i2mo,  *2  00 

Goldschmidt,  R.  Alternating  Current  Commutator  Motor 8vo,  *300 

Goodchild,  W.  Precious  Stones 8vo,  2 50 

Goodell,  J.  M.  The  Location,  Construction  and  Maintenance  of 

Roads  8vo,  2 00 

Goodeve,  T.  M.  Textbook  on  the  Steam-engine 12010,  2 50 

Gore,  G.  Electrolytic  Separation  of  Metals 8vo,  4 50 

Gould,  E.  S.  Arithmetic  of  the  Steam-engine T2mo,  1 00 

Calculus  i6mo,  o 75 

High  Masonry  Dams x6mo,  o 75 

Gould,  E.  S.  Practical  Hydrostaticsi  and  Hydrostatic  Formulas.  . i6mo,  o 75 

Goulding,  E.  Cotton  and  Other  Vegetable  Fibres 8vo,  3 00 

Gratacap,  L.  P.  A Popular  Guide  to  Minerals 8vo,  *2  00 

Gray,  H.  H.  Gas-Works  Products 8vo  (In  Press.) 

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Greenhill,  G.  Dynamics  of  Mechanical  Flight 8vo,  *2  50 

Greenwood,  H.  C.  The  Industrial  Gases 8vo,  5 00 

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Grierson,  R.  Some  Modern  Methods  of  Ventilation 8vo,  *3  00 

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Gross,  E.  Hops 8vo,  *5  00 

Grossman,  J.  Ammonia  and  Its  Compounds i2mo,  1 50 

Groth,  L.  A.  Welding  and  Cutting  Metals  by  Gases  or  Electricity. 

8vo,  3 00 

Grover,  F.  Modern  Gas  and  Oil  Engines 8vo,  *3  00 

Gruner,  A.  Power-loom  Weaving 8vo,  *3  50 

Grunsky,  C.  E.  Topographic  Stadia  Surveying i6mo,  2 00 

Gunther,  C.  0.  Integration 8vo,  1 50 

Gurden,  R.  L.  Traverse  Tables : folio,  7 50 

Guy,  A.  E.  Experiments  on  the  Flexure  of  Beams 8vo,  *r  25 


Haenig,  A.  Emery  and  Emery  Industry 8vo,  *2  50 

Hainbach,  R.  Pottery  Decoration i2mo,  3 50 

Hale,  A.  J.  The  Manufacture  of  Chemicals  by  Electrolysis 8vo,  2 00 

Hale,  Harrison.  American  Chemistry i2mo  (In  Press.) 

Hale,  W.  J.  Calculations  of  General  Chemistry i2mo,  1 50 

Hall,  C.  H.  Chemistry  of  Paints  and  Paint  Vehicles nmo,  *2  00 

Hall,  R.  H.  Governors  and  Governing  Mechanism nmo,  *2  50 

Hall,  W.  S.  Elements  of  th«  Differential  and  Integral  Calculus.  ..  .8vo,  2 75 

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Haller,  G.  F.,  and  Cunningham,  E.  T.  The  Tesla  Coil i2mo, 

Halsey,  F.  A.  Slide  Valve  Gears nmo, 

The  Use  of  the  Slide  Rules i6mo, 

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Hamlin,  M.  L.  Action  of  Chemicals  on  Industrial  Materials.  .8vo, 

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*1  25 
1 50 
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12  D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG 


Hancock,  H.  Textbook  of  Mechanics  and  Hydrostatics . ,8vo,  i 50 

Hardy,  E.  Elementary  Principles  of  Graphic  Statics i2mo,  *1  50 

Haring,  H.  Engineering  Law. 

Vol.  I.  Law  of  Contract 8vo,  *4  00 

Harper,  J.  H.  Hydraulic  Tables  on  the  Flow  of  Water i6mo,  *2  00 

Harris,  S.  M.  Practical  Topographical  Surveying (In  Press.) 


Harrow,  B.  Eminent  Chemists  of  Our  Times:  Their  Lives  and  Work.  2 50 


From  Newton  to  Einstein i2mo, 

Harvey,  A.  Practical  Leather  Chemistry 8vo, 

Haskins,  C.  H.  The  Galvanometer  and  Its  Uses i6mo, 

Hatt,  J.  A.  H.  The  Colorist. . *. square  nmo, 

Hausbrand,  E.  Drying  by  Means  of  Air  and  Steam nmo, 

Evaporating,  Condensing  and  Cooling  Apparatus 8vo, 

Hausmann,  E.  Telegraph  Engineering 8vo, 


Hausner,  A.  Manufacture  of  Preserved  Foods  and  Sweetmeats.  ..  .8vo, 
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4to, 

Hay,  A.  Continuous  Current  Engineering 8vo, 

Hayes,  H.  V.  Public  Utilities,  Their  Cost  New  and  Depreciation. . .8vo, 

Public  Utilities,  Their  Fair  Present  Value  and  Return 8vo, 

Heath,  F.  H.  Chemistry  of  Photography 8vo.  (In  Press.) 

Heather,  H.  J.  S.  Electrical  Engineering 8vo, 

Heaviside,  0.  Electromagnetic  Theory.  Vols.  I and  II....8vo,  each, 


( Reprinting .) 

Vol.  Ill 8vo  (Reprinting.)' 

Heck,  R.  C.  H.  The  Steam  Engine  and  the  Turbine 8vo, 

Steam-Engine  and  Other  Steam  Motors.  Two  Volumes. 

Vol.  I.  Thermodynamics  and  the  Mechanics 8vo, 

Vol.  II.  Form,  Construction,  and  Working 8vo, 

Notes  on  Elementary  Kinematics 8vo,  boards, 

Graphics  of  Machine  Forces 8vo,  boards, 

Heermann,  P.  Dyers’  Materials i2mo, 

Hellot,  Macquer  and  D’Apligny.  Art  of  Dyeing  Wool,  Silk  and  Cotton.  8vo, 
Hering,  C.,  and  Getman,  F.  H.  Standard  Tables  of  Electro-Chemical 

Equivalents  i2mo, 

Hering,  D.  W.  Essentials  of  Physics  for  College  Students 8vo, 

Herington,  C.  F.  Powdered  Coal  as  Fuel.  8vo, 

Herrmann,  G.  The  Graphical  Statics  of  Mechanism nmo, 

Herzfeld,  J.  Testing  of  Yarns  and  Textile  Fabrics 8vo. 


1 00 
6 00 

1 50 
* 2 00 

2 50 
6 00 

*3  00 

3 50 

2 00 

3 75 
*2  00 
*2  00 

4 50 


4 50 

4 5° 

5 5° 
*1  00 
*1  00 

3 00 
*2  00 

*2  00 
2 25 

4 50 
2 00 

6 00 


Hildenbrand,  B.  W.  Cable-Making i6mo. 

Hilditch,  T.  P.  A Concise  History  of  Chemistry nmo, 

Hill,  M.  J.  M.  The  Theory  of  Proportion 8vo, 

Hillhouse,  P.  A.  Ship  Stability  and  Trim 8vo, 

Hiroi,  I.  Plate  Girder  Construction i6mo, 

' Statically-Indeterminate  Stresses 1 2mo, 

Hirshfeld,  C.  F.  Engineering  Thermodynamics i6mo, 

Hoar,  A.  The  Submarine  Torpedo  Boat nmo. 

Hobart,  H.  M.  Heavy  Electrical  Engineering 8vo, 

Design  of  Static  Transformers nmo, 

Electricity 8vo, 

Electric  Trains 8vo  (Reprinting.) 

- Electric  Propulsion  of  Ships 8vo, 


o 75 
*1  50 
*2  50 
5 00 

o 75 
2 50 
o 75 
*2  00 

*4  50 
2 50 
*2  00 

*2  50 


D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG 


13 


Hobart,  J.  F.  Hard  Soldering,  Soft  Soldering  and  Brazing 121T10,  1 25 

Hobbs,  W.  R.  P.  The  Arithmetic  of  Electrical  Measurements. ..  ,i2mo,  o 75 

Hoff,  J.  N.  Paint  and  Varnish  Facts  and  Formulas..... i2mo,  2 00 

Hole,  W.  The  Distribution  of  Gas 8vo,  *8  50 

Holmes,  A.  Nomenclature  of  Petrology 8vo,  5 00 

Hopkins,  N.  M.  Model  Engines  and  Small  Boats i2mo,  1 25 

The  Outlook  for  Research  and  Invention i2mo.  2 00 

Hopkinson,  J.,  Shoolbred,  J.  N.,  and  Day,  R.  E.  Dynamic  Electricity. 

i6mo.  o 75 

Horner,  J.  Practical  Ironfounding 8vo,  *2  00 

Gear  Cutting,  in  Theory  and  Practice 8vo  ( Reprinting .) 

Houghton,  C.  E.  The  Elements  of  Mechanics  of  Materials i2mo,  2 50 

Houstoun,  R.  A.  Studies  in  Light  Production i2mo,  2 00 

Hovenden,  F.  Practical  Mathematics  for  Young  Engineers i2mo,  *1  50 

Howe,  G.  Mathematics  for  the  Practical  Man i2mo,  1 50 

Eoworth,  J.  Repairing  and  Riveting  Glass,  China  and  Earthenware. 


8vo,  paper, 

*0  50 

Hoyt,  W.  E. 

Chemistry  by  Experimentation 

8vo, 

*0  70 

Hubbard,  E. 

The  Utilization  of  Wood-waste 

8 vo, 

4 5° 

Eiibner,  J.  Bleaching  and  Dyeing  of  Vegetable  and  Fibrous  Materials. 


8vo,  7 50 

Hudson,  0.  F.  Iron  and  Steel 8vo,  2 50 

Humphreys,  A.  C.  The  Business  Features  of  Engineering  Practice . 8 vo,  2 50 

Hunter,  A.  Bridge  Work 8vo.  (In  Press.) 

Hurst,  G.  H.  Handbook  of  the  Theory  of  Color 8vo,  *3  50 

Dictionary  of  Chemicals  and  Raw  Products 8vo,  *5  00 

Lubricating  Oils,  Fats  and  Greases 8vo,  *5  00 

Soaps  8vo,  *6  00 

Hurst,  G.  H.,  and  Simmons,  W.  H.  Textile  Soaps  and  Oils 8vo,  3 50 

Hurst,  H.  E.,  and  Lattey,  R.  T.  Text-book  of  Physics 8vo,  *3  00 

Also  published  in  three  parts. 

Part  I.  Dynamics  and  Heat 2 00 

Part  II.  Sound  and  Light 2 00 

Part  III.  Magnetism  and  Electricity 2 00 


Hutchinson,  R.  W.,  Jr.  Long  Distance  Electric  Power  Transmission. 

i2mo,  3 00 


Hutchinson,  R.  W.,  Jr.,  and  Thomas,  W.  A.  Electricity  in  Mining.  i2mo, 

(In  Press.) 


Hyde,  E.  W.  Skew  Arches i6mo.  0 75 

Hyde,  F.  S.  Solvents,  Oils,  Gums,  Waxes 8vo,  *2  00 


Induction  Coils  r6mo.  o 75 

Ingham,  A.  E.  Gearing.  A practical  treatise 8vo,  *2  50 

Ingle,  H.  Manual  of  Agricultural  Chemistry 8vo,  5 00 

Inness,  C.  H.  Problems  in  Machine  Design T2mo,  *3  00 

Centrifugal  Pumps  i2mo,  *3  00 

The  Fan  i2mo,  *4  00 

Jacob,  A.,  and  Gould,  E.  S.  On  the  Designing  and  Construction  of 

Storage  Reservoirs  o 75 


I4  D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG 


Jacobs,  F.  B.  Cam  Design  and  Manufacture ( In  Press.) 

James,  F.  D.  Controllers  for  Electric  Motors 8vo. 

Jehl,  F.  Manufacture  of  Carbons 8vo. 

Jennings,  A.  S.  Commercial  Paints  and  Painting 8vo. 

Jennison,  F.  H.  The  Manufacture  of  Lake  Pigments 8vo, 


Jepson,  G.  Cams  and  the  Principles  of  their  Construction 8vo, 

Mechanical  Drawing 8vo  (In  Preparation.) 

Jervis-Smith,  F.  J.  Dynamometers 8vo. 

Jockin,  W.  Arithmetic  of  the  Gold  and  Silversmith i2mo, 

Johnson,  C.  H.,  and  Earle,  R.  P.  Practical  Tests  for  the  Electrical 

Laboratory  ( In  Press.) 

Johnson,  J.  H.  Arc  Lamps  and  Accessory  Apparatus i2mo, 

Johnson,  T.  M.  Ship  Wiring  and  Fitting i2mo  ( Reprinting .) 


Johnston,  J.  F.  W.,  and  Cameron,  C.  Elements  of  Agricultural  Chemistry 

and  Geology i2mo, 

Joly,  J.  Radioactivity  and  Geology i2mo  (Reprinting.) 

Jones,  H.  C.  Electrical  Nature  of  Matter  and  Radioactivity.  ... i2mo, 

Nature  of  Solution 8vo, 

New  Era  in  Chemistry nmo, 

Jones,  J.  H.  Tinplate  Industry 8vo 

Jones,  M.  W.  Testing  Raw  Materials  Used  in  Paint i2mo, 


Jordan,  L.  C.  Practical  Railway  Spiral i2mo,  leather, 

Jiiptner,  H.  F.  V.  Siderclogy:  The  Science  of  Iron 8vo, 


* 


Kapp,  G.  Alternate  Current  Machinery i6mo, 

Kapper,  F.  Overhead  Transmission  Lines 4to, 

Keim,  A.  W.  Prevention  of  Dampness  in  Buildings 8vo, 

Keller,  S.  S.,  and  Knox,  W.  E.  Analytical  Geometry  and  Calculus... 
Kemble,  W.  T.,  and  Underhill,  C.  R.  The  Periodic  Law  and  the  Hydrogen 

Spectrum i. . . 8vo,  paper, 

Kemp,  J.  F.  Handbook  of  Rocks 8vo, 

Kennedy,  A.  B.  W.,  and  Thurston,  R.  H.  Kinematics  of  Machinery. 

i6mo, 

Kennedy,  A.  B.  W.,  Unwin,  W.  C.,  and  Idell,  F.  E.  Compressed  Air. 


i6mo, 

Kennedy,  R.  Flying  Machines:  Practice  and  Design nmo, 

Principles  of  Aeroplane  Construction 8vo, 

Kent,  W.  Strength  of  Materials i6mo, 


Kershaw,  J.  B.  C.  Fuel,  Water  and  Gas  Analysis 8vo, 

Electrometallurgy  8vo, 

— — Electro-Thermal  Methods  of  Iron  and  Steel  Production.  ..  .8vo, 

The  Use  of  Low  Grade  and  Waste  Fuel  for  Power  Generation . 8vo, 

Kingzett,  C.  T.  Popular  Chemical  Dictionary 8vo, 

Kinzbrunner,  C.  Continuous  Current  Armatures 8vo, 

— ■—  Testing  of  Alternating  Current  Machines 8vo,  * 

Kinzer,  H.,  and  Walter,  K.  Theory  and  Practice  of  Damask  Weaving, 

8vo, 

Kirkaldy,  A..  W.,  and  Evans,  A.  D.  History  and  Economics  of 

Transport  8vo,  * 

’’irkbride,  J.  Engraving  for  Illustration 8vo,  * 


2 oo 

5 oo 
2 so 

6 oo 

i 50 

4 00 
I 00 


0 75 

2 6o 

2 25 

3 75 
2 00 

3 oo 
2 50 

1 50 
’5  00 

0 75 
■4  00 
■2  50 

2 00 

d 50 

1 75 

o 75 

o 75 

2 50 
'2  00 

0 75 

3 50 

2 50 

3 00 

4 00 
4 00 

1 50 

2 00 

4 OO 

3 00 
1 00 


D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG  15 

Kirschke,  A.  Gas  and  Oil  Engines izmo,  *1  50 

Klein,  J.  F.  Design  of  a High-speed  Steam-engine 8vo,  *5  00 

Physical  Significance  of  Entropy 8vo,  *1  50 

Klingenberg,  G.  Large  Electric  Power  Stations 4to,  9 00 

Knight,  R.-Adm.  A.  M.  Modern  Seamanship 8vo,  *6  50 

Pocket  Edition i2mo,  fabrikoid,  3 00 

Knott,  C.  G.,  and  Mackay,  J.  S.  Practical  Mathematics 8vo,  2 50 

Knox,  J.  Physico-Chemical  Calculations nmo,  x 50 

— —Fixation  of  Atmospheric  Nitrogen i2mo,  1 00 

Koester,  F.  Steam-Electric  Power  Plants 4to,  *500 

Hydroelectric  Developments  and  Engineering 4to,  6 00 

Koller,  T.  The  Utilization  of  Waste  Products 8vo,  *5  00 

Cosmetics  8vc,  3 50 

Koppe,  S.  W.  Glycerine 121110,  *3  50 

Kozmin,  P.  A.  Flour  Milling 8vo,  8 50 

Krauch,  C.  Chemical  Reagents 8vo,  7 co 

Kremann,  R.  Application  of  the  Physico-Chemical  Theory  to  Tech- 
nical Process  and  Manufacturing  Methods Svo,  3 00 

Kretchmar,  K.  Yarn  and  Warp  Sizing 8vo,  *5  00 

Laffargue,  A.  Attack  in  Trench  Warfare i6mo,  o 50 

Lallier,  E.  V.  Elementary  Manual  of  the  Steam  Engine iamo,  *2  00 

Lambert,  T.  Lead  and  Its  Compounds 8vo,  *3  50 

Bone  Products  and  Manures 8vo,  *3  50 

Lamborn,  L.  L.  Cottonseed  Products 8vo,  4 00 

Modern  Soaps,  Candles,  and  Glycerin Svo,  10  00 

Lamprecht,  R.  Recovery  Work  After  Pit  Fires 8vo,  5 00 

Lanchester,  F.  W.  Aerial  Flight.  Two  Volumes.  8vo. 

Vol.  I.  Aerodynamics *6  00 

Vol.  II.  Aerodonetics *6  00 

Lanchester,  F.  W.  The  Flying  Machine 8vo,  *3  00 

Industrial  Engineering:  Present  and  Post-War  Outlook.  .. i2mo,  1 00 

Lange,  K.  R.  By-Products  of  Coal-Gas  Manufacture i2mo,  2 50 

La  Rue,  B.  F.  Swing  Bridges i6mo,  o 75 

Lassar-Cohn,  Dr.  Modern  Scientific  Chemistry i2mo,  2 25 

Latimer,  L.  H.,  Field,  C.  J.,  and  Howell,  J.  W.  Incandescent  Electric 

Lighting  i6mo,  o 75 

Latta,  M.  N.  Handbook  of  American  Gas-Engineering  Practice.  ,8vo,  5 00 

American  Producer  Gas  Practice 4to,  *6  00 

Laws,  B.  C.  Stability  and  Equilibrium  of  Floating  Bodies 8vo,  4 50 

Lawson,  W.  R.  British  Railways.  A Financial  and  Commercial 

Survey 8vo,  2 00 

Leask,  A.  R.  Refrigerating  Machinery nmo  ( Reprinting .) 

Lecky,  S.  T.  S.  “Wrinkles”  in  Practical  Navigation 8vo,  10  00 

Pocket  Edition  r2mo,  5 00 

Danger  Angle  i6mo,  2 50 

Le  Doux,  M.  Ice-Making  Machines i6mo,  o 75 

Leeds,  C.  C.  Mechanical  Drawing  for  Trade  Schools oblong  4t»,  2 25 

Mechanical  Drawing  for  High  and  Vocational  Schools 4to,  r 50 

Principles  of  Engineering  Drawing 8vo,  2 50 

Lefevre,  L.  Architectural  Pottery 4to,  7 00 

Lehner,  S.  Ink  Manufacture 8vo,  2 50 

Lemstrom,  S.  Electricity  in  Agriculture  and  Horticulture 8vo,  *r  50 

Letts,  E.  A.  Fundamental  Problems  in  Chemistry .-.  ,8vo,  *2  00 


1 6 D.  VAN  NOSTRAND  cO.’S  SHORT  "ITLE  CATALOG 


Le  Van,  W.  B.  Steam-Engine  Indicator i6mo,  o 75 

Lewes,  V.  B.  Liquid  and  Gaseous  Fuels 8vo,  3 00 

• Carbonization  of  Coal 8vo,  *5  oo 

Lewis  Automatic  Machine  Rifle;  Operation  of i6mo,  *060 

Licks,  H.  E.  Recreations  in  Mathematics 121110,  1 50 

Lieber,  B.  F.  Lieber’s  Five  Letter  American  Telegraphic  Code  .8vo,  *15  00 

Spanish  Edition  8vo,  *15  00 

French  Edition  Svo,  *r5  00 

Terminal  Index 8vo,  *250 

Lieber’s  Appendix folio,  *15  00 

Handy  Tables 4to,  *2  50 

Bankers  and  Stockbrokers’  Code  and  Merchants  and  Shippers’ 

Blank  Tables 8vo,  *15  00 

100,000,000  Combination  Code 8vo,  *10  00 


Livermore,  V.  P.,  and  Williams,  J.  How  to  Become  a Competent  Motor- 


man  i2mo,  *T  00 

Livingstone,  R.  Design  and  Construction  of  Commutators 8vo,  4 50 

Mechanical  Design  and  Construction  of  Generators 8vo,  4 50 


Lloyd,  S.  L.  Fertilizer  Materials i2mo,  2 00 

Lockwood,  T.  D.  Electricity,  Magnetism,  and  Electro-telegraph  . . . 8vo,  2 50 

— Electrical  Measurement  and  the  Galvanometer i2mo,  o 75 

Lodge,  O.  J.  Elementary  Mechanics nmo,  1 50 

Loewenstein,  L.  C.,  and  Crissey,  C.  P.  Centrifugal  Pumps 5 00 

Lomax,  J.  W.  Cotton  Spinning i2mo,  1 50 

Lord,  R.  T.  Decorative  and  Fancy  Fabrics Svo,  *3  50 

Loring,  A.  E.  A Handbook  of  the  Electromagnetic  Telegraph.  ..i6mo,  o 75 

Lowy,  A.  Organic  Type  Formulas o 10 

Lubschez,  B.  J.  Perspective nmo,  2 00 


Lucke,  C.  E.  Gas  Engine  Design Svo, 

Power  Plants:  Design,  Efficiency,  and  Power  Costs.  2 vols. 

(In  Preparation.) 

Luckiesh,  M.  Color  and  Its  Application 8vo, 

Light  and  Shade  and  Their  Applications Svo, 

Visual  Illusions (In  Preparation .) 

Lunge,  G.  Coal-tar  and  Ammonia.  Three  Volumes 8vo, 

Technical  Gas  Analysis Svo, 

Manufacture  of  Sulphuric  Acid  and  Alkali.  Four  Volumes. . . .8vo, 

Vol.  I.  Sulphuric  Acid.  In  three  parts ( Reprinting .) 

Vol.  I.  Supplement  8vo  ( Reprinting .) 

Vol.  H.  Salt  Cake,  Hydrochloric  Acid  and  Leblanc  Soda.  In  two 

parts  (In  Press.) 

Vol.  III.  Ammonia  Soda (In  Press.) 


*3  00 


3 50 
3 00 

*25  00 
*4  50 


Vol.  IV.  Electrolytic  Methods (In  Press.) 

- Technical  Chemists’  Handbook izmo,  leather,  *400 

Technical  Methods  of  Chemical  Analysis. 

Vol.  I.  In  two  parts Svo  (New  Edition  in  Press.) 

Vol.  II.  In  two  parts 8vo  (New  Edition  in  Press.) 

Vol.  III.  In  two  parts 8vo  (New  Edition  in  Press.) 

The  set  (3  vols.)  complete 


D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG  17 


Luquer,  L.  M.  Minerals  in  Rock  Sections 8vo,  1 75 

MacBride,  J.  D.  A Handbook  of  Practical  Shipbuilding, 

i2mo,  fabrikoid,  2 00 

Macewen,  H.  A.  Food  Inspection 8vo,  *2  50 

Mackenzie,  N.  F.  Notes  on  Irrigation  Works 8vo,  *2  50 

Mackie,  J.  How  to  Make  a Woolen  Mill  Pay 8vo,  *2  00 

Maguire,  Wm.  R.  Domestic  Sanitary  Drainage  and  Plumbing  . . . .8vo,  4 00 

Malcolm,  H.  W.  Submarine  Telegraph  Cable 9 00 

Malinovzsky,  A.  Analysis  of  Ceramic  Materials  and  Methods  of 

Calculation  (In  Press.) 

Mallet,  A.  Compound  Engines i6mo, 

Mansfield,  A.  N.  Electro-magnets i6mo,  o 75 

Marks,  E.  C.  R.  Construction  of  Cranes  and  Lifting  Machinery . i2mo,  *2  75 

Manufacture  of  Iron  and  Steel  Tubes i2mo,  2 50 

■ Mechanical  Engineering  Materials i2mo,  *r  50 

Marks,  G.  C.  Hydraulic  Power  Engineering 8vo,  4 50 

Marlow,  T.  G.  Drying  Machinery  and  Practice. ..  .8vo  ( Reprinting .) 


Marsh,  C.  F.  Concise  Treatise  on  Reinforced  Concrete  8vo,  *2  50 

* Reinforced  Concrete  Compression  Member  Diagram.  Mounted  on 

Cloth  Boards *1.50 

Marsh,  C.  F.,  and  Dunn,  W.  Manual  of  Reinforced  Concrete  and  Con- 
crete Block  Construction i6mo,  2 00 

Marshall,  W.  J.,  and  Sankey,  H.  R.  Gas  Engines 8vo,  2 00 

Martin,  G.  Triumphs  and  Wonders  of  Modern  Chemistry 8vo,  *3  00 

- — —Modern  Chemistry  and  Its  Wonders 8vo,  *3  00 

Martin,  N.  Properties  and  Design  of  Reinforced  Concrete 8vo,  1 50 

Martin,  W.  D.  Hints  to  Engineers i2mo,  2 00 

Massie,  W.  W.,  and  Underhill,  C.  R.  Wireless  Telegraphy  and  Telephony. 

i2mo,  *r  00 

Mathot,  R.  E.  Internal  Combustion  Engines 8vo,  5 00 

Maurice,  W.  Electric  Blasting  Apparatus  and  Explosives 8vo,  *3  50 

Shot  Firer’s  Guide 8vo,  *1  50 

Maxwell,  F.  Sulphitation  in  White  Sugar  Manufacture i2mo,  4 00 

Maxwell,  J.  C.  Matter  and  Motion i6mo,  o 75 

Maxwell,  W.  H.,  and  Brown,  J.  T.  Encyclopedia  of  Muni  ipal  and  Sani- 
tary Engineering 4to,  *ro  00 

Mayer,  A.  M.  Lecture  Notes  on  Physics 8vo,  2 00 


McCracken,  E.  M.,  and  Sampson,  C.  H.  Course  in  Pattern  Making. 

(In  Press.) 

McCullough,  E.  Practical  Surveying i2mo,  3 00 

McCullough,  R.  S.  Mechanical  Theory  of  Heat 8vo,  3 50 

McGibbon.  W.  C.  Indicator  D’ag'ams  for  Marine  Engineers 8vo,  *3  50 

Marine  Engineers’  Drawing  Book oblong  4to,  *2  50 

McGibbon,  W.  C.  Marine  Engineers  Pocketbook i2mo,  *4  50 

McIntosh,  J.  G.  Technology  of  Sugar 8vo,  *6  00 

Industrial  Alcohol  8vo,  *3  50 

Manufacture  of  Varnishes  and  Kindred  Industries.  Three  Volumes. 


8vo. 

Vol.  I.  Oil  Crushing,  Refining  and  Boiling 7 00 

Vol.  II.  Varnish  Materials  and  Oil  Varnish  Making 5 00 

Vol.  III.  Spirit  Varnishes  and  Materials 600 


IS  D VAN  > OSTRAND  CO.’S  SHORT  TITLE  CATALOG 


McKillop.  M.,  arc  McKillop,  A.  D.  Efficiency  Methods .i2mo,  i 50 

McKnight  } D.,  and  Brown,  A.  W.  Marine  Multitubular  Boilers....  *2  50 

McMaster  J B Bridge  and  Tunnel  Centres i6mo,  o 75 

McMe'-hen,  F L.  Tests  for  Ores,  Minerals  and  Metals i2mo,  1 50 

McNair,  F.  V Handbook  for  Naval  Officers i2mo,  4 00 

Meade,  A.  Modern  Gas  Works  Practice ...8vo,  *8  50 

Melick,  C.  W.  Fairy  Laboratory  Guide  . nmo,  *1  25 

“Mentor.”  Self-Instruction  for  Students  in  Gas  Supply.  i2mo. 

Elementary  . 2 50 

Advanced  . 2 50 

Self-Instruction  for  Students  in  Gas  Engineering.  i2mo. 

Elementary  2 00 

Advanced  2 00 

Merivale,  J.  H.  Notes  and  Formulae  for  Mining  Students nmo,  1 00 

Merritt,  Wm.  H.  Field  Testing  for  Gold  and  Silver.  ...  i6mo,  leather,  2 50 

Mertens.  Tactics  and  Technique  of  River  Crossings ,8vo,  3 00 

Mierzinski,  S.  Waterproofing  of  Fabrics 8vo,  2 50 

Miessner,  B.  F.  Radio  Dynamics '. nmo,  *2  00 

Miller,  G.  A.  Determinants i6mo, 

Miller,  W.  J Introduction  to  Historical  Geology nmo,  2 50 

Milroy,  M.  E.  W.  Home  Lace-making nmo,  *1  00 

Church  Lace  nmo,  2 50 

Mills,  C.  N.  Elementary  Mechanics  for  Engineers 8vo,  1 25 

Mitchell,  C.  A.  Mineral  and  Aerated  Waters 8vo,  *3  00 

Mitchell,  C A.,  and  Prideaux,  R.  M.  Fibres  Used  in  Textile  and  Allied 

Industries  8vo,  3 50 

Mitchell,  C.  F.,  and  G.  A.  Building  Construction  and  Drawing,  nmo. 

Elementary  Course  2 50 

Advanced  Course  4 50 

Monckto'*  C.  C.  F,  Radiotelegraphy 8vo,  2 00 

Monteverde*  R.  D.  Vest  Pocket  Glossary  of  English-Spanisn,  Spanish- 

English  Technical  Terms 64mo,  leather,  1 50 

Montgor  ./y,  J.  H.  Electric  Wiring  Specifications i6mo,  *1  00 

Moore,  E,  C.  S New  Tables  for  the  Complete  Solution  of  Ganguillet  and 

Kutter’s  Formula  8vo,  *6  00 


Moore,  Harold.  Liquid  Fuel  for  Internal  Combustion  Engines.  . ,8vo,  5 00 

Morecroft,  J.  H.,  and  Hehre,  F.  W.  Short  Course  in  Electrical  Testing. 

8vo,  2 00 

Morgan,  A.  P Wireless  Telegraph  Construction  for  Amateurs.  . nmo,  1 so 

Morgan,  J.  D Principles  of  Electric  Spark  Ignition 8vo,  3 50 

Morrell,  R.  S.,  and  Waele,  A.  E.  Rubber,  Resins,  Paints  and  Var- 
nishes   8vo  (In  Press.) 

Moses,  A.  J The  Characters  of  Crystals 8vo,  *2  00 

and  Parsons,  C.  L.  Elements  of  Mineralogy 8vo,  4 50 

Moss,  S.  A.  Elements  of  Gas  Engine  Design i6mo,  o 75 

The  Lay-out  of  Corliss  Valve  Gears i6mo,  o 75 

Mulford,  A.  C.  Boundaries  and  Landmarks i2mo,  1 00 

Munby,  A.  E.  Chemistry  and  Physics  of  Building  Materials.  ..  .8vo,  2 50 

Murphy,  J G.  Practical  Mining i6mo,  1 00 

Murray,  B.  M.  Chemical  Reagents 8vo,  3 00 

Murray,  J.  A.  Soils  and  Manures ,,,,,,,,  .8vo,  2 00 


Nasmith,  J.  The  Student’s  Cotton  Spinning 
Recent  Cotton  Mill  Construction 


.8vo, 

i2mo, 


4 50 

3 00 


D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG  19 

Neave,  G.  B.,  and  Heilbron,  I.  M.  Identification  of  Organic  Compounds. 

i2mo,  x 50 

Neilson,  R.  M.  Aeroplane  Patents 8vo,  *2  00 

Nerz,  F.  Searchlights 8vo  (Reprinting.) 

Newbigin,  M.  I.,  and  Flett,  J.  S.  James  Geikie,  the  Man  and  the 

Geologist 8vo,  3 50 

Newbiging,  T.  Handbook  for  Gas  Engineers  and  Managers 8vo,  7 50 

Newell,  F.  H.,  and  Drayer,  C.  E.  Engineering  as  a Career.  ,i2mo,  cloth,  *1  00 

Nicol,  G.  Ship  Construction  and  Calculations 8vo,  *10  00 

Nipher,  F.  E.  Theory  of  Magnetic  Measurements i2mo,  1 00 

Nisbet,  H.  Grammar  of  Textile  Design 8vo,  7 50 

Nolan,  H.  The  Telescope i6mo,  o 75 

Norie,  J.  W.  Epitome  of  Navigation  (2  Vols.) octavo,  15  00 

A Complete  Set  of  Nautical  Tables  with  Explanations  of  Their 

Use  octavo,  6*50 

North,  H.  B.  Laboratory  Experiments  in  General  Chemistry i2mo,  *1  00 

O’Connor,  H.  The  Gas  Engineer’s  Pocketbook i2mo,  leather,  5 00 

Ohm,  G.  S.,  and  Lockwood,  T.  D.  Galvanic  Circuit i6mo,  o 75 

Olsen,  J.  C.  Text-book  of  Quantitative  Chemical  Analysis 8vo,  4 00 

Ormsby,  M.  T.  M.  Surveying i2mo,  2 00 

Gudin,  M.  A.  Standard  Polyphase  Apparatus  and  Systems 8vo,  *3  00 

Pakes,  W.  C.  C.,  and  Nankivell,  A.  T.  The  Science  of  Hygiene  . .8vo,  *1  75 

Palaz,  A.  Industrial  Photometry 8vo,  5 00 

Palmer,  A.  R.  Electrical  Experiments i2mo,  o 75 

Magnetic  Measurements  and  Experiments i2mo,  o 75 

Pamely,  C.  Colliery  Manager’s  Handbook 8vo,  *10  00 

Parker,  P.  A.  M.  The  Control  of  Water 8vo,  6 00 

Parr,  G.  D.  A.  Electrical  Engineering  Measuring  Instruments.  ..  .8vo,  *3  50 

Parry,  E.  J.  Chemistry  of  Essential  Oils  and  Artificial  Perfumes. 

Vol.  I.  Monographs  on  Essential  Oils 9 00 

Vol.  II.  Constituents  of  Essential  Oils,  Analysis 7 00 

Foods  and  Drugs.  Two  Volumes. 

Vol.  I.  The  Analysis  of  Food  and  Drugs 8vo,  9 50 

Vol.  II.  The  Sale  of  Food  and  Drugs  Acts 8vo,  3 50 

and  Coste,  J.  H.  Chemistry  of  Pigments 8vo,  *5  00 

Parry,  L.  Notes  on  Alloys 8vo,  *3  50 

Metalliferous  Wastes  8vo,  *2  50 

-Analysis  of  Ashes  and  Alloys 8vo,  *2  50 

Parry,  L.  A.  Risk  and  Dangers  of  Various  Occupations 8vo,  *3  50 

Parshall,  H.  F.,  and  Hobart,  H.  M.  Electric  Railway  Engineering . 4to,  7 50 

Parsons,  J.  L.  Land  Drainage 8vo,  *1  50 

Parsons,  S.  T.  Malleable  Cast  Iron 8vo,  3 50 

Partington,  T.  R.  Higher  Mathematics  for  Chemical  Students.  . nmo,  2 50 

Textbook  of  Thermodynamics 8vo,  *4  00 

The  Alkali  Industry .....8vo,  3 00 

Patchell,  W.  H.  Electric  Power  in  Mines 8vo,  *4  00 

Paterson,  G.  W.  L.  Wiring  Calculations nmo,  *2  30 

Electric  Mine  Signalling  Installations nmo,  *1  50 

Patterson,  D.  The  Color  Printing  of  Carpet  Yarns 8vo,  *3  50 

Color  Matching  on  Textiles 8vo,  *3  50 

Textile  Color  Mixing 8vo,  *3  50 


20 


D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG 


Paulding,  C.  P.  Condensation  of  Steam  in  Covered  and  Bare  Pipes . . 8vo,  *2  00 

Transmission  of  Heat  through  Cold-storage  Insulation nmo,  *1  00 

Payne,  D.  W.  Iron  Founders’  Manual 8vo,  4 50 

Peddie,  R.  A.  Engineering  and  Metallurgical  Books nmo,  *1  50 

Peirce,  B.  System  of  Analytic  Mechanics 4to,  10  00 

Linear  Associative  Algebra 4to,  2 50 

Perkin,  F.  M.,  and  Jaggers,  E.  M.  Elementary  Chemistry  . . . nmo,  1 00 

Perrin,  J.  Atoms 8vo,  *2  50 

Petit,  G.  White  Lead  and  Zinc  White  Paints 8vo,  *2  00 

Petit,  R.  How  to  Build  an  Aeroplane 8vo,  1 50 

Pettit,  Lieut.  J.  S.  Graphic  Processes . ...i6mo,  075 

Philbrick,  P.  H.  Beams  and  Girders i6mo, 

Phin,  J.  Seven  Follies  of  Science 12  mo,  *1  50 

Pickworth,  C.  N.  Logarithms  for  Beginners nmo,  boards,  1 00 

x The  Slide  Rule nmo,  1 50 

Pilcher,  R.  B.  The  Profession  of  Chemistry nmo,  2 00 

Pilcher,  R.  B.,  and  Butler-Jones,  F.  What  Industry  Owes  to  Chemical 

Science nmo,  1 50 

Plattner’s  Manual  of  Blow-pipe  Analysis.  Eighth  Edition,  revised. 8vo,  4 00 

Plympton,  G.  W.  The  Aneroid  Barometer i6mo,  o 75 

How  to  Become  an  Engineer i6mo,  o 75 

Van  Nostrand’s  Table  Book  i6mo,  0 75 

Pochet,  M.  L.  Steam  Injectors i6mo,  o 75 

Pocket  Logarithms  to  Four  Places i6mo,  o 75 

i6mo,  leather,  1 00 

Polleyn,  F.  Dressings  and  Finishings  for  Textile  Fabrics Svo,  *3  50 

Pollock,  W.  Hot  Bulb  Oil  Engines  and  Suitable  Vessels 8vo,  10  00 

Pope,  F.  G.  Organic  Chemistry nmo,  3 00 

Pope,  F.  L.  Modern  Practice  of  the  Electric  Telegraph 8vo,  1 50 

Popplewell,  W.  C.  Prevention  of  Smoke Svo,  *3  50 

Strength  of  Materials 8vo,  *2  50 

Porritt,  B.  D.  The  Chemistry  of  Rubber nmo,  1 00 

Porter,  J.  R.  Helicopter  Flying  Machine nmo,  1 50 

Potts,  H.  E.  Chemistry  of  the  Rubber  Industry 8vo,  2 50 

Practical  Compounding  of  Oils,  Tallows  and  Grease..  8vo,  *3  50 

Pratt,  A.  E.  Economic  Metallurgy (In  Press.) 

Pratt,  Jas.  A.  Elementary  Machine  Shop  Practice (In  Press.) 

Pratt,  K.  Boiler  Draught nmo,  *1  25 

Prelini,  C.  Earth  and  Rock  Excavation 8vo,  *3  00 

Graphical  Determination  of  Earth  Slopes 8vo,  *2  00 

Tunneling.  New  Edition  8vo,  *3  00 

• Dredging.  A Practical  Treatise 8vo,  *3  00 

Prescott,  A.  B.,  and  Johnson,  0.  C.  Qualitative  Chemical  Analysis.  ,8vo,  4 00 

Prescott,  A.  B.,  and  Sullivan,  E.  C.  First  Book  in  Qualitative  Chemistry.  1 50 

Prideaux,  E.  B.  R.  Problems  in  Physical  Chemistry 8vo,  4 50 

The  Theory  and  Use  of  Indicators 8vo,  5 00 

Prince,  G.  T.  Flow  of  Water i2mo,  *2  00 

Pull,  E.  Modern  Steam  Boilers 8vo,  5 00 

Pullen,  W.  W.  F.  Application  of  Graphic  Methods  to  the  Design  of 

nmo,  *1  50 

Structures  nmo,  3 00 

Injectors:  Theory,  Construction  and  Working nmo,  *2  00 

Indicator  Diagrams  8vo,  3 00 

Engine  Testing  8vo,  *5  50 


D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG 


21 


Purday,  H.  F.  P.  The  Diesel  Engine  Design 8vo,  7 50 

Putsch,  A.  Gas  and  Coal-dust  Firing 8vo,  *2  50 


Rafter,  G.  W.  Mechanics  of  Ventilation i6mo, 

Potable  Water  i6mo, 

-Treatment  of  Septic  Sewage i6mo, 

and  Baker,  M.  N.  Sewage  Disposal  in  the  United  States.  ..  .4to, 

Raikes,  H.  P.  Sewage  Disposal  Works 8vo, 

Randau,  P.  Enamels  and  Enamelling 8vo, 

Rankine,  W.  J.  M.  A Manual  of  Applied  Mechanics 8vo, 

Civil  Engineering  8vo. 

Machinery  and  Millwork 8vo, 

-The  Steam-engine  and  Other  Prime  Movers 8vo, 

Rankine,  W.  J.  M.,  and  Bamber,  E.  F.  A Mechanical  Text-book.  .8vo, 

Purday,  H.  F.  P.  The  Diesel  Engine  Design 8vo  (In  Press.) 

Raphael,  F.  C.  Localization  of  Faults  in  Electric  Light  and  Power  Mains. 

8vo, 

Rasch,  E.  Electric  Arc  Phenomena 8vo, 

Rathbone,  R.  L.  B.  Simple  Jewellery 8vo, 

Rausenberger,  F.  The  Theory  of  the  Recoil  Guns 8vo, 


Rautenstrauch,  W.  Notes  on  the  Elements  of  Machine  Design. 8vo,  boards, 
Rautenstrauch,  W.,  and  Williams,  J.  T.  Machine  Drafting  and  Empirical 


Design. 

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Part  II.  Empirical  Design (In  Preparation.) 

Raymond,  E.  B.  Alternating  Current  Engineering nmo, 

Rayner,  H.  Silk  Throwing  and  Waste  Silk  Spinning 8vo, 

Recipes  for  the  Color,  Paint,  Varnish,  Oil,  Soap  and  Drysaltery  Trades, 

Svo, 

Recipes  for  Flint  Glass  Making nmo, 

Redfern,  J.  B.,  and  Savin,  J.  Bells,  Telephones i6mo, 

Redgrove,  H.  S.  Experimental  Mensuration i2mo, 

Reed,  S.  Turbines  Applied  to  Marine  Propulsion 

Reed’s  Engineers’  Handbook 8vo, 

Key  to  the  Nineteenth  Edition  of  Reed’s  Engineers’  Handbook.  .8vo, 

— —Useful  Hints  to  Sea -going  Engineers nmo, 


Reid,  E.  E.  Introduction  to  Research  in  Organic  Chemistry.  (In  Press.) 


Reinhardt,  C.  W.  Lettering  for  Draftsmen,  Engineers,  and  Students. 

oblong  4to,  boards, 

Reinhardt,  C.  W.  The  Technic  of  Mechanical  Drafting, 

oblong,  4to,  boards, 

Reiser,  F.  Hardening  and  Tempering  of  Steel nmo, 

Reiser,  N.  Faults  in  the  Manufacture  of  Woolen  Goods 8vo, 

Spinning  and  Weaving  Calculations 8vo, 

Renwick,  W.  G.  Marble  and  Marble  Working.  ..  ,8vo  (Reprinting.) 

Reuleaux,  F.  The  Constructor 4to, 

Rey,  Jean.  The  Range  of  Electric  Searchlight  Projectors 8vo, 

( Reprinting .) 

Reynolds,  0.,  and  Idell,  F.  E.  Triple  Expansion  Engines r6mo, 

Rhead,  G.  F.  Simple  Structural  Woodwork nmo, 

Rhead,  G.  W.  British  Pottery  Marks 8vo, 

Rhodes,  H.  J.  Art  of  Lithography 8vo, 

Rice,  J.  M and  Johnson,  W.  W.  A New  Method  of  Obtaining  the  Differ- 
ential of  Functions 12  mo, 


o 75 
o 75 
' o 75 

6 00 
*4  00 
*5  00 

6 00 

7 5° 
6 00 
6 00 
4 00 


5 00 
2 00 
2 50 
*5  00 
*1  50 


1 5° 
*2  50 


*5  00 
*5  00 

0 75 

1 50 
*5  00 
12  00 
4 00 
3 00 


1 25 

*1  00 

2 50 
2 50 

*5  00 

4 00 


0 75 
*1  25 
3 50 
5 00 

0 50 


22 


D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG 


Richards,  W.  A.  Forging  of  Iron  and  Steel i2mo,  2 25 

Richards,  W.  A.,  and  North,  H.  B.  Manual  of  Cement  Testing. . . . i2mo,  *1  50 

Richardson,  J.  The  Modern  Steam  Engine 8vo,  *3  30 

Richardson,  S.  S.  Magnetism  and  Electricity i2mo,  *2  00 

Rideal,  E.  E.  Industrial  Electrometallurgy 8vo,  3 00 

-The  Rare  Earths  and  Metals 8vo  ( In  Press.) 

— —Ozone  8vo,  4 00 

Rideal,  S.  Glue  and  Glue  Testing 8vo,  *5  00 

The  Carbohydrates 8vo  {In  Press.) 

Riesenberg,  F.  The  Men  on  Deck 12010,  3 00 

Standard  Seamanship  for  the  Merchant  Marine.  i2mo  ( In  Press.) 

Rimmer,  E.  J.  Boiler  Explosions,  Collapses  and  Mishaps 8vo,  2 25 

Rings,  F.  Reinforced  Concrete  in  Theory  and  Practice 121110,  *4  5c 

Reinforced  Concrete  Bridges 4to,  *5  00 

Ripper,  W.  Course  of  Instruction  in  Machine  Drawing folio,  *600 

Roberts,  F.  C.  Figure  of  the  Earth i6mo,  o 75 

Roberts,  J.,  Jr.  Laboratory  Work  in  Electrical  Engineering 8vo,  *2  00 

Robertson,  J.  B.  The  Chemistry  of  Coal i2mo,  1 25 

Robertson,  L.  S.  Water-tube  Boilers 8vo,  200 

Robinson,  J.  B.  Architectural  Composition 8vo,  3 50 

Robinson,  S.  W.  Practical  Treatise  on  the  Teeth  of  Wheels. . i6mo,  o 75 

Railroad  Economics  i6mo,  o 75 

Wrought  Iron  Bridge  Members i6mo,  o 75 

Robson,  J.  H.  Machine  Drawing  and  Sketching 8vo,  *2  00 

Roebling,  J.  A.  Long  and  Short  Span  Railway  Bridges folio,  25  00 

Rogers,  A.  A Laboratory  Guide  of  Industrial  Chemistry 8vo,  2 00 

• Elements  of  Industrial  Chemistry nmo,  *300 

Manual  of  Industrial  Chemistry Svo,  7 50 

Rogers,  F.  Magnetism  of  Iron  Vessels i6mo,  o 75 

Rohland,  P.  Colloidal  and  Crystalloidal  State  of  Matter i2mo, 

( Reprinting .) 

Rollinson,  C.  Alphabets Oblong,  i2mo,  *1  00 

Rose,  J.  The  Pattern-makers’  Assistant 8vo,  2 50 

Key  to  Engines  and  Engine-running i2iro,  2 50 

Rose,  T.  K.  The  Precious  Metals 8vo,  2 50 

Rosenhain,  W.  Glass  Manufacture 8vo,  4 00 

Physical  Metallurgy,  An  Introduction  to 8vo,  4 00 

Roth,  W.  A.  Physical  Chemistry 8vo,  *2  00 

Rowan,  F.  T.  Practical  Physics  of  the  Modern  Steam-boiler 8vo,  *3  00 

and  Idell,  F.  E.  Boiler  Incrustation  and  Corrosion i6mo,  o 75 

Roxburgh,  W.  General  Foundry  Practice 8vo,  2 50 

Ruhmer,  E.  Wireless  Telephony 8vo,  4 50 

Russell,  A.  Theory  of  Electric  Cables  and  Networks 8vo,  *300 

Rutley,  F.  Elements  of  Mineralogy i2mo,  2 50 

Rust,  A.  Practical  Tables  for  Navigators  and  Aviators 8vo,  3 50 

Sandeman,  E.  A.  Notes  on  the  Manufacture  of  Earthenware. . i2mo,  3 50 

Sanford,  P.  G.  Nitro-explosives 8vo,  *4  00 

Saunders,  C.  H.  Handbook  of  Practical  Mechanics i6mo,  1 50 

leather,  2 00 

Sayers,  H.  M.  Brakes  for  Tram  Cars 8vo,  *1  25 

Schaefer,  C.  T.  Motor  Truck  Design 8vo,  2 50 

Scheele,  C.  W.  Chemical  Essays Svo,  *2  50 


D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG 


23 


Scheithauer,  W.  Shale  Oils  and  Tars 8vo,  *4  00 

Scherer,  R.  Casein... 8vo,  3 50 

Schidrowitz,  P.  Rubber,  Its  Production  and  Industrial  Uses 8vo,  *6  00 

Schindler,  K.  Iron  and  Steel  Construction  Works rsmo,  *2  00 

Schmall,  C.  N.  First  Course  in  Analytic  Geometry,  Plane  and  Solid. 

i2mo,  half  leather,  *1  75 

and  Shack,  S.  M.  Elements  of  Plane  Geometry i2mo,  1 25 

Schmeer,  L.  Flow  of  Water 8vo,  1 50 

Schwarz,  E.  H.  L.  Causal  Geology 8vo,  *3  00 

Schweizer,  V.  Distillations  of  Resins Svo,  5 00 

Scott,  A.  H.  Reinforced  Concrete  in  Practice i2mo,  2 00 

Scott,  W.  W.  Qualitative  Analysis.  A Laboratory  Manual.  New 

Edition  3 00 

Standard  Methods  of  Chemical  Analysis 8vo,  7 50 

Scribner,  J.  M.  Engineers’  and  Mechanics’  Companion.  . i6mo,  leather,  1 50 
Scudder,  H.  Electrical  Conductivity  and  Ionization  Constants  of 

Organic  Compounds 8v.o,  *3  00 

Seamanship,  Lectures  on j.2mo,  2 00 

Searle,  A.  B.  Modern  Brickmaking 8vo,  7 00 

— — -Cement,  Concrete  and  Bricks 8vo,  3 00 


Searle,  G.  M.  “Sumners’  Method.”  Condensed  and  Improved. 

iGmo,  o 75 

Seaton,  A.  E.  Manual  of  Marine  Engineering 8vo,  10  00 

Seaton,  A.  E.,  and  Rounthwaite,  H.  M.  Pocket-book  of  Marine  Engi- 
neering   i6mo,  leather,  6 00 

Seeligmann,  T.,  Torrilhon,  G.  L.,  and  Falconnet,  H.  India  Rubber  and 

Gutta  Percha  8vo,  6 00 

Seidell,  A.  Solubilities  of  Inorganic  and  Organic  Substances. ..  ,8vo,  7 50 

Sellew,  W.  H.  Steel  Rails 4to,  *10  00 

-Railway  Maintenance  Engineering nmo,  3 00 

Setter,  G.  Outlines  of  Physical  Chemistry i2mo,  3 00 

Text-book  of  Inorganic  Chemistry i2roo,  *3  00 

Sever,  G.  F.  Electric  Engineering  Experiments 8vo,  boards,  *1  00 

Sever,  G.  F.,  and  Townsend,  F.  Laboratory  and  Factory  Tests  in  Elec- 


Sexton,  A.  H.  Fuel  and  Refractory  Materials. 


The  Common  Metals  (Non-Ferrous) 

Seymour,  A.  Modern  Printing  Inks 

Shaw,  Henry  S.  H.  Mechanical  Integrators 

Shaw,  S.  History  of  the  Staffordshire  Potteries 

-Chemistry  of  Compounds  Used  in  Porcelain  Manufac 

Shaw,  T.  R.  Driving  of  Machine  -Tools 

Precision  Grinding  Machines 

Shaw,  W.  N.  Forecasting  Weather 8vo  ( Reprinting .) 

Sheldon,  S.,  and  Hausmann,  E.  Dynamo  Electric  Machinery,  A.C. 

and  D.C 8vo  (In  Press.) 

Electric  Traction  and  Transmission  Engineering i2mo, 

Physical  Laboratory  Experiments,  for  Engineering  Students.  .8vo, 


*2 

5° 

*2 

00 

*1 

00 

int-itn 7.) 

. . i?mo, 

*3 

00 

3 

50 

d Steel. 

8vo, 

6 

50 

4 

00 

. . . . 8vo, 

3 

00 

0 

75 

. . .Svo, 

2 

50 

. . . . 8vo, 

*6 

00 

*2 

00 

. . isnio, 

5 

00 

3 00 
1 5° 


24  D-  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG 


Sherriff,  F.  F.  Oil  Merchants’  Manual  and  Oil  Trade  Ready  Reckoner, 


8 vo,  3 50 

Shields,  J.  E.  Notes  on  Engineering  Construction i2mo,  i 50 

Shreve,  S.  H.  Strength  of  Bridges  and  Roofs 8vo,  3 50 


Shunk,  W.  F.  The  Field  Engineer  i2mo,  fabrikoid,  3 00 

Silverman,  A.,  and  Harvey,  A.  W.  Laboratory  Directions  and  Study 

Questions  in  Inorganic  Chemistry 4to,  loose  leaf,  2 00 

Simmons,  W.  H.  Fats,  Waxes  and  Essential  Oils.  ,8vo  (In  Press.) 
Simmons,  W.  H.,  and  Appleton,  H.  A.  Handbook  of  Soap  Manufacture, 

8 vo,  *4  co 

Simmons,  H.,  and  Mitchell,  C.  A.  Edible  Fats  and  Oils 8vo,  *3  50 

Simpson,  G.  The  Naval  Constructor nmo,  fabrikoid,  *5  00 

Simpson,  W.  Foundations 8vo.  (In  Press.) 

Sinclair,  A.  Development  of  the  Locomotive  Engine. . . 8vo,  half  leather,  5 00 

Sindall,  R.  W.  Manufacture  of  Paper 8vo,  3 00 

Sindall,  R.  W.,  and  Bacon,  W.  N.  The  Testing  of  Wood  Pulp.  ..  .8vo,  2 50 

Wood  and  Cellulose 8vo  (In  Press.) 

Sloane,  T.  O’C.  Elementary  Electrical  Calculations nmo,  2 50 

Smallwood,  J.  C.  Mechanical  Laboratory  Methods.  ... i2mo,  fabrikoid,  3 00 
Smith,  C.  A.  M.  Handbook  of  Testing,  MATERIALS 8vo,  5 00 

Smith,  C.  A.  M.,  and  Warren,  A.  G.  New  Steam  Tables 8vo,  *1  25 

Smith,  C.  F.  Practical  Alternating  Currents  and  Testing 8vo,  *3  50 

Practical  Testing  of  Dynamos  and  Motors 8vo,  *3  00 


Smith,  F.  E.  Handbook  of  General  Instruction  for  Mechanics . . . nmo, 


Smith,  G.  C.  Trinitrotoluenes  and  Mono-  and  Dinitrotoluenes,  Their 


Manufacture  and  Properties i2mo, 

Smith,  H.  G.  Minerals  and  the  Microscope i2mo, 

Smith,  J.  C.  Manufacture  of  Paint 8vo, 

Smith,  R.  H.  Principles  of  Machine  Work i2mo, 

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Smith,  W.  Chemistry  of  Hat  Manufacturing i2mo, 

Snell,  F.  D.  Colorimetric  Analysis i2mo  (In  Press.) 

Snow,  W.  G.,  and  Nolan,  T.  Ventilation  of  Buildings i6mo, 

Soddy,  F.  Radioactivity 8vo  (Reprinting.) 

Solomon,  M.  Electric  Lamps 8vo, 

Somerscales,  A.  N.  Mechanics  for  Marine  Engineers nmo, 

Mechanical  and  Marine  Engineering  Science 8vo, 

Sothern,  J.  W.  The  Marine  Steam  Turbine $vo, 

Verbal  Notes  and  Sketches  for  Marine  Engineers.. 8vo, 

Marine  Engine  Indicator  Cards 8vo, 


Sothern,  J.  W.,  and  Sothern,  R.  M.  Simple  Problems  in  Marine 


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Souster,  E.  G.  W.  Design  of  Factory  and  Industrial  Buildings. . .8vo, 

Southcombe,  J.  E.  Chemistry  of  the  Oil  Industries ,.8vo, 

Soxhlet,  D.  H.  Dyeing  and  Staining  Marble 8vo, 

Spangenburg,  L.  Fatigue  of  Metals i6mo, 

Specht,  G.  J.,  Hardy,  A.  S.,  McMaster,  J.  B.,  and  Walling.  Topographical 

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Spencer,  A.  S.  Design  of  Steel-Framed  Sheds 8vo, 

Spiegel,  L.  Chemical  Constitution  and  Physiological  Action. ..  .i2mo. 


1 50 

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o 75 

2 00 

2 50 
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*12  50 
15  00 
4 50 

3 00 

4 00 
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2 so 

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« 04 
*3  so 

T 25 


D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG 


25 


Sprague,  E.  H.  Hydraulics i2mo,  2 co 

Elements  of  Graphic  Statics 8vo,  2 co 

— Stability  of  Masonry ramo,  2 00 

Elementary  Mathematics  for  Engineers i2mo,  2 00 

■ Stability  of  Arches i?.mo,  2 00 

Strength  of  Structural  Elements i2mo,  2 00 

Moving  Loads  by  Influence  Lines  and  Other  Methods i2mo,  2 00 

Stahl,  A.  W.  Transmission  of  Power i6mo, 

Stahl,  A.  W.,  and  Woods,  A.  T.  Elementary  Mechanism i2mo,  2 25 

Standage,  H.  C Leatherworkers’  Manual ?.  .8vo,  4 50 

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Stanley,  H.  Practical  Applied  Physics (In  Press.) 

Stansbie,  J.  H.  Iron  and  Steel 8vo,  2 50 

Steadman,  F.  M.  Unit  Photography nmo,  2 50 

Stecher,  G.  E.  Cork.  Its  Origin  and  Industrial  Uses i2mo,  1 00 

Steinheil,  A.,  and  Voit,  E.  Applied  Optics,  Vols.  I.  and  II.  8vo, 

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Steinman,  D.  B.  Suspension  Bridges  and  Cantilevers.  (Science  Series 

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Melan’s  Steel  Arches  and  Suspension  Bridges 8vo,  *3  co 

Stevens,  A.  B.  Arithmetric  of  Pharmacy i2mo,  1 50 

Stevens,  E.  J.  Field  Telephones  and  Telegraphs 1 20 

Stevens,  H.  P.  Paper  Mill  Chemist i6mo,  4 00 

Stevens,  J.  S.  Theory  of  Measurements i2mo,  *%  25 

Stevenson,  J.  L.  Blast-Furnace  Calculations i2mo,  leather,  2 50 

Stewart,  G.  Modern  Steam  Traps i2mo,  *1  75 

Stiles,  A.  Tables  for  Field  Engineers i2mo,  1 00 

Stodola,  A.  Steam  Turbines 8vo,  5 00 

Stone,  E.  W.  Elements  of  Radiotelegraphy i2mo,  fabrikoid,  2 50 

Stone,  H.  The  Timbers  of  Commerce Svo,  4 00 


Stopes,  M.  The  Study  of  Plant  Life 8vo,  2 00 

Sudborough,  J.  J.,  and  James,  T.  C.  Practical  Organic  Chemistry . urao,  3 50 

Suffling,  E.  R.  Treatise  on  the  Art  of  Glass  Painting Svo,  *3  50 

Sullivan,  T.  V.,  and  Underwood,  N.  Testing  and  Valuation  of  Build- 
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Svenson,  C.  L.  Handbook  on  Piping 8vo,  4 00 

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Swan,  K.  Patents,  Designs  and  Trade  Marks 8vo,  2 00 

Swinburne,  J.,  Wordingham,  C.  H.,  and  Martin,  T.  C.  Electric  Currents. 

. i6mo,  o 75 

Swoope,  C.  W.  Lessons  in  Practical  Electricity umo,  2 50 

Tailfer,  L.  Bleaching  Linen  and  Cotton  Yarn  and  Fabrics Svo,  7 00 

Tate,  J.  S.  Surcharged  and  Different  Forms  of  Retaining- walls.  .i6mo,  o 75 

Taylor,  F.  N.  Small  Water  Supplies umc,  ■ 3 00 

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Taylor,  H.  S.  Fuel  Production  and  Utilization 8vo,  4 00 

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Terry,  H.  L.  India  Rubber  and  its  Manufacture 8vo,  3 50 


26  D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG 

Thayer,  H.  R.  Structural  Design.  8vo. 

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Vol.  II.  Design  of  Simple  Structures...,. 450 

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Thomas,  J.  B.  Strength  of  Ships 8vo,  2 50 

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Thompson,  A.  B.  Oil  Fields  of  Russia 4to,  10  00 

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Thompson,  S.  P.  Dynamo  Electric  Machines i6mo,  o 75 

Thompson,  W.  P.  Handbook  of  Patent  Law  of  All  Countries i6mo,  1 50 

Thomson,  G.  Modern  Sanitary  Engineering i2mo,  *3  00 

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Thornley,  T.  Cotton  Combing  Machines..... 8vo,  *3  50 

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Tilmans,  J.  Water  Purification  and  Sewage  Disposal 8vo,  2 50 

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Townsend,  F.  Alternating  Current  Engineering 8vo,  boards,  *075 

Townsend,  J.  S.  Ionization  of  Gases  by  Collision 8vo,  *1  25 

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Treiber,  E.  Foundry  Machinery mmo,  2 00 

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Trinks,  W.,  and  Housum,  C.  Shaft  Governors i6mo,  o 75 

Trowbridge,  W.  P.  Turbine  Wheels i6mo,  o 75 

Tucker,  J.  H.  A Manual  of  Sugar  Analysis 8vo,  3 50 

Turnbull,  Jr.,  J.,  and  Robinson,  S.  W.  A Treatise  on  the  Compound 

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Turrill,  S.  M.  Elementary  Course  in  Perspective i2mo,  *1  25 

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D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG  27 

Underhill,  C.  R.  Solenoids,  Electromagnets  and  Electromagnetic  Wind- 

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Van  Wagenen,  T.  F.  Manual  of  Hydraulic  Mining i6mo,  1 00 

Vega,  Baron  Von.  Logarithmic  Tables 8vo,  2 50 

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Vincent,  C.  Ammonia  and  its  Compounds 8vo,  2 50 

Virgin,  R.  Z.  Coal  Mine  Management (In  Press.) 

Volk,  C.  Haulage  and  Winding  Appliances 8vo,  *4  00 

Von  Georgievics,  G.  Chemical  Technology  of  Textile  Fibres 8vo,  7 00 

A Text  Book  of  Dye  Chemistry 8vo,  12  00 

Vose,  G.  L.  Graphic  Method  for  Solving  Certain  Questions  in  Arithmetic 

and  Algebra  i6tno,  o 75 

Vosmaer,  A.  Ozone 8vo,  *2  5c 

Wabner,  R.  Ventilation  in  Mines 8vo,  5 00 

Wadmore,  T.  M.  Elementary  Chemical  Theory nmo,  *1  50 

Wagner,  E.  Preserving  Fruits,  Vegetables,  and  Meat i2mo,  *2  50 

Wagner,  H.  E.,  and  Edwards,  H.  W.  Railway  Engineering  Estimates. 

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Wagner,  J.  B.  Seasoning  of  Wood • 8vo,  4 00 

Waldram,  P.  J.  Principles  of  Structural  Mechanics i2mo,  4 00 

Walker,  F.  Dynamo  Building i6mo,  o 75 

Walker,  J.  Organic  Chemistry  for  Students  of  Medicine 8vo,  4 00 

Walker,  S.  F.  Refrigeration,  Heating  and  Ventilation  on  Shipboard 

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Electric  Wiring  and  Fitting 8vo,  2 50 

Wallis-Tayler,  A.  J.  Bearings  and  Lubrication 8vo,  *1  50 

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Walsh,  J.  J.  Chemistry  and  Physics  of  Mining  and  Mine  Ventilation, 

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Wanklyn,  J.  A.  Water  Analysis i2mo,  2 00 

Wansbrough,  W.  D.  The  A B C of  the  Differential  Calculus. ... i2mo,  *2  50 

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Waring,  Jr.,  G.  E.  Sanitary  Conditions i6mo,  o 75 

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28  D.  VAN  NOSTRAND  CO.’S  SHORT  TITLE  CATALOG 


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Warren,  F.  D.  Handbook  on  Reinforced  Concrete i2mo,  2 50 

Watkins,  A.  Photography 8vo,  3 oc 

Watson,  E.  P.  Small  Engines  and  Boilers. i2mo,  1 25 

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Leather  Manufacture  8vo,  6 00 

The  Art  of  Soap  Making 8vo,  4 00 

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Webb,  H.  L.  Guide  to  the  Testing  of  Insulated  Wires  and  Cables. i2mo,  1 00 

Wegmann,  Edward.  Conveyance  and  Distribution  of  Water  for 

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Weisbach,  J.  A Manual  of  Theoretical  Mechanics 8vo,  *6  00 

Weisbach,  J.,  and  Herrmann,  G.  Mechanics  of  Air  Machinery ...  .8vo,  *3  75 

Wells,  M.  B.  Steel  Bridge  Designing 8vo,  *2  54 

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Weston,  E.  B.  Loss  of  Head  Due  to  Friction  of  Water  in  Pipes.  .i2mo,  2 00 

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Whipple,  S.  An  Elementary  and.  Practical  Treatise  on  Bridge  Building. 

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Wright,  A.  C.  Simple  Method  for  Testing  Painters’  Materials. . ,8vo,  2 50 

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Wynne,  W.  E.,  and  Sparagen,  W.  Handbook  of  Engineering  Mathe- 
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Yoder,  J.  H.,  and  Wharen,  G.  B.  Locomotive  Valves  and  Valve  Gears, 

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